/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) IFR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4)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) DependencyGraphProof [EQUIVALENT, 0 ms] (15) QDP (16) QDPOrderProof [EQUIVALENT, 43 ms] (17) QDP (18) DependencyGraphProof [EQUIVALENT, 0 ms] (19) QDP (20) QDPSizeChangeProof [EQUIVALENT, 0 ms] (21) YES (22) QDP (23) TransformationProof [EQUIVALENT, 0 ms] (24) QDP (25) TransformationProof [EQUIVALENT, 0 ms] (26) QDP (27) TransformationProof [EQUIVALENT, 0 ms] (28) QDP (29) TransformationProof [EQUIVALENT, 0 ms] (30) QDP (31) TransformationProof [EQUIVALENT, 0 ms] (32) QDP (33) TransformationProof [EQUIVALENT, 0 ms] (34) QDP (35) TransformationProof [EQUIVALENT, 0 ms] (36) QDP (37) TransformationProof [EQUIVALENT, 0 ms] (38) QDP (39) TransformationProof [EQUIVALENT, 0 ms] (40) QDP (41) TransformationProof [EQUIVALENT, 0 ms] (42) QDP (43) TransformationProof [EQUIVALENT, 0 ms] (44) QDP (45) TransformationProof [EQUIVALENT, 0 ms] (46) QDP (47) TransformationProof [EQUIVALENT, 0 ms] (48) QDP (49) TransformationProof [EQUIVALENT, 0 ms] (50) QDP (51) TransformationProof [EQUIVALENT, 0 ms] (52) QDP (53) TransformationProof [EQUIVALENT, 0 ms] (54) QDP (55) TransformationProof [EQUIVALENT, 0 ms] (56) QDP (57) TransformationProof [EQUIVALENT, 0 ms] (58) QDP (59) QDPSizeChangeProof [EQUIVALENT, 0 ms] (60) YES (61) QDP (62) QDPSizeChangeProof [EQUIVALENT, 0 ms] (63) YES (64) QDP (65) DependencyGraphProof [EQUIVALENT, 0 ms] (66) QDP (67) TransformationProof [EQUIVALENT, 0 ms] (68) QDP (69) TransformationProof [EQUIVALENT, 2 ms] (70) QDP (71) TransformationProof [EQUIVALENT, 0 ms] (72) QDP (73) TransformationProof [EQUIVALENT, 0 ms] (74) QDP (75) TransformationProof [EQUIVALENT, 0 ms] (76) QDP (77) TransformationProof [EQUIVALENT, 0 ms] (78) QDP (79) DependencyGraphProof [EQUIVALENT, 0 ms] (80) QDP (81) TransformationProof [EQUIVALENT, 0 ms] (82) QDP (83) DependencyGraphProof [EQUIVALENT, 0 ms] (84) QDP (85) TransformationProof [EQUIVALENT, 0 ms] (86) QDP (87) DependencyGraphProof [EQUIVALENT, 0 ms] (88) QDP (89) TransformationProof [EQUIVALENT, 0 ms] (90) QDP (91) DependencyGraphProof [EQUIVALENT, 0 ms] (92) QDP (93) TransformationProof [EQUIVALENT, 0 ms] (94) QDP (95) DependencyGraphProof [EQUIVALENT, 0 ms] (96) QDP (97) TransformationProof [EQUIVALENT, 0 ms] (98) QDP (99) DependencyGraphProof [EQUIVALENT, 0 ms] (100) QDP (101) TransformationProof [EQUIVALENT, 0 ms] (102) QDP (103) DependencyGraphProof [EQUIVALENT, 0 ms] (104) QDP (105) TransformationProof [EQUIVALENT, 4 ms] (106) QDP (107) DependencyGraphProof [EQUIVALENT, 0 ms] (108) QDP (109) TransformationProof [EQUIVALENT, 0 ms] (110) QDP (111) DependencyGraphProof [EQUIVALENT, 0 ms] (112) QDP (113) TransformationProof [EQUIVALENT, 0 ms] (114) QDP (115) DependencyGraphProof [EQUIVALENT, 0 ms] (116) QDP (117) TransformationProof [EQUIVALENT, 0 ms] (118) QDP (119) DependencyGraphProof [EQUIVALENT, 0 ms] (120) QDP (121) TransformationProof [EQUIVALENT, 0 ms] (122) QDP (123) DependencyGraphProof [EQUIVALENT, 0 ms] (124) QDP (125) TransformationProof [EQUIVALENT, 0 ms] (126) QDP (127) TransformationProof [EQUIVALENT, 0 ms] (128) QDP (129) DependencyGraphProof [EQUIVALENT, 0 ms] (130) QDP (131) TransformationProof [EQUIVALENT, 0 ms] (132) QDP (133) DependencyGraphProof [EQUIVALENT, 0 ms] (134) QDP (135) TransformationProof [EQUIVALENT, 0 ms] (136) QDP (137) DependencyGraphProof [EQUIVALENT, 0 ms] (138) QDP (139) TransformationProof [EQUIVALENT, 0 ms] (140) QDP (141) DependencyGraphProof [EQUIVALENT, 0 ms] (142) QDP (143) TransformationProof [EQUIVALENT, 0 ms] (144) QDP (145) QDPSizeChangeProof [EQUIVALENT, 0 ms] (146) YES (147) QDP (148) DependencyGraphProof [EQUIVALENT, 0 ms] (149) QDP (150) QDPOrderProof [EQUIVALENT, 0 ms] (151) QDP (152) DependencyGraphProof [EQUIVALENT, 0 ms] (153) QDP (154) QDPSizeChangeProof [EQUIVALENT, 0 ms] (155) YES (156) QDP (157) DependencyGraphProof [EQUIVALENT, 0 ms] (158) QDP (159) TransformationProof [EQUIVALENT, 0 ms] (160) QDP (161) UsableRulesProof [EQUIVALENT, 0 ms] (162) QDP (163) QReductionProof [EQUIVALENT, 0 ms] (164) QDP (165) MNOCProof [EQUIVALENT, 0 ms] (166) QDP (167) InductionCalculusProof [EQUIVALENT, 0 ms] (168) QDP (169) TransformationProof [EQUIVALENT, 0 ms] (170) QDP (171) DependencyGraphProof [EQUIVALENT, 0 ms] (172) QDP (173) TransformationProof [EQUIVALENT, 0 ms] (174) QDP (175) DependencyGraphProof [EQUIVALENT, 0 ms] (176) QDP (177) TransformationProof [EQUIVALENT, 0 ms] (178) QDP (179) DependencyGraphProof [EQUIVALENT, 0 ms] (180) QDP (181) TransformationProof [EQUIVALENT, 0 ms] (182) QDP (183) DependencyGraphProof [EQUIVALENT, 0 ms] (184) QDP (185) MNOCProof [EQUIVALENT, 0 ms] (186) QDP (187) InductionCalculusProof [EQUIVALENT, 0 ms] (188) QDP (189) Narrow [COMPLETE, 0 ms] (190) 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; " The following If expression "if primGEqNatS x y then primModNatP (primMinusNatS x y) (Succ y) else primMinusNatS y x" is transformed to "primModNatP0 x y True = primModNatP (primMinusNatS x y) (Succ y); primModNatP0 x y False = primMinusNatS y x; " The following If expression "if b then (showChar '(') . p . showChar ')' else p" is transformed to "showParen0 p True = (showChar '(') . p . showChar ')'; showParen0 p False = p; " ---------------------------------------- (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 "undefined |Falseundefined; " is transformed to "undefined = undefined1; " "undefined0 True = undefined; " "undefined1 = undefined0 False; " ---------------------------------------- (6) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (7) LetRed (EQUIVALENT) Let/Where Reductions: The bindings of the following Let/Where expression "(showChar '[') . (shows x) . showl xs where { showl [] = showChar ']'; showl (x : xs) = (showChar ',') . (shows x) . showl xs; } " are unpacked to the following functions on top level "showListShowl [] = showChar ']'; showListShowl (x : xs) = (showChar ',') . (shows x) . showListShowl xs; " ---------------------------------------- (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="showList",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="showList ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="showList ww3 ww4",fontsize=16,color="burlywood",shape="triangle"];1769[label="ww3/ww30 : ww31",fontsize=10,color="white",style="solid",shape="box"];4 -> 1769[label="",style="solid", color="burlywood", weight=9]; 1769 -> 5[label="",style="solid", color="burlywood", weight=3]; 1770[label="ww3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 1770[label="",style="solid", color="burlywood", weight=9]; 1770 -> 6[label="",style="solid", color="burlywood", weight=3]; 5[label="showList (ww30 : ww31) ww4",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="showList [] ww4",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 7 -> 9[label="",style="dashed", color="red", weight=0]; 7[label="(showChar (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) . (shows ww30) . showListShowl ww31",fontsize=16,color="magenta"];7 -> 10[label="",style="dashed", color="magenta", weight=3]; 7 -> 11[label="",style="dashed", color="magenta", weight=3]; 7 -> 12[label="",style="dashed", color="magenta", weight=3]; 7 -> 13[label="",style="dashed", color="magenta", weight=3]; 8 -> 18[label="",style="dashed", color="red", weight=0]; 8[label="showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) : []) ww4",fontsize=16,color="magenta"];8 -> 19[label="",style="dashed", color="magenta", weight=3]; 8 -> 20[label="",style="dashed", color="magenta", weight=3]; 8 -> 21[label="",style="dashed", color="magenta", weight=3]; 10[label="ww31",fontsize=16,color="green",shape="box"];11[label="ww4",fontsize=16,color="green",shape="box"];12[label="ww30",fontsize=16,color="green",shape="box"];13[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];9[label="(showChar (Char (Succ ww6))) . (shows ww7) . showListShowl ww8",fontsize=16,color="black",shape="triangle"];9 -> 17[label="",style="solid", color="black", weight=3]; 19[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];20[label="ww4",fontsize=16,color="green",shape="box"];21[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];18[label="showString (Char (Succ ww14) : Char (Succ ww15) : []) ww16",fontsize=16,color="black",shape="triangle"];18 -> 25[label="",style="solid", color="black", weight=3]; 17 -> 180[label="",style="dashed", color="red", weight=0]; 17[label="showChar (Char (Succ ww6)) ((shows ww7) . showListShowl ww8)",fontsize=16,color="magenta"];17 -> 181[label="",style="dashed", color="magenta", weight=3]; 17 -> 182[label="",style="dashed", color="magenta", weight=3]; 25 -> 461[label="",style="dashed", color="red", weight=0]; 25[label="(++) (Char (Succ ww14) : Char (Succ ww15) : []) ww16",fontsize=16,color="magenta"];25 -> 462[label="",style="dashed", color="magenta", weight=3]; 25 -> 463[label="",style="dashed", color="magenta", weight=3]; 181[label="(shows ww7) . showListShowl ww8",fontsize=16,color="black",shape="box"];181 -> 185[label="",style="solid", color="black", weight=3]; 182[label="ww6",fontsize=16,color="green",shape="box"];180[label="showChar (Char (Succ ww57)) ww58",fontsize=16,color="black",shape="triangle"];180 -> 186[label="",style="solid", color="black", weight=3]; 462[label="ww16",fontsize=16,color="green",shape="box"];463[label="Char (Succ ww14) : Char (Succ ww15) : []",fontsize=16,color="green",shape="box"];461[label="ww126 ++ ww106",fontsize=16,color="burlywood",shape="triangle"];1771[label="ww126/ww1260 : ww1261",fontsize=10,color="white",style="solid",shape="box"];461 -> 1771[label="",style="solid", color="burlywood", weight=9]; 1771 -> 601[label="",style="solid", color="burlywood", weight=3]; 1772[label="ww126/[]",fontsize=10,color="white",style="solid",shape="box"];461 -> 1772[label="",style="solid", color="burlywood", weight=9]; 1772 -> 602[label="",style="solid", color="burlywood", weight=3]; 185[label="shows ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];185 -> 187[label="",style="solid", color="black", weight=3]; 186[label="(:) Char (Succ ww57) ww58",fontsize=16,color="green",shape="box"];601[label="(ww1260 : ww1261) ++ ww106",fontsize=16,color="black",shape="box"];601 -> 657[label="",style="solid", color="black", weight=3]; 602[label="[] ++ ww106",fontsize=16,color="black",shape="box"];602 -> 658[label="",style="solid", color="black", weight=3]; 187[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="blue",shape="box"];1773[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1773[label="",style="solid", color="blue", weight=9]; 1773 -> 188[label="",style="solid", color="blue", weight=3]; 1774[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1774[label="",style="solid", color="blue", weight=9]; 1774 -> 189[label="",style="solid", color="blue", weight=3]; 1775[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1775[label="",style="solid", color="blue", weight=9]; 1775 -> 190[label="",style="solid", color="blue", weight=3]; 1776[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1776[label="",style="solid", color="blue", weight=9]; 1776 -> 191[label="",style="solid", color="blue", weight=3]; 1777[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1777[label="",style="solid", color="blue", weight=9]; 1777 -> 192[label="",style="solid", color="blue", weight=3]; 1778[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1778[label="",style="solid", color="blue", weight=9]; 1778 -> 193[label="",style="solid", color="blue", weight=3]; 1779[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1779[label="",style="solid", color="blue", weight=9]; 1779 -> 194[label="",style="solid", color="blue", weight=3]; 1780[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1780[label="",style="solid", color="blue", weight=9]; 1780 -> 195[label="",style="solid", color="blue", weight=3]; 1781[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1781[label="",style="solid", color="blue", weight=9]; 1781 -> 196[label="",style="solid", color="blue", weight=3]; 1782[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1782[label="",style="solid", color="blue", weight=9]; 1782 -> 197[label="",style="solid", color="blue", weight=3]; 1783[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1783[label="",style="solid", color="blue", weight=9]; 1783 -> 198[label="",style="solid", color="blue", weight=3]; 1784[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1784[label="",style="solid", color="blue", weight=9]; 1784 -> 199[label="",style="solid", color="blue", weight=3]; 1785[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1785[label="",style="solid", color="blue", weight=9]; 1785 -> 200[label="",style="solid", color="blue", weight=3]; 1786[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1786[label="",style="solid", color="blue", weight=9]; 1786 -> 201[label="",style="solid", color="blue", weight=3]; 1787[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1787[label="",style="solid", color="blue", weight=9]; 1787 -> 202[label="",style="solid", color="blue", weight=3]; 1788[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1788[label="",style="solid", color="blue", weight=9]; 1788 -> 203[label="",style="solid", color="blue", weight=3]; 1789[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1789[label="",style="solid", color="blue", weight=9]; 1789 -> 204[label="",style="solid", color="blue", weight=3]; 1790[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1790[label="",style="solid", color="blue", weight=9]; 1790 -> 205[label="",style="solid", color="blue", weight=3]; 657[label="ww1260 : ww1261 ++ ww106",fontsize=16,color="green",shape="box"];657 -> 683[label="",style="dashed", color="green", weight=3]; 658[label="ww106",fontsize=16,color="green",shape="box"];188[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];188 -> 206[label="",style="solid", color="black", weight=3]; 189[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];189 -> 207[label="",style="solid", color="black", weight=3]; 190[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];190 -> 208[label="",style="solid", color="black", weight=3]; 191[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];191 -> 209[label="",style="solid", color="black", weight=3]; 192[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];192 -> 210[label="",style="solid", color="black", weight=3]; 193[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];193 -> 211[label="",style="solid", color="black", weight=3]; 194[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];194 -> 212[label="",style="solid", color="black", weight=3]; 195[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];195 -> 213[label="",style="solid", color="black", weight=3]; 196[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];196 -> 214[label="",style="solid", color="black", weight=3]; 197[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];197 -> 215[label="",style="solid", color="black", weight=3]; 198[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="burlywood",shape="box"];1791[label="ww7/ww70 :% ww71",fontsize=10,color="white",style="solid",shape="box"];198 -> 1791[label="",style="solid", color="burlywood", weight=9]; 1791 -> 216[label="",style="solid", color="burlywood", weight=3]; 199[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];199 -> 217[label="",style="solid", color="black", weight=3]; 200[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];200 -> 218[label="",style="solid", color="black", weight=3]; 201[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];201 -> 219[label="",style="solid", color="black", weight=3]; 202[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];202 -> 220[label="",style="solid", color="black", weight=3]; 203[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];203 -> 221[label="",style="solid", color="black", weight=3]; 204[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];204 -> 222[label="",style="solid", color="black", weight=3]; 205[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];205 -> 223[label="",style="solid", color="black", weight=3]; 683 -> 461[label="",style="dashed", color="red", weight=0]; 683[label="ww1261 ++ ww106",fontsize=16,color="magenta"];683 -> 707[label="",style="dashed", color="magenta", weight=3]; 206 -> 461[label="",style="dashed", color="red", weight=0]; 206[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];206 -> 468[label="",style="dashed", color="magenta", weight=3]; 206 -> 469[label="",style="dashed", color="magenta", weight=3]; 207 -> 461[label="",style="dashed", color="red", weight=0]; 207[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];207 -> 470[label="",style="dashed", color="magenta", weight=3]; 207 -> 471[label="",style="dashed", color="magenta", weight=3]; 208 -> 461[label="",style="dashed", color="red", weight=0]; 208[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];208 -> 472[label="",style="dashed", color="magenta", weight=3]; 208 -> 473[label="",style="dashed", color="magenta", weight=3]; 209 -> 461[label="",style="dashed", color="red", weight=0]; 209[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];209 -> 474[label="",style="dashed", color="magenta", weight=3]; 209 -> 475[label="",style="dashed", color="magenta", weight=3]; 210 -> 461[label="",style="dashed", color="red", weight=0]; 210[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];210 -> 476[label="",style="dashed", color="magenta", weight=3]; 210 -> 477[label="",style="dashed", color="magenta", weight=3]; 211 -> 461[label="",style="dashed", color="red", weight=0]; 211[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];211 -> 478[label="",style="dashed", color="magenta", weight=3]; 211 -> 479[label="",style="dashed", color="magenta", weight=3]; 212 -> 461[label="",style="dashed", color="red", weight=0]; 212[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];212 -> 480[label="",style="dashed", color="magenta", weight=3]; 212 -> 481[label="",style="dashed", color="magenta", weight=3]; 213 -> 461[label="",style="dashed", color="red", weight=0]; 213[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];213 -> 482[label="",style="dashed", color="magenta", weight=3]; 213 -> 483[label="",style="dashed", color="magenta", weight=3]; 214 -> 461[label="",style="dashed", color="red", weight=0]; 214[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];214 -> 484[label="",style="dashed", color="magenta", weight=3]; 214 -> 485[label="",style="dashed", color="magenta", weight=3]; 215 -> 461[label="",style="dashed", color="red", weight=0]; 215[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];215 -> 486[label="",style="dashed", color="magenta", weight=3]; 215 -> 487[label="",style="dashed", color="magenta", weight=3]; 216[label="showsPrec (Pos Zero) (ww70 :% ww71) (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];216 -> 234[label="",style="solid", color="black", weight=3]; 217 -> 461[label="",style="dashed", color="red", weight=0]; 217[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];217 -> 488[label="",style="dashed", color="magenta", weight=3]; 217 -> 489[label="",style="dashed", color="magenta", weight=3]; 218 -> 461[label="",style="dashed", color="red", weight=0]; 218[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];218 -> 490[label="",style="dashed", color="magenta", weight=3]; 218 -> 491[label="",style="dashed", color="magenta", weight=3]; 219 -> 461[label="",style="dashed", color="red", weight=0]; 219[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];219 -> 492[label="",style="dashed", color="magenta", weight=3]; 219 -> 493[label="",style="dashed", color="magenta", weight=3]; 220 -> 461[label="",style="dashed", color="red", weight=0]; 220[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];220 -> 494[label="",style="dashed", color="magenta", weight=3]; 220 -> 495[label="",style="dashed", color="magenta", weight=3]; 221 -> 461[label="",style="dashed", color="red", weight=0]; 221[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];221 -> 496[label="",style="dashed", color="magenta", weight=3]; 221 -> 497[label="",style="dashed", color="magenta", weight=3]; 222 -> 461[label="",style="dashed", color="red", weight=0]; 222[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];222 -> 498[label="",style="dashed", color="magenta", weight=3]; 222 -> 499[label="",style="dashed", color="magenta", weight=3]; 223 -> 461[label="",style="dashed", color="red", weight=0]; 223[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];223 -> 500[label="",style="dashed", color="magenta", weight=3]; 223 -> 501[label="",style="dashed", color="magenta", weight=3]; 707[label="ww1261",fontsize=16,color="green",shape="box"];468 -> 296[label="",style="dashed", color="red", weight=0]; 468[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];469[label="show ww7",fontsize=16,color="black",shape="triangle"];469 -> 603[label="",style="solid", color="black", weight=3]; 470 -> 296[label="",style="dashed", color="red", weight=0]; 470[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];471[label="show ww7",fontsize=16,color="black",shape="triangle"];471 -> 604[label="",style="solid", color="black", weight=3]; 472 -> 296[label="",style="dashed", color="red", weight=0]; 472[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];473[label="show ww7",fontsize=16,color="black",shape="triangle"];473 -> 605[label="",style="solid", color="black", weight=3]; 474 -> 296[label="",style="dashed", color="red", weight=0]; 474[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];475[label="show ww7",fontsize=16,color="black",shape="triangle"];475 -> 606[label="",style="solid", color="black", weight=3]; 476 -> 296[label="",style="dashed", color="red", weight=0]; 476[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];477[label="show ww7",fontsize=16,color="black",shape="triangle"];477 -> 607[label="",style="solid", color="black", weight=3]; 478 -> 296[label="",style="dashed", color="red", weight=0]; 478[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];479[label="show ww7",fontsize=16,color="black",shape="triangle"];479 -> 608[label="",style="solid", color="black", weight=3]; 480 -> 296[label="",style="dashed", color="red", weight=0]; 480[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];481[label="show ww7",fontsize=16,color="black",shape="triangle"];481 -> 609[label="",style="solid", color="black", weight=3]; 482 -> 296[label="",style="dashed", color="red", weight=0]; 482[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];483[label="show ww7",fontsize=16,color="black",shape="triangle"];483 -> 610[label="",style="solid", color="black", weight=3]; 484 -> 296[label="",style="dashed", color="red", weight=0]; 484[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];485[label="show ww7",fontsize=16,color="black",shape="triangle"];485 -> 611[label="",style="solid", color="black", weight=3]; 486 -> 296[label="",style="dashed", color="red", weight=0]; 486[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];487[label="show ww7",fontsize=16,color="black",shape="triangle"];487 -> 612[label="",style="solid", color="black", weight=3]; 234 -> 687[label="",style="dashed", color="red", weight=0]; 234[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww70) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww71) (showListShowl ww8 ww9)",fontsize=16,color="magenta"];234 -> 688[label="",style="dashed", color="magenta", weight=3]; 234 -> 689[label="",style="dashed", color="magenta", weight=3]; 234 -> 690[label="",style="dashed", color="magenta", weight=3]; 234 -> 691[label="",style="dashed", color="magenta", weight=3]; 234 -> 692[label="",style="dashed", color="magenta", weight=3]; 234 -> 693[label="",style="dashed", color="magenta", weight=3]; 488 -> 296[label="",style="dashed", color="red", weight=0]; 488[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];489[label="show ww7",fontsize=16,color="black",shape="triangle"];489 -> 613[label="",style="solid", color="black", weight=3]; 490 -> 296[label="",style="dashed", color="red", weight=0]; 490[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];491[label="show ww7",fontsize=16,color="black",shape="triangle"];491 -> 614[label="",style="solid", color="black", weight=3]; 492 -> 296[label="",style="dashed", color="red", weight=0]; 492[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];493[label="show ww7",fontsize=16,color="black",shape="triangle"];493 -> 615[label="",style="solid", color="black", weight=3]; 494 -> 296[label="",style="dashed", color="red", weight=0]; 494[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];495[label="show ww7",fontsize=16,color="black",shape="triangle"];495 -> 616[label="",style="solid", color="black", weight=3]; 496 -> 296[label="",style="dashed", color="red", weight=0]; 496[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];497[label="show ww7",fontsize=16,color="black",shape="triangle"];497 -> 617[label="",style="solid", color="black", weight=3]; 498 -> 296[label="",style="dashed", color="red", weight=0]; 498[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];499[label="show ww7",fontsize=16,color="black",shape="triangle"];499 -> 618[label="",style="solid", color="black", weight=3]; 500 -> 296[label="",style="dashed", color="red", weight=0]; 500[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];501[label="show ww7",fontsize=16,color="black",shape="triangle"];501 -> 619[label="",style="solid", color="black", weight=3]; 296[label="showListShowl ww8 ww9",fontsize=16,color="burlywood",shape="triangle"];1792[label="ww8/ww80 : ww81",fontsize=10,color="white",style="solid",shape="box"];296 -> 1792[label="",style="solid", color="burlywood", weight=9]; 1792 -> 312[label="",style="solid", color="burlywood", weight=3]; 1793[label="ww8/[]",fontsize=10,color="white",style="solid",shape="box"];296 -> 1793[label="",style="solid", color="burlywood", weight=9]; 1793 -> 313[label="",style="solid", color="burlywood", weight=3]; 603[label="error []",fontsize=16,color="red",shape="box"];604[label="error []",fontsize=16,color="red",shape="box"];605[label="error []",fontsize=16,color="red",shape="box"];606[label="error []",fontsize=16,color="red",shape="box"];607[label="error []",fontsize=16,color="red",shape="box"];608[label="error []",fontsize=16,color="red",shape="box"];609[label="error []",fontsize=16,color="red",shape="box"];610[label="error []",fontsize=16,color="red",shape="box"];611[label="error []",fontsize=16,color="red",shape="box"];612[label="error []",fontsize=16,color="red",shape="box"];688[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];689[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];690[label="ww71",fontsize=16,color="green",shape="box"];691[label="ww70",fontsize=16,color="green",shape="box"];692[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];693 -> 296[label="",style="dashed", color="red", weight=0]; 693[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];687[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) ww148",fontsize=16,color="black",shape="triangle"];687 -> 708[label="",style="solid", color="black", weight=3]; 613[label="error []",fontsize=16,color="red",shape="box"];614[label="error []",fontsize=16,color="red",shape="box"];615[label="error []",fontsize=16,color="red",shape="box"];616[label="error []",fontsize=16,color="red",shape="box"];617[label="error []",fontsize=16,color="red",shape="box"];618[label="error []",fontsize=16,color="red",shape="box"];619[label="primShowInt ww7",fontsize=16,color="burlywood",shape="triangle"];1794[label="ww7/Pos ww70",fontsize=10,color="white",style="solid",shape="box"];619 -> 1794[label="",style="solid", color="burlywood", weight=9]; 1794 -> 659[label="",style="solid", color="burlywood", weight=3]; 1795[label="ww7/Neg ww70",fontsize=10,color="white",style="solid",shape="box"];619 -> 1795[label="",style="solid", color="burlywood", weight=9]; 1795 -> 660[label="",style="solid", color="burlywood", weight=3]; 312[label="showListShowl (ww80 : ww81) ww9",fontsize=16,color="black",shape="box"];312 -> 319[label="",style="solid", color="black", weight=3]; 313[label="showListShowl [] ww9",fontsize=16,color="black",shape="box"];313 -> 320[label="",style="solid", color="black", weight=3]; 708[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww148",fontsize=16,color="black",shape="box"];708 -> 712[label="",style="solid", color="black", weight=3]; 659[label="primShowInt (Pos ww70)",fontsize=16,color="burlywood",shape="box"];1796[label="ww70/Succ ww700",fontsize=10,color="white",style="solid",shape="box"];659 -> 1796[label="",style="solid", color="burlywood", weight=9]; 1796 -> 684[label="",style="solid", color="burlywood", weight=3]; 1797[label="ww70/Zero",fontsize=10,color="white",style="solid",shape="box"];659 -> 1797[label="",style="solid", color="burlywood", weight=9]; 1797 -> 685[label="",style="solid", color="burlywood", weight=3]; 660[label="primShowInt (Neg ww70)",fontsize=16,color="black",shape="box"];660 -> 686[label="",style="solid", color="black", weight=3]; 319 -> 9[label="",style="dashed", color="red", weight=0]; 319[label="(showChar (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))) . (shows ww80) . showListShowl ww81",fontsize=16,color="magenta"];319 -> 330[label="",style="dashed", color="magenta", weight=3]; 319 -> 331[label="",style="dashed", color="magenta", weight=3]; 319 -> 332[label="",style="dashed", color="magenta", weight=3]; 320 -> 180[label="",style="dashed", color="red", weight=0]; 320[label="showChar (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ww9",fontsize=16,color="magenta"];320 -> 333[label="",style="dashed", color="magenta", weight=3]; 320 -> 334[label="",style="dashed", color="magenta", weight=3]; 712[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww148",fontsize=16,color="black",shape="box"];712 -> 716[label="",style="solid", color="black", weight=3]; 684[label="primShowInt (Pos (Succ ww700))",fontsize=16,color="black",shape="box"];684 -> 709[label="",style="solid", color="black", weight=3]; 685[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];685 -> 710[label="",style="solid", color="black", weight=3]; 686[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))) : primShowInt (Pos ww70)",fontsize=16,color="green",shape="box"];686 -> 711[label="",style="dashed", color="green", weight=3]; 330[label="ww81",fontsize=16,color="green",shape="box"];331[label="ww80",fontsize=16,color="green",shape="box"];332[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];333[label="ww9",fontsize=16,color="green",shape="box"];334[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];716[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww148",fontsize=16,color="black",shape="box"];716 -> 719[label="",style="solid", color="black", weight=3]; 709 -> 461[label="",style="dashed", color="red", weight=0]; 709[label="primShowInt (div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];709 -> 713[label="",style="dashed", color="magenta", weight=3]; 709 -> 714[label="",style="dashed", color="magenta", weight=3]; 710[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))) : []",fontsize=16,color="green",shape="box"];711 -> 619[label="",style="dashed", color="red", weight=0]; 711[label="primShowInt (Pos ww70)",fontsize=16,color="magenta"];711 -> 715[label="",style="dashed", color="magenta", weight=3]; 719[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww148",fontsize=16,color="black",shape="box"];719 -> 723[label="",style="solid", color="black", weight=3]; 713[label="toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];713 -> 717[label="",style="dashed", color="green", weight=3]; 714 -> 619[label="",style="dashed", color="red", weight=0]; 714[label="primShowInt (div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];714 -> 718[label="",style="dashed", color="magenta", weight=3]; 715[label="Pos ww70",fontsize=16,color="green",shape="box"];723[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (LT == GT) ww148",fontsize=16,color="black",shape="box"];723 -> 727[label="",style="solid", color="black", weight=3]; 717[label="toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];717 -> 739[label="",style="solid", color="black", weight=3]; 718 -> 724[label="",style="dashed", color="red", weight=0]; 718[label="div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];718 -> 725[label="",style="dashed", color="magenta", weight=3]; 718 -> 726[label="",style="dashed", color="magenta", weight=3]; 727[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) False ww148",fontsize=16,color="black",shape="box"];727 -> 738[label="",style="solid", color="black", weight=3]; 739 -> 751[label="",style="dashed", color="red", weight=0]; 739[label="primIntToChar (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];739 -> 752[label="",style="dashed", color="magenta", weight=3]; 739 -> 753[label="",style="dashed", color="magenta", weight=3]; 725[label="ww700",fontsize=16,color="green",shape="box"];726[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];724[label="div Pos (Succ ww153) Pos (Succ ww154)",fontsize=16,color="black",shape="triangle"];724 -> 737[label="",style="solid", color="black", weight=3]; 738[label="(shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="black",shape="box"];738 -> 750[label="",style="solid", color="black", weight=3]; 752[label="ww700",fontsize=16,color="green",shape="box"];753[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];751[label="primIntToChar (mod Pos (Succ ww156) Pos (Succ ww157))",fontsize=16,color="black",shape="triangle"];751 -> 754[label="",style="solid", color="black", weight=3]; 737[label="primDivInt (Pos (Succ ww153)) (Pos (Succ ww154))",fontsize=16,color="black",shape="box"];737 -> 749[label="",style="solid", color="black", weight=3]; 750[label="shows ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];750 -> 755[label="",style="solid", color="black", weight=3]; 754[label="primIntToChar (primModInt (Pos (Succ ww156)) (Pos (Succ ww157)))",fontsize=16,color="black",shape="box"];754 -> 757[label="",style="solid", color="black", weight=3]; 749[label="Pos (primDivNatS (Succ ww153) (Succ ww154))",fontsize=16,color="green",shape="box"];749 -> 756[label="",style="dashed", color="green", weight=3]; 755[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="blue",shape="box"];1798[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1798[label="",style="solid", color="blue", weight=9]; 1798 -> 758[label="",style="solid", color="blue", weight=3]; 1799[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1799[label="",style="solid", color="blue", weight=9]; 1799 -> 759[label="",style="solid", color="blue", weight=3]; 1800[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1800[label="",style="solid", color="blue", weight=9]; 1800 -> 760[label="",style="solid", color="blue", weight=3]; 1801[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1801[label="",style="solid", color="blue", weight=9]; 1801 -> 761[label="",style="solid", color="blue", weight=3]; 1802[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1802[label="",style="solid", color="blue", weight=9]; 1802 -> 762[label="",style="solid", color="blue", weight=3]; 1803[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1803[label="",style="solid", color="blue", weight=9]; 1803 -> 763[label="",style="solid", color="blue", weight=3]; 1804[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1804[label="",style="solid", color="blue", weight=9]; 1804 -> 764[label="",style="solid", color="blue", weight=3]; 1805[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1805[label="",style="solid", color="blue", weight=9]; 1805 -> 765[label="",style="solid", color="blue", weight=3]; 1806[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1806[label="",style="solid", color="blue", weight=9]; 1806 -> 766[label="",style="solid", color="blue", weight=3]; 1807[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1807[label="",style="solid", color="blue", weight=9]; 1807 -> 767[label="",style="solid", color="blue", weight=3]; 1808[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1808[label="",style="solid", color="blue", weight=9]; 1808 -> 768[label="",style="solid", color="blue", weight=3]; 1809[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1809[label="",style="solid", color="blue", weight=9]; 1809 -> 769[label="",style="solid", color="blue", weight=3]; 1810[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1810[label="",style="solid", color="blue", weight=9]; 1810 -> 770[label="",style="solid", color="blue", weight=3]; 1811[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1811[label="",style="solid", color="blue", weight=9]; 1811 -> 771[label="",style="solid", color="blue", weight=3]; 1812[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1812[label="",style="solid", color="blue", weight=9]; 1812 -> 772[label="",style="solid", color="blue", weight=3]; 1813[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1813[label="",style="solid", color="blue", weight=9]; 1813 -> 773[label="",style="solid", color="blue", weight=3]; 1814[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1814[label="",style="solid", color="blue", weight=9]; 1814 -> 774[label="",style="solid", color="blue", weight=3]; 1815[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1815[label="",style="solid", color="blue", weight=9]; 1815 -> 775[label="",style="solid", color="blue", weight=3]; 757[label="primIntToChar (Pos (primModNatS (Succ ww156) (Succ ww157)))",fontsize=16,color="black",shape="box"];757 -> 777[label="",style="solid", color="black", weight=3]; 756[label="primDivNatS (Succ ww153) (Succ ww154)",fontsize=16,color="black",shape="triangle"];756 -> 776[label="",style="solid", color="black", weight=3]; 758[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];758 -> 778[label="",style="solid", color="black", weight=3]; 759[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];759 -> 779[label="",style="solid", color="black", weight=3]; 760[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];760 -> 780[label="",style="solid", color="black", weight=3]; 761[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];761 -> 781[label="",style="solid", color="black", weight=3]; 762[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];762 -> 782[label="",style="solid", color="black", weight=3]; 763[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];763 -> 783[label="",style="solid", color="black", weight=3]; 764[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];764 -> 784[label="",style="solid", color="black", weight=3]; 765[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];765 -> 785[label="",style="solid", color="black", weight=3]; 766[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];766 -> 786[label="",style="solid", color="black", weight=3]; 767[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];767 -> 787[label="",style="solid", color="black", weight=3]; 768[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="burlywood",shape="box"];1816[label="ww138/ww1380 :% ww1381",fontsize=10,color="white",style="solid",shape="box"];768 -> 1816[label="",style="solid", color="burlywood", weight=9]; 1816 -> 788[label="",style="solid", color="burlywood", weight=3]; 769[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];769 -> 789[label="",style="solid", color="black", weight=3]; 770[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];770 -> 790[label="",style="solid", color="black", weight=3]; 771[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];771 -> 791[label="",style="solid", color="black", weight=3]; 772[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];772 -> 792[label="",style="solid", color="black", weight=3]; 773[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];773 -> 793[label="",style="solid", color="black", weight=3]; 774[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];774 -> 794[label="",style="solid", color="black", weight=3]; 775[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];775 -> 795[label="",style="solid", color="black", weight=3]; 777[label="Char (primModNatS (Succ ww156) (Succ ww157))",fontsize=16,color="green",shape="box"];777 -> 798[label="",style="dashed", color="green", weight=3]; 776[label="primDivNatS0 ww153 ww154 (primGEqNatS ww153 ww154)",fontsize=16,color="burlywood",shape="box"];1817[label="ww153/Succ ww1530",fontsize=10,color="white",style="solid",shape="box"];776 -> 1817[label="",style="solid", color="burlywood", weight=9]; 1817 -> 796[label="",style="solid", color="burlywood", weight=3]; 1818[label="ww153/Zero",fontsize=10,color="white",style="solid",shape="box"];776 -> 1818[label="",style="solid", color="burlywood", weight=9]; 1818 -> 797[label="",style="solid", color="burlywood", weight=3]; 778 -> 461[label="",style="dashed", color="red", weight=0]; 778[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];778 -> 799[label="",style="dashed", color="magenta", weight=3]; 778 -> 800[label="",style="dashed", color="magenta", weight=3]; 779 -> 461[label="",style="dashed", color="red", weight=0]; 779[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];779 -> 801[label="",style="dashed", color="magenta", weight=3]; 779 -> 802[label="",style="dashed", color="magenta", weight=3]; 780 -> 461[label="",style="dashed", color="red", weight=0]; 780[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];780 -> 803[label="",style="dashed", color="magenta", weight=3]; 780 -> 804[label="",style="dashed", color="magenta", weight=3]; 781 -> 461[label="",style="dashed", color="red", weight=0]; 781[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];781 -> 805[label="",style="dashed", color="magenta", weight=3]; 781 -> 806[label="",style="dashed", color="magenta", weight=3]; 782 -> 461[label="",style="dashed", color="red", weight=0]; 782[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];782 -> 807[label="",style="dashed", color="magenta", weight=3]; 782 -> 808[label="",style="dashed", color="magenta", weight=3]; 783 -> 461[label="",style="dashed", color="red", weight=0]; 783[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];783 -> 809[label="",style="dashed", color="magenta", weight=3]; 783 -> 810[label="",style="dashed", color="magenta", weight=3]; 784 -> 461[label="",style="dashed", color="red", weight=0]; 784[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];784 -> 811[label="",style="dashed", color="magenta", weight=3]; 784 -> 812[label="",style="dashed", color="magenta", weight=3]; 785 -> 461[label="",style="dashed", color="red", weight=0]; 785[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];785 -> 813[label="",style="dashed", color="magenta", weight=3]; 785 -> 814[label="",style="dashed", color="magenta", weight=3]; 786 -> 461[label="",style="dashed", color="red", weight=0]; 786[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];786 -> 815[label="",style="dashed", color="magenta", weight=3]; 786 -> 816[label="",style="dashed", color="magenta", weight=3]; 787 -> 461[label="",style="dashed", color="red", weight=0]; 787[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];787 -> 817[label="",style="dashed", color="magenta", weight=3]; 787 -> 818[label="",style="dashed", color="magenta", weight=3]; 788[label="showsPrec (Pos Zero) (ww1380 :% ww1381) ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];788 -> 819[label="",style="solid", color="black", weight=3]; 789 -> 461[label="",style="dashed", color="red", weight=0]; 789[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];789 -> 820[label="",style="dashed", color="magenta", weight=3]; 789 -> 821[label="",style="dashed", color="magenta", weight=3]; 790 -> 461[label="",style="dashed", color="red", weight=0]; 790[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];790 -> 822[label="",style="dashed", color="magenta", weight=3]; 790 -> 823[label="",style="dashed", color="magenta", weight=3]; 791 -> 461[label="",style="dashed", color="red", weight=0]; 791[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];791 -> 824[label="",style="dashed", color="magenta", weight=3]; 791 -> 825[label="",style="dashed", color="magenta", weight=3]; 792 -> 461[label="",style="dashed", color="red", weight=0]; 792[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];792 -> 826[label="",style="dashed", color="magenta", weight=3]; 792 -> 827[label="",style="dashed", color="magenta", weight=3]; 793 -> 461[label="",style="dashed", color="red", weight=0]; 793[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];793 -> 828[label="",style="dashed", color="magenta", weight=3]; 793 -> 829[label="",style="dashed", color="magenta", weight=3]; 794 -> 461[label="",style="dashed", color="red", weight=0]; 794[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];794 -> 830[label="",style="dashed", color="magenta", weight=3]; 794 -> 831[label="",style="dashed", color="magenta", weight=3]; 795 -> 461[label="",style="dashed", color="red", weight=0]; 795[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];795 -> 832[label="",style="dashed", color="magenta", weight=3]; 795 -> 833[label="",style="dashed", color="magenta", weight=3]; 798[label="primModNatS (Succ ww156) (Succ ww157)",fontsize=16,color="black",shape="triangle"];798 -> 838[label="",style="solid", color="black", weight=3]; 796[label="primDivNatS0 (Succ ww1530) ww154 (primGEqNatS (Succ ww1530) ww154)",fontsize=16,color="burlywood",shape="box"];1819[label="ww154/Succ ww1540",fontsize=10,color="white",style="solid",shape="box"];796 -> 1819[label="",style="solid", color="burlywood", weight=9]; 1819 -> 834[label="",style="solid", color="burlywood", weight=3]; 1820[label="ww154/Zero",fontsize=10,color="white",style="solid",shape="box"];796 -> 1820[label="",style="solid", color="burlywood", weight=9]; 1820 -> 835[label="",style="solid", color="burlywood", weight=3]; 797[label="primDivNatS0 Zero ww154 (primGEqNatS Zero ww154)",fontsize=16,color="burlywood",shape="box"];1821[label="ww154/Succ ww1540",fontsize=10,color="white",style="solid",shape="box"];797 -> 1821[label="",style="solid", color="burlywood", weight=9]; 1821 -> 836[label="",style="solid", color="burlywood", weight=3]; 1822[label="ww154/Zero",fontsize=10,color="white",style="solid",shape="box"];797 -> 1822[label="",style="solid", color="burlywood", weight=9]; 1822 -> 837[label="",style="solid", color="burlywood", weight=3]; 799[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="black",shape="triangle"];799 -> 839[label="",style="solid", color="black", weight=3]; 800 -> 469[label="",style="dashed", color="red", weight=0]; 800[label="show ww138",fontsize=16,color="magenta"];800 -> 840[label="",style="dashed", color="magenta", weight=3]; 801 -> 799[label="",style="dashed", color="red", weight=0]; 801[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];802 -> 471[label="",style="dashed", color="red", weight=0]; 802[label="show ww138",fontsize=16,color="magenta"];802 -> 841[label="",style="dashed", color="magenta", weight=3]; 803 -> 799[label="",style="dashed", color="red", weight=0]; 803[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];804 -> 473[label="",style="dashed", color="red", weight=0]; 804[label="show ww138",fontsize=16,color="magenta"];804 -> 842[label="",style="dashed", color="magenta", weight=3]; 805 -> 799[label="",style="dashed", color="red", weight=0]; 805[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];806 -> 475[label="",style="dashed", color="red", weight=0]; 806[label="show ww138",fontsize=16,color="magenta"];806 -> 843[label="",style="dashed", color="magenta", weight=3]; 807 -> 799[label="",style="dashed", color="red", weight=0]; 807[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];808 -> 477[label="",style="dashed", color="red", weight=0]; 808[label="show ww138",fontsize=16,color="magenta"];808 -> 844[label="",style="dashed", color="magenta", weight=3]; 809 -> 799[label="",style="dashed", color="red", weight=0]; 809[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];810 -> 479[label="",style="dashed", color="red", weight=0]; 810[label="show ww138",fontsize=16,color="magenta"];810 -> 845[label="",style="dashed", color="magenta", weight=3]; 811 -> 799[label="",style="dashed", color="red", weight=0]; 811[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];812 -> 481[label="",style="dashed", color="red", weight=0]; 812[label="show ww138",fontsize=16,color="magenta"];812 -> 846[label="",style="dashed", color="magenta", weight=3]; 813 -> 799[label="",style="dashed", color="red", weight=0]; 813[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];814 -> 483[label="",style="dashed", color="red", weight=0]; 814[label="show ww138",fontsize=16,color="magenta"];814 -> 847[label="",style="dashed", color="magenta", weight=3]; 815 -> 799[label="",style="dashed", color="red", weight=0]; 815[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];816 -> 485[label="",style="dashed", color="red", weight=0]; 816[label="show ww138",fontsize=16,color="magenta"];816 -> 848[label="",style="dashed", color="magenta", weight=3]; 817 -> 799[label="",style="dashed", color="red", weight=0]; 817[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];818 -> 487[label="",style="dashed", color="red", weight=0]; 818[label="show ww138",fontsize=16,color="magenta"];818 -> 849[label="",style="dashed", color="magenta", weight=3]; 819 -> 687[label="",style="dashed", color="red", weight=0]; 819[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1380) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww1381) ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="magenta"];819 -> 850[label="",style="dashed", color="magenta", weight=3]; 819 -> 851[label="",style="dashed", color="magenta", weight=3]; 819 -> 852[label="",style="dashed", color="magenta", weight=3]; 819 -> 853[label="",style="dashed", color="magenta", weight=3]; 819 -> 854[label="",style="dashed", color="magenta", weight=3]; 819 -> 855[label="",style="dashed", color="magenta", weight=3]; 820 -> 799[label="",style="dashed", color="red", weight=0]; 820[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];821 -> 489[label="",style="dashed", color="red", weight=0]; 821[label="show ww138",fontsize=16,color="magenta"];821 -> 856[label="",style="dashed", color="magenta", weight=3]; 822 -> 799[label="",style="dashed", color="red", weight=0]; 822[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];823 -> 491[label="",style="dashed", color="red", weight=0]; 823[label="show ww138",fontsize=16,color="magenta"];823 -> 857[label="",style="dashed", color="magenta", weight=3]; 824 -> 799[label="",style="dashed", color="red", weight=0]; 824[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];825 -> 493[label="",style="dashed", color="red", weight=0]; 825[label="show ww138",fontsize=16,color="magenta"];825 -> 858[label="",style="dashed", color="magenta", weight=3]; 826 -> 799[label="",style="dashed", color="red", weight=0]; 826[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];827 -> 495[label="",style="dashed", color="red", weight=0]; 827[label="show ww138",fontsize=16,color="magenta"];827 -> 859[label="",style="dashed", color="magenta", weight=3]; 828 -> 799[label="",style="dashed", color="red", weight=0]; 828[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];829 -> 497[label="",style="dashed", color="red", weight=0]; 829[label="show ww138",fontsize=16,color="magenta"];829 -> 860[label="",style="dashed", color="magenta", weight=3]; 830 -> 799[label="",style="dashed", color="red", weight=0]; 830[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];831 -> 499[label="",style="dashed", color="red", weight=0]; 831[label="show ww138",fontsize=16,color="magenta"];831 -> 861[label="",style="dashed", color="magenta", weight=3]; 832 -> 799[label="",style="dashed", color="red", weight=0]; 832[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];833 -> 501[label="",style="dashed", color="red", weight=0]; 833[label="show ww138",fontsize=16,color="magenta"];833 -> 862[label="",style="dashed", color="magenta", weight=3]; 838[label="primModNatS0 ww156 ww157 (primGEqNatS ww156 ww157)",fontsize=16,color="burlywood",shape="box"];1823[label="ww156/Succ ww1560",fontsize=10,color="white",style="solid",shape="box"];838 -> 1823[label="",style="solid", color="burlywood", weight=9]; 1823 -> 867[label="",style="solid", color="burlywood", weight=3]; 1824[label="ww156/Zero",fontsize=10,color="white",style="solid",shape="box"];838 -> 1824[label="",style="solid", color="burlywood", weight=9]; 1824 -> 868[label="",style="solid", color="burlywood", weight=3]; 834[label="primDivNatS0 (Succ ww1530) (Succ ww1540) (primGEqNatS (Succ ww1530) (Succ ww1540))",fontsize=16,color="black",shape="box"];834 -> 863[label="",style="solid", color="black", weight=3]; 835[label="primDivNatS0 (Succ ww1530) Zero (primGEqNatS (Succ ww1530) Zero)",fontsize=16,color="black",shape="box"];835 -> 864[label="",style="solid", color="black", weight=3]; 836[label="primDivNatS0 Zero (Succ ww1540) (primGEqNatS Zero (Succ ww1540))",fontsize=16,color="black",shape="box"];836 -> 865[label="",style="solid", color="black", weight=3]; 837[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];837 -> 866[label="",style="solid", color="black", weight=3]; 839[label="showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : []) (shows ww142 ww148)",fontsize=16,color="black",shape="box"];839 -> 869[label="",style="solid", color="black", weight=3]; 840[label="ww138",fontsize=16,color="green",shape="box"];841[label="ww138",fontsize=16,color="green",shape="box"];842[label="ww138",fontsize=16,color="green",shape="box"];843[label="ww138",fontsize=16,color="green",shape="box"];844[label="ww138",fontsize=16,color="green",shape="box"];845[label="ww138",fontsize=16,color="green",shape="box"];846[label="ww138",fontsize=16,color="green",shape="box"];847[label="ww138",fontsize=16,color="green",shape="box"];848[label="ww138",fontsize=16,color="green",shape="box"];849[label="ww138",fontsize=16,color="green",shape="box"];850[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];851[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];852[label="ww1381",fontsize=16,color="green",shape="box"];853[label="ww1380",fontsize=16,color="green",shape="box"];854[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];855 -> 799[label="",style="dashed", color="red", weight=0]; 855[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];856[label="ww138",fontsize=16,color="green",shape="box"];857[label="ww138",fontsize=16,color="green",shape="box"];858[label="ww138",fontsize=16,color="green",shape="box"];859[label="ww138",fontsize=16,color="green",shape="box"];860[label="ww138",fontsize=16,color="green",shape="box"];861[label="ww138",fontsize=16,color="green",shape="box"];862[label="ww138",fontsize=16,color="green",shape="box"];867[label="primModNatS0 (Succ ww1560) ww157 (primGEqNatS (Succ ww1560) ww157)",fontsize=16,color="burlywood",shape="box"];1825[label="ww157/Succ ww1570",fontsize=10,color="white",style="solid",shape="box"];867 -> 1825[label="",style="solid", color="burlywood", weight=9]; 1825 -> 875[label="",style="solid", color="burlywood", weight=3]; 1826[label="ww157/Zero",fontsize=10,color="white",style="solid",shape="box"];867 -> 1826[label="",style="solid", color="burlywood", weight=9]; 1826 -> 876[label="",style="solid", color="burlywood", weight=3]; 868[label="primModNatS0 Zero ww157 (primGEqNatS Zero ww157)",fontsize=16,color="burlywood",shape="box"];1827[label="ww157/Succ ww1570",fontsize=10,color="white",style="solid",shape="box"];868 -> 1827[label="",style="solid", color="burlywood", weight=9]; 1827 -> 877[label="",style="solid", color="burlywood", weight=3]; 1828[label="ww157/Zero",fontsize=10,color="white",style="solid",shape="box"];868 -> 1828[label="",style="solid", color="burlywood", weight=9]; 1828 -> 878[label="",style="solid", color="burlywood", weight=3]; 863 -> 1485[label="",style="dashed", color="red", weight=0]; 863[label="primDivNatS0 (Succ ww1530) (Succ ww1540) (primGEqNatS ww1530 ww1540)",fontsize=16,color="magenta"];863 -> 1486[label="",style="dashed", color="magenta", weight=3]; 863 -> 1487[label="",style="dashed", color="magenta", weight=3]; 863 -> 1488[label="",style="dashed", color="magenta", weight=3]; 863 -> 1489[label="",style="dashed", color="magenta", weight=3]; 864[label="primDivNatS0 (Succ ww1530) Zero True",fontsize=16,color="black",shape="box"];864 -> 872[label="",style="solid", color="black", weight=3]; 865[label="primDivNatS0 Zero (Succ ww1540) False",fontsize=16,color="black",shape="box"];865 -> 873[label="",style="solid", color="black", weight=3]; 866[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];866 -> 874[label="",style="solid", color="black", weight=3]; 869 -> 461[label="",style="dashed", color="red", weight=0]; 869[label="(++) (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : []) shows ww142 ww148",fontsize=16,color="magenta"];869 -> 879[label="",style="dashed", color="magenta", weight=3]; 869 -> 880[label="",style="dashed", color="magenta", weight=3]; 875[label="primModNatS0 (Succ ww1560) (Succ ww1570) (primGEqNatS (Succ ww1560) (Succ ww1570))",fontsize=16,color="black",shape="box"];875 -> 887[label="",style="solid", color="black", weight=3]; 876[label="primModNatS0 (Succ ww1560) Zero (primGEqNatS (Succ ww1560) Zero)",fontsize=16,color="black",shape="box"];876 -> 888[label="",style="solid", color="black", weight=3]; 877[label="primModNatS0 Zero (Succ ww1570) (primGEqNatS Zero (Succ ww1570))",fontsize=16,color="black",shape="box"];877 -> 889[label="",style="solid", color="black", weight=3]; 878[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];878 -> 890[label="",style="solid", color="black", weight=3]; 1486[label="ww1540",fontsize=16,color="green",shape="box"];1487[label="ww1540",fontsize=16,color="green",shape="box"];1488[label="ww1530",fontsize=16,color="green",shape="box"];1489[label="ww1530",fontsize=16,color="green",shape="box"];1485[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS ww202 ww203)",fontsize=16,color="burlywood",shape="triangle"];1829[label="ww202/Succ ww2020",fontsize=10,color="white",style="solid",shape="box"];1485 -> 1829[label="",style="solid", color="burlywood", weight=9]; 1829 -> 1526[label="",style="solid", color="burlywood", weight=3]; 1830[label="ww202/Zero",fontsize=10,color="white",style="solid",shape="box"];1485 -> 1830[label="",style="solid", color="burlywood", weight=9]; 1830 -> 1527[label="",style="solid", color="burlywood", weight=3]; 872[label="Succ (primDivNatS (primMinusNatS (Succ ww1530) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];872 -> 885[label="",style="dashed", color="green", weight=3]; 873[label="Zero",fontsize=16,color="green",shape="box"];874[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];874 -> 886[label="",style="dashed", color="green", weight=3]; 879[label="shows ww142 ww148",fontsize=16,color="black",shape="box"];879 -> 891[label="",style="solid", color="black", weight=3]; 880[label="Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : []",fontsize=16,color="green",shape="box"];887 -> 1546[label="",style="dashed", color="red", weight=0]; 887[label="primModNatS0 (Succ ww1560) (Succ ww1570) (primGEqNatS ww1560 ww1570)",fontsize=16,color="magenta"];887 -> 1547[label="",style="dashed", color="magenta", weight=3]; 887 -> 1548[label="",style="dashed", color="magenta", weight=3]; 887 -> 1549[label="",style="dashed", color="magenta", weight=3]; 887 -> 1550[label="",style="dashed", color="magenta", weight=3]; 888[label="primModNatS0 (Succ ww1560) Zero True",fontsize=16,color="black",shape="box"];888 -> 900[label="",style="solid", color="black", weight=3]; 889[label="primModNatS0 Zero (Succ ww1570) False",fontsize=16,color="black",shape="box"];889 -> 901[label="",style="solid", color="black", weight=3]; 890[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];890 -> 902[label="",style="solid", color="black", weight=3]; 1526[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS (Succ ww2020) ww203)",fontsize=16,color="burlywood",shape="box"];1831[label="ww203/Succ ww2030",fontsize=10,color="white",style="solid",shape="box"];1526 -> 1831[label="",style="solid", color="burlywood", weight=9]; 1831 -> 1538[label="",style="solid", color="burlywood", weight=3]; 1832[label="ww203/Zero",fontsize=10,color="white",style="solid",shape="box"];1526 -> 1832[label="",style="solid", color="burlywood", weight=9]; 1832 -> 1539[label="",style="solid", color="burlywood", weight=3]; 1527[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS Zero ww203)",fontsize=16,color="burlywood",shape="box"];1833[label="ww203/Succ ww2030",fontsize=10,color="white",style="solid",shape="box"];1527 -> 1833[label="",style="solid", color="burlywood", weight=9]; 1833 -> 1540[label="",style="solid", color="burlywood", weight=3]; 1834[label="ww203/Zero",fontsize=10,color="white",style="solid",shape="box"];1527 -> 1834[label="",style="solid", color="burlywood", weight=9]; 1834 -> 1541[label="",style="solid", color="burlywood", weight=3]; 885 -> 1729[label="",style="dashed", color="red", weight=0]; 885[label="primDivNatS (primMinusNatS (Succ ww1530) Zero) (Succ Zero)",fontsize=16,color="magenta"];885 -> 1730[label="",style="dashed", color="magenta", weight=3]; 885 -> 1731[label="",style="dashed", color="magenta", weight=3]; 885 -> 1732[label="",style="dashed", color="magenta", weight=3]; 886 -> 1729[label="",style="dashed", color="red", weight=0]; 886[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];886 -> 1733[label="",style="dashed", color="magenta", weight=3]; 886 -> 1734[label="",style="dashed", color="magenta", weight=3]; 886 -> 1735[label="",style="dashed", color="magenta", weight=3]; 891[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="blue",shape="box"];1835[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1835[label="",style="solid", color="blue", weight=9]; 1835 -> 903[label="",style="solid", color="blue", weight=3]; 1836[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1836[label="",style="solid", color="blue", weight=9]; 1836 -> 904[label="",style="solid", color="blue", weight=3]; 1837[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1837[label="",style="solid", color="blue", weight=9]; 1837 -> 905[label="",style="solid", color="blue", weight=3]; 1838[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1838[label="",style="solid", color="blue", weight=9]; 1838 -> 906[label="",style="solid", color="blue", weight=3]; 1839[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1839[label="",style="solid", color="blue", weight=9]; 1839 -> 907[label="",style="solid", color="blue", weight=3]; 1840[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1840[label="",style="solid", color="blue", weight=9]; 1840 -> 908[label="",style="solid", color="blue", weight=3]; 1841[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1841[label="",style="solid", color="blue", weight=9]; 1841 -> 909[label="",style="solid", color="blue", weight=3]; 1842[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1842[label="",style="solid", color="blue", weight=9]; 1842 -> 910[label="",style="solid", color="blue", weight=3]; 1843[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1843[label="",style="solid", color="blue", weight=9]; 1843 -> 911[label="",style="solid", color="blue", weight=3]; 1844[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1844[label="",style="solid", color="blue", weight=9]; 1844 -> 912[label="",style="solid", color="blue", weight=3]; 1845[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1845[label="",style="solid", color="blue", weight=9]; 1845 -> 913[label="",style="solid", color="blue", weight=3]; 1846[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1846[label="",style="solid", color="blue", weight=9]; 1846 -> 914[label="",style="solid", color="blue", weight=3]; 1847[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1847[label="",style="solid", color="blue", weight=9]; 1847 -> 915[label="",style="solid", color="blue", weight=3]; 1848[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1848[label="",style="solid", color="blue", weight=9]; 1848 -> 916[label="",style="solid", color="blue", weight=3]; 1849[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1849[label="",style="solid", color="blue", weight=9]; 1849 -> 917[label="",style="solid", color="blue", weight=3]; 1850[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1850[label="",style="solid", color="blue", weight=9]; 1850 -> 918[label="",style="solid", color="blue", weight=3]; 1851[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1851[label="",style="solid", color="blue", weight=9]; 1851 -> 919[label="",style="solid", color="blue", weight=3]; 1852[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1852[label="",style="solid", color="blue", weight=9]; 1852 -> 920[label="",style="solid", color="blue", weight=3]; 1547[label="ww1570",fontsize=16,color="green",shape="box"];1548[label="ww1560",fontsize=16,color="green",shape="box"];1549[label="ww1570",fontsize=16,color="green",shape="box"];1550[label="ww1560",fontsize=16,color="green",shape="box"];1546[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS ww207 ww208)",fontsize=16,color="burlywood",shape="triangle"];1853[label="ww207/Succ ww2070",fontsize=10,color="white",style="solid",shape="box"];1546 -> 1853[label="",style="solid", color="burlywood", weight=9]; 1853 -> 1587[label="",style="solid", color="burlywood", weight=3]; 1854[label="ww207/Zero",fontsize=10,color="white",style="solid",shape="box"];1546 -> 1854[label="",style="solid", color="burlywood", weight=9]; 1854 -> 1588[label="",style="solid", color="burlywood", weight=3]; 900 -> 1633[label="",style="dashed", color="red", weight=0]; 900[label="primModNatS (primMinusNatS (Succ ww1560) Zero) (Succ Zero)",fontsize=16,color="magenta"];900 -> 1634[label="",style="dashed", color="magenta", weight=3]; 900 -> 1635[label="",style="dashed", color="magenta", weight=3]; 900 -> 1636[label="",style="dashed", color="magenta", weight=3]; 901[label="Succ Zero",fontsize=16,color="green",shape="box"];902 -> 1633[label="",style="dashed", color="red", weight=0]; 902[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];902 -> 1637[label="",style="dashed", color="magenta", weight=3]; 902 -> 1638[label="",style="dashed", color="magenta", weight=3]; 902 -> 1639[label="",style="dashed", color="magenta", weight=3]; 1538[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS (Succ ww2020) (Succ ww2030))",fontsize=16,color="black",shape="box"];1538 -> 1589[label="",style="solid", color="black", weight=3]; 1539[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS (Succ ww2020) Zero)",fontsize=16,color="black",shape="box"];1539 -> 1590[label="",style="solid", color="black", weight=3]; 1540[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS Zero (Succ ww2030))",fontsize=16,color="black",shape="box"];1540 -> 1591[label="",style="solid", color="black", weight=3]; 1541[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1541 -> 1592[label="",style="solid", color="black", weight=3]; 1730[label="Succ ww1530",fontsize=16,color="green",shape="box"];1731[label="Zero",fontsize=16,color="green",shape="box"];1732[label="Zero",fontsize=16,color="green",shape="box"];1729[label="primDivNatS (primMinusNatS ww214 ww215) (Succ ww216)",fontsize=16,color="burlywood",shape="triangle"];1855[label="ww214/Succ ww2140",fontsize=10,color="white",style="solid",shape="box"];1729 -> 1855[label="",style="solid", color="burlywood", weight=9]; 1855 -> 1754[label="",style="solid", color="burlywood", weight=3]; 1856[label="ww214/Zero",fontsize=10,color="white",style="solid",shape="box"];1729 -> 1856[label="",style="solid", color="burlywood", weight=9]; 1856 -> 1755[label="",style="solid", color="burlywood", weight=3]; 1733[label="Zero",fontsize=16,color="green",shape="box"];1734[label="Zero",fontsize=16,color="green",shape="box"];1735[label="Zero",fontsize=16,color="green",shape="box"];903[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];903 -> 935[label="",style="solid", color="black", weight=3]; 904[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];904 -> 936[label="",style="solid", color="black", weight=3]; 905[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];905 -> 937[label="",style="solid", color="black", weight=3]; 906[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];906 -> 938[label="",style="solid", color="black", weight=3]; 907[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];907 -> 939[label="",style="solid", color="black", weight=3]; 908[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];908 -> 940[label="",style="solid", color="black", weight=3]; 909[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];909 -> 941[label="",style="solid", color="black", weight=3]; 910[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];910 -> 942[label="",style="solid", color="black", weight=3]; 911[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];911 -> 943[label="",style="solid", color="black", weight=3]; 912[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];912 -> 944[label="",style="solid", color="black", weight=3]; 913[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="burlywood",shape="box"];1857[label="ww142/ww1420 :% ww1421",fontsize=10,color="white",style="solid",shape="box"];913 -> 1857[label="",style="solid", color="burlywood", weight=9]; 1857 -> 945[label="",style="solid", color="burlywood", weight=3]; 914[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];914 -> 946[label="",style="solid", color="black", weight=3]; 915[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];915 -> 947[label="",style="solid", color="black", weight=3]; 916[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];916 -> 948[label="",style="solid", color="black", weight=3]; 917[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];917 -> 949[label="",style="solid", color="black", weight=3]; 918[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];918 -> 950[label="",style="solid", color="black", weight=3]; 919[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];919 -> 951[label="",style="solid", color="black", weight=3]; 920[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];920 -> 952[label="",style="solid", color="black", weight=3]; 1587[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS (Succ ww2070) ww208)",fontsize=16,color="burlywood",shape="box"];1858[label="ww208/Succ ww2080",fontsize=10,color="white",style="solid",shape="box"];1587 -> 1858[label="",style="solid", color="burlywood", weight=9]; 1858 -> 1597[label="",style="solid", color="burlywood", weight=3]; 1859[label="ww208/Zero",fontsize=10,color="white",style="solid",shape="box"];1587 -> 1859[label="",style="solid", color="burlywood", weight=9]; 1859 -> 1598[label="",style="solid", color="burlywood", weight=3]; 1588[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS Zero ww208)",fontsize=16,color="burlywood",shape="box"];1860[label="ww208/Succ ww2080",fontsize=10,color="white",style="solid",shape="box"];1588 -> 1860[label="",style="solid", color="burlywood", weight=9]; 1860 -> 1599[label="",style="solid", color="burlywood", weight=3]; 1861[label="ww208/Zero",fontsize=10,color="white",style="solid",shape="box"];1588 -> 1861[label="",style="solid", color="burlywood", weight=9]; 1861 -> 1600[label="",style="solid", color="burlywood", weight=3]; 1634[label="Zero",fontsize=16,color="green",shape="box"];1635[label="Succ ww1560",fontsize=16,color="green",shape="box"];1636[label="Zero",fontsize=16,color="green",shape="box"];1633[label="primModNatS (primMinusNatS ww210 ww211) (Succ ww212)",fontsize=16,color="burlywood",shape="triangle"];1862[label="ww210/Succ ww2100",fontsize=10,color="white",style="solid",shape="box"];1633 -> 1862[label="",style="solid", color="burlywood", weight=9]; 1862 -> 1664[label="",style="solid", color="burlywood", weight=3]; 1863[label="ww210/Zero",fontsize=10,color="white",style="solid",shape="box"];1633 -> 1863[label="",style="solid", color="burlywood", weight=9]; 1863 -> 1665[label="",style="solid", color="burlywood", weight=3]; 1637[label="Zero",fontsize=16,color="green",shape="box"];1638[label="Zero",fontsize=16,color="green",shape="box"];1639[label="Zero",fontsize=16,color="green",shape="box"];1589 -> 1485[label="",style="dashed", color="red", weight=0]; 1589[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS ww2020 ww2030)",fontsize=16,color="magenta"];1589 -> 1601[label="",style="dashed", color="magenta", weight=3]; 1589 -> 1602[label="",style="dashed", color="magenta", weight=3]; 1590[label="primDivNatS0 (Succ ww200) (Succ ww201) True",fontsize=16,color="black",shape="triangle"];1590 -> 1603[label="",style="solid", color="black", weight=3]; 1591[label="primDivNatS0 (Succ ww200) (Succ ww201) False",fontsize=16,color="black",shape="box"];1591 -> 1604[label="",style="solid", color="black", weight=3]; 1592 -> 1590[label="",style="dashed", color="red", weight=0]; 1592[label="primDivNatS0 (Succ ww200) (Succ ww201) True",fontsize=16,color="magenta"];1754[label="primDivNatS (primMinusNatS (Succ ww2140) ww215) (Succ ww216)",fontsize=16,color="burlywood",shape="box"];1864[label="ww215/Succ ww2150",fontsize=10,color="white",style="solid",shape="box"];1754 -> 1864[label="",style="solid", color="burlywood", weight=9]; 1864 -> 1756[label="",style="solid", color="burlywood", weight=3]; 1865[label="ww215/Zero",fontsize=10,color="white",style="solid",shape="box"];1754 -> 1865[label="",style="solid", color="burlywood", weight=9]; 1865 -> 1757[label="",style="solid", color="burlywood", weight=3]; 1755[label="primDivNatS (primMinusNatS Zero ww215) (Succ ww216)",fontsize=16,color="burlywood",shape="box"];1866[label="ww215/Succ ww2150",fontsize=10,color="white",style="solid",shape="box"];1755 -> 1866[label="",style="solid", color="burlywood", weight=9]; 1866 -> 1758[label="",style="solid", color="burlywood", weight=3]; 1867[label="ww215/Zero",fontsize=10,color="white",style="solid",shape="box"];1755 -> 1867[label="",style="solid", color="burlywood", weight=9]; 1867 -> 1759[label="",style="solid", color="burlywood", weight=3]; 935 -> 461[label="",style="dashed", color="red", weight=0]; 935[label="show ww142 ++ ww148",fontsize=16,color="magenta"];935 -> 966[label="",style="dashed", color="magenta", weight=3]; 935 -> 967[label="",style="dashed", color="magenta", weight=3]; 936 -> 461[label="",style="dashed", color="red", weight=0]; 936[label="show ww142 ++ ww148",fontsize=16,color="magenta"];936 -> 968[label="",style="dashed", color="magenta", weight=3]; 936 -> 969[label="",style="dashed", color="magenta", weight=3]; 937 -> 461[label="",style="dashed", color="red", weight=0]; 937[label="show ww142 ++ ww148",fontsize=16,color="magenta"];937 -> 970[label="",style="dashed", color="magenta", weight=3]; 937 -> 971[label="",style="dashed", color="magenta", weight=3]; 938 -> 461[label="",style="dashed", color="red", weight=0]; 938[label="show ww142 ++ ww148",fontsize=16,color="magenta"];938 -> 972[label="",style="dashed", color="magenta", weight=3]; 938 -> 973[label="",style="dashed", color="magenta", weight=3]; 939 -> 461[label="",style="dashed", color="red", weight=0]; 939[label="show ww142 ++ ww148",fontsize=16,color="magenta"];939 -> 974[label="",style="dashed", color="magenta", weight=3]; 939 -> 975[label="",style="dashed", color="magenta", weight=3]; 940 -> 461[label="",style="dashed", color="red", weight=0]; 940[label="show ww142 ++ ww148",fontsize=16,color="magenta"];940 -> 976[label="",style="dashed", color="magenta", weight=3]; 940 -> 977[label="",style="dashed", color="magenta", weight=3]; 941 -> 461[label="",style="dashed", color="red", weight=0]; 941[label="show ww142 ++ ww148",fontsize=16,color="magenta"];941 -> 978[label="",style="dashed", color="magenta", weight=3]; 941 -> 979[label="",style="dashed", color="magenta", weight=3]; 942 -> 461[label="",style="dashed", color="red", weight=0]; 942[label="show ww142 ++ ww148",fontsize=16,color="magenta"];942 -> 980[label="",style="dashed", color="magenta", weight=3]; 942 -> 981[label="",style="dashed", color="magenta", weight=3]; 943 -> 461[label="",style="dashed", color="red", weight=0]; 943[label="show ww142 ++ ww148",fontsize=16,color="magenta"];943 -> 982[label="",style="dashed", color="magenta", weight=3]; 943 -> 983[label="",style="dashed", color="magenta", weight=3]; 944 -> 461[label="",style="dashed", color="red", weight=0]; 944[label="show ww142 ++ ww148",fontsize=16,color="magenta"];944 -> 984[label="",style="dashed", color="magenta", weight=3]; 944 -> 985[label="",style="dashed", color="magenta", weight=3]; 945[label="showsPrec (Pos Zero) (ww1420 :% ww1421) ww148",fontsize=16,color="black",shape="box"];945 -> 986[label="",style="solid", color="black", weight=3]; 946 -> 461[label="",style="dashed", color="red", weight=0]; 946[label="show ww142 ++ ww148",fontsize=16,color="magenta"];946 -> 987[label="",style="dashed", color="magenta", weight=3]; 946 -> 988[label="",style="dashed", color="magenta", weight=3]; 947 -> 461[label="",style="dashed", color="red", weight=0]; 947[label="show ww142 ++ ww148",fontsize=16,color="magenta"];947 -> 989[label="",style="dashed", color="magenta", weight=3]; 947 -> 990[label="",style="dashed", color="magenta", weight=3]; 948 -> 461[label="",style="dashed", color="red", weight=0]; 948[label="show ww142 ++ ww148",fontsize=16,color="magenta"];948 -> 991[label="",style="dashed", color="magenta", weight=3]; 948 -> 992[label="",style="dashed", color="magenta", weight=3]; 949 -> 461[label="",style="dashed", color="red", weight=0]; 949[label="show ww142 ++ ww148",fontsize=16,color="magenta"];949 -> 993[label="",style="dashed", color="magenta", weight=3]; 949 -> 994[label="",style="dashed", color="magenta", weight=3]; 950 -> 461[label="",style="dashed", color="red", weight=0]; 950[label="show ww142 ++ ww148",fontsize=16,color="magenta"];950 -> 995[label="",style="dashed", color="magenta", weight=3]; 950 -> 996[label="",style="dashed", color="magenta", weight=3]; 951 -> 461[label="",style="dashed", color="red", weight=0]; 951[label="show ww142 ++ ww148",fontsize=16,color="magenta"];951 -> 997[label="",style="dashed", color="magenta", weight=3]; 951 -> 998[label="",style="dashed", color="magenta", weight=3]; 952 -> 461[label="",style="dashed", color="red", weight=0]; 952[label="show ww142 ++ ww148",fontsize=16,color="magenta"];952 -> 999[label="",style="dashed", color="magenta", weight=3]; 952 -> 1000[label="",style="dashed", color="magenta", weight=3]; 1597[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS (Succ ww2070) (Succ ww2080))",fontsize=16,color="black",shape="box"];1597 -> 1611[label="",style="solid", color="black", weight=3]; 1598[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS (Succ ww2070) Zero)",fontsize=16,color="black",shape="box"];1598 -> 1612[label="",style="solid", color="black", weight=3]; 1599[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS Zero (Succ ww2080))",fontsize=16,color="black",shape="box"];1599 -> 1613[label="",style="solid", color="black", weight=3]; 1600[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1600 -> 1614[label="",style="solid", color="black", weight=3]; 1664[label="primModNatS (primMinusNatS (Succ ww2100) ww211) (Succ ww212)",fontsize=16,color="burlywood",shape="box"];1868[label="ww211/Succ ww2110",fontsize=10,color="white",style="solid",shape="box"];1664 -> 1868[label="",style="solid", color="burlywood", weight=9]; 1868 -> 1670[label="",style="solid", color="burlywood", weight=3]; 1869[label="ww211/Zero",fontsize=10,color="white",style="solid",shape="box"];1664 -> 1869[label="",style="solid", color="burlywood", weight=9]; 1869 -> 1671[label="",style="solid", color="burlywood", weight=3]; 1665[label="primModNatS (primMinusNatS Zero ww211) (Succ ww212)",fontsize=16,color="burlywood",shape="box"];1870[label="ww211/Succ ww2110",fontsize=10,color="white",style="solid",shape="box"];1665 -> 1870[label="",style="solid", color="burlywood", weight=9]; 1870 -> 1672[label="",style="solid", color="burlywood", weight=3]; 1871[label="ww211/Zero",fontsize=10,color="white",style="solid",shape="box"];1665 -> 1871[label="",style="solid", color="burlywood", weight=9]; 1871 -> 1673[label="",style="solid", color="burlywood", weight=3]; 1601[label="ww2030",fontsize=16,color="green",shape="box"];1602[label="ww2020",fontsize=16,color="green",shape="box"];1603[label="Succ (primDivNatS (primMinusNatS (Succ ww200) (Succ ww201)) (Succ (Succ ww201)))",fontsize=16,color="green",shape="box"];1603 -> 1615[label="",style="dashed", color="green", weight=3]; 1604[label="Zero",fontsize=16,color="green",shape="box"];1756[label="primDivNatS (primMinusNatS (Succ ww2140) (Succ ww2150)) (Succ ww216)",fontsize=16,color="black",shape="box"];1756 -> 1760[label="",style="solid", color="black", weight=3]; 1757[label="primDivNatS (primMinusNatS (Succ ww2140) Zero) (Succ ww216)",fontsize=16,color="black",shape="box"];1757 -> 1761[label="",style="solid", color="black", weight=3]; 1758[label="primDivNatS (primMinusNatS Zero (Succ ww2150)) (Succ ww216)",fontsize=16,color="black",shape="box"];1758 -> 1762[label="",style="solid", color="black", weight=3]; 1759[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww216)",fontsize=16,color="black",shape="box"];1759 -> 1763[label="",style="solid", color="black", weight=3]; 966[label="ww148",fontsize=16,color="green",shape="box"];967 -> 469[label="",style="dashed", color="red", weight=0]; 967[label="show ww142",fontsize=16,color="magenta"];967 -> 1012[label="",style="dashed", color="magenta", weight=3]; 968[label="ww148",fontsize=16,color="green",shape="box"];969 -> 471[label="",style="dashed", color="red", weight=0]; 969[label="show ww142",fontsize=16,color="magenta"];969 -> 1013[label="",style="dashed", color="magenta", weight=3]; 970[label="ww148",fontsize=16,color="green",shape="box"];971 -> 473[label="",style="dashed", color="red", weight=0]; 971[label="show ww142",fontsize=16,color="magenta"];971 -> 1014[label="",style="dashed", color="magenta", weight=3]; 972[label="ww148",fontsize=16,color="green",shape="box"];973 -> 475[label="",style="dashed", color="red", weight=0]; 973[label="show ww142",fontsize=16,color="magenta"];973 -> 1015[label="",style="dashed", color="magenta", weight=3]; 974[label="ww148",fontsize=16,color="green",shape="box"];975 -> 477[label="",style="dashed", color="red", weight=0]; 975[label="show ww142",fontsize=16,color="magenta"];975 -> 1016[label="",style="dashed", color="magenta", weight=3]; 976[label="ww148",fontsize=16,color="green",shape="box"];977 -> 479[label="",style="dashed", color="red", weight=0]; 977[label="show ww142",fontsize=16,color="magenta"];977 -> 1017[label="",style="dashed", color="magenta", weight=3]; 978[label="ww148",fontsize=16,color="green",shape="box"];979 -> 481[label="",style="dashed", color="red", weight=0]; 979[label="show ww142",fontsize=16,color="magenta"];979 -> 1018[label="",style="dashed", color="magenta", weight=3]; 980[label="ww148",fontsize=16,color="green",shape="box"];981 -> 483[label="",style="dashed", color="red", weight=0]; 981[label="show ww142",fontsize=16,color="magenta"];981 -> 1019[label="",style="dashed", color="magenta", weight=3]; 982[label="ww148",fontsize=16,color="green",shape="box"];983 -> 485[label="",style="dashed", color="red", weight=0]; 983[label="show ww142",fontsize=16,color="magenta"];983 -> 1020[label="",style="dashed", color="magenta", weight=3]; 984[label="ww148",fontsize=16,color="green",shape="box"];985 -> 487[label="",style="dashed", color="red", weight=0]; 985[label="show ww142",fontsize=16,color="magenta"];985 -> 1021[label="",style="dashed", color="magenta", weight=3]; 986 -> 687[label="",style="dashed", color="red", weight=0]; 986[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1420) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww1421) ww148",fontsize=16,color="magenta"];986 -> 1022[label="",style="dashed", color="magenta", weight=3]; 986 -> 1023[label="",style="dashed", color="magenta", weight=3]; 986 -> 1024[label="",style="dashed", color="magenta", weight=3]; 986 -> 1025[label="",style="dashed", color="magenta", weight=3]; 986 -> 1026[label="",style="dashed", color="magenta", weight=3]; 987[label="ww148",fontsize=16,color="green",shape="box"];988 -> 489[label="",style="dashed", color="red", weight=0]; 988[label="show ww142",fontsize=16,color="magenta"];988 -> 1027[label="",style="dashed", color="magenta", weight=3]; 989[label="ww148",fontsize=16,color="green",shape="box"];990 -> 491[label="",style="dashed", color="red", weight=0]; 990[label="show ww142",fontsize=16,color="magenta"];990 -> 1028[label="",style="dashed", color="magenta", weight=3]; 991[label="ww148",fontsize=16,color="green",shape="box"];992 -> 493[label="",style="dashed", color="red", weight=0]; 992[label="show ww142",fontsize=16,color="magenta"];992 -> 1029[label="",style="dashed", color="magenta", weight=3]; 993[label="ww148",fontsize=16,color="green",shape="box"];994 -> 495[label="",style="dashed", color="red", weight=0]; 994[label="show ww142",fontsize=16,color="magenta"];994 -> 1030[label="",style="dashed", color="magenta", weight=3]; 995[label="ww148",fontsize=16,color="green",shape="box"];996 -> 497[label="",style="dashed", color="red", weight=0]; 996[label="show ww142",fontsize=16,color="magenta"];996 -> 1031[label="",style="dashed", color="magenta", weight=3]; 997[label="ww148",fontsize=16,color="green",shape="box"];998 -> 499[label="",style="dashed", color="red", weight=0]; 998[label="show ww142",fontsize=16,color="magenta"];998 -> 1032[label="",style="dashed", color="magenta", weight=3]; 999[label="ww148",fontsize=16,color="green",shape="box"];1000 -> 501[label="",style="dashed", color="red", weight=0]; 1000[label="show ww142",fontsize=16,color="magenta"];1000 -> 1033[label="",style="dashed", color="magenta", weight=3]; 1611 -> 1546[label="",style="dashed", color="red", weight=0]; 1611[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS ww2070 ww2080)",fontsize=16,color="magenta"];1611 -> 1620[label="",style="dashed", color="magenta", weight=3]; 1611 -> 1621[label="",style="dashed", color="magenta", weight=3]; 1612[label="primModNatS0 (Succ ww205) (Succ ww206) True",fontsize=16,color="black",shape="triangle"];1612 -> 1622[label="",style="solid", color="black", weight=3]; 1613[label="primModNatS0 (Succ ww205) (Succ ww206) False",fontsize=16,color="black",shape="box"];1613 -> 1623[label="",style="solid", color="black", weight=3]; 1614 -> 1612[label="",style="dashed", color="red", weight=0]; 1614[label="primModNatS0 (Succ ww205) (Succ ww206) True",fontsize=16,color="magenta"];1670[label="primModNatS (primMinusNatS (Succ ww2100) (Succ ww2110)) (Succ ww212)",fontsize=16,color="black",shape="box"];1670 -> 1678[label="",style="solid", color="black", weight=3]; 1671[label="primModNatS (primMinusNatS (Succ ww2100) Zero) (Succ ww212)",fontsize=16,color="black",shape="box"];1671 -> 1679[label="",style="solid", color="black", weight=3]; 1672[label="primModNatS (primMinusNatS Zero (Succ ww2110)) (Succ ww212)",fontsize=16,color="black",shape="box"];1672 -> 1680[label="",style="solid", color="black", weight=3]; 1673[label="primModNatS (primMinusNatS Zero Zero) (Succ ww212)",fontsize=16,color="black",shape="box"];1673 -> 1681[label="",style="solid", color="black", weight=3]; 1615 -> 1729[label="",style="dashed", color="red", weight=0]; 1615[label="primDivNatS (primMinusNatS (Succ ww200) (Succ ww201)) (Succ (Succ ww201))",fontsize=16,color="magenta"];1615 -> 1736[label="",style="dashed", color="magenta", weight=3]; 1615 -> 1737[label="",style="dashed", color="magenta", weight=3]; 1615 -> 1738[label="",style="dashed", color="magenta", weight=3]; 1760 -> 1729[label="",style="dashed", color="red", weight=0]; 1760[label="primDivNatS (primMinusNatS ww2140 ww2150) (Succ ww216)",fontsize=16,color="magenta"];1760 -> 1764[label="",style="dashed", color="magenta", weight=3]; 1760 -> 1765[label="",style="dashed", color="magenta", weight=3]; 1761 -> 756[label="",style="dashed", color="red", weight=0]; 1761[label="primDivNatS (Succ ww2140) (Succ ww216)",fontsize=16,color="magenta"];1761 -> 1766[label="",style="dashed", color="magenta", weight=3]; 1761 -> 1767[label="",style="dashed", color="magenta", weight=3]; 1762[label="primDivNatS Zero (Succ ww216)",fontsize=16,color="black",shape="triangle"];1762 -> 1768[label="",style="solid", color="black", weight=3]; 1763 -> 1762[label="",style="dashed", color="red", weight=0]; 1763[label="primDivNatS Zero (Succ ww216)",fontsize=16,color="magenta"];1012[label="ww142",fontsize=16,color="green",shape="box"];1013[label="ww142",fontsize=16,color="green",shape="box"];1014[label="ww142",fontsize=16,color="green",shape="box"];1015[label="ww142",fontsize=16,color="green",shape="box"];1016[label="ww142",fontsize=16,color="green",shape="box"];1017[label="ww142",fontsize=16,color="green",shape="box"];1018[label="ww142",fontsize=16,color="green",shape="box"];1019[label="ww142",fontsize=16,color="green",shape="box"];1020[label="ww142",fontsize=16,color="green",shape="box"];1021[label="ww142",fontsize=16,color="green",shape="box"];1022[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1023[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1024[label="ww1421",fontsize=16,color="green",shape="box"];1025[label="ww1420",fontsize=16,color="green",shape="box"];1026[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1027[label="ww142",fontsize=16,color="green",shape="box"];1028[label="ww142",fontsize=16,color="green",shape="box"];1029[label="ww142",fontsize=16,color="green",shape="box"];1030[label="ww142",fontsize=16,color="green",shape="box"];1031[label="ww142",fontsize=16,color="green",shape="box"];1032[label="ww142",fontsize=16,color="green",shape="box"];1033[label="ww142",fontsize=16,color="green",shape="box"];1620[label="ww2070",fontsize=16,color="green",shape="box"];1621[label="ww2080",fontsize=16,color="green",shape="box"];1622 -> 1633[label="",style="dashed", color="red", weight=0]; 1622[label="primModNatS (primMinusNatS (Succ ww205) (Succ ww206)) (Succ (Succ ww206))",fontsize=16,color="magenta"];1622 -> 1646[label="",style="dashed", color="magenta", weight=3]; 1622 -> 1647[label="",style="dashed", color="magenta", weight=3]; 1622 -> 1648[label="",style="dashed", color="magenta", weight=3]; 1623[label="Succ (Succ ww205)",fontsize=16,color="green",shape="box"];1678 -> 1633[label="",style="dashed", color="red", weight=0]; 1678[label="primModNatS (primMinusNatS ww2100 ww2110) (Succ ww212)",fontsize=16,color="magenta"];1678 -> 1688[label="",style="dashed", color="magenta", weight=3]; 1678 -> 1689[label="",style="dashed", color="magenta", weight=3]; 1679 -> 798[label="",style="dashed", color="red", weight=0]; 1679[label="primModNatS (Succ ww2100) (Succ ww212)",fontsize=16,color="magenta"];1679 -> 1690[label="",style="dashed", color="magenta", weight=3]; 1679 -> 1691[label="",style="dashed", color="magenta", weight=3]; 1680[label="primModNatS Zero (Succ ww212)",fontsize=16,color="black",shape="triangle"];1680 -> 1692[label="",style="solid", color="black", weight=3]; 1681 -> 1680[label="",style="dashed", color="red", weight=0]; 1681[label="primModNatS Zero (Succ ww212)",fontsize=16,color="magenta"];1736[label="Succ ww200",fontsize=16,color="green",shape="box"];1737[label="Succ ww201",fontsize=16,color="green",shape="box"];1738[label="Succ ww201",fontsize=16,color="green",shape="box"];1764[label="ww2140",fontsize=16,color="green",shape="box"];1765[label="ww2150",fontsize=16,color="green",shape="box"];1766[label="ww2140",fontsize=16,color="green",shape="box"];1767[label="ww216",fontsize=16,color="green",shape="box"];1768[label="Zero",fontsize=16,color="green",shape="box"];1646[label="Succ ww206",fontsize=16,color="green",shape="box"];1647[label="Succ ww205",fontsize=16,color="green",shape="box"];1648[label="Succ ww206",fontsize=16,color="green",shape="box"];1688[label="ww2110",fontsize=16,color="green",shape="box"];1689[label="ww2100",fontsize=16,color="green",shape="box"];1690[label="ww2100",fontsize=16,color="green",shape="box"];1691[label="ww212",fontsize=16,color="green",shape="box"];1692[label="Zero",fontsize=16,color="green",shape="box"];} ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(ww200, ww201, Zero, Zero) -> new_primDivNatS00(ww200, ww201) new_primDivNatS00(ww200, ww201) -> new_primDivNatS(Succ(ww200), Succ(ww201), Succ(ww201)) new_primDivNatS(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS(ww2140, ww2150, ww216) new_primDivNatS1(Succ(ww1530), Zero) -> new_primDivNatS(Succ(ww1530), Zero, Zero) new_primDivNatS0(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS0(ww200, ww201, ww2020, ww2030) new_primDivNatS0(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS(Succ(ww200), Succ(ww201), Succ(ww201)) new_primDivNatS1(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS0(ww1530, ww1540, ww1530, ww1540) new_primDivNatS1(Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) new_primDivNatS(Succ(ww2140), Zero, ww216) -> new_primDivNatS1(ww2140, ww216) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (14) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (15) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS00(ww200, ww201) -> new_primDivNatS(Succ(ww200), Succ(ww201), Succ(ww201)) new_primDivNatS(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS(ww2140, ww2150, ww216) new_primDivNatS(Succ(ww2140), Zero, ww216) -> new_primDivNatS1(ww2140, ww216) new_primDivNatS1(Succ(ww1530), Zero) -> new_primDivNatS(Succ(ww1530), Zero, Zero) new_primDivNatS1(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS0(ww1530, ww1540, ww1530, ww1540) new_primDivNatS0(ww200, ww201, Zero, Zero) -> new_primDivNatS00(ww200, ww201) new_primDivNatS0(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS0(ww200, ww201, ww2020, ww2030) new_primDivNatS0(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS(Succ(ww200), Succ(ww201), Succ(ww201)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (16) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_primDivNatS(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS(ww2140, ww2150, ww216) new_primDivNatS1(Succ(ww1530), Zero) -> new_primDivNatS(Succ(ww1530), Zero, Zero) new_primDivNatS1(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS0(ww1530, ww1540, ww1530, ww1540) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_primDivNatS(x_1, x_2, x_3)) = x_1 POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1 POL(new_primDivNatS1(x_1, x_2)) = 1 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: none ---------------------------------------- (17) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS00(ww200, ww201) -> new_primDivNatS(Succ(ww200), Succ(ww201), Succ(ww201)) new_primDivNatS(Succ(ww2140), Zero, ww216) -> new_primDivNatS1(ww2140, ww216) new_primDivNatS0(ww200, ww201, Zero, Zero) -> new_primDivNatS00(ww200, ww201) new_primDivNatS0(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS0(ww200, ww201, ww2020, ww2030) new_primDivNatS0(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS(Succ(ww200), Succ(ww201), Succ(ww201)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (18) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. ---------------------------------------- (19) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS0(ww200, ww201, ww2020, ww2030) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (20) 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_primDivNatS0(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS0(ww200, ww201, ww2020, ww2030) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (21) YES ---------------------------------------- (22) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww6, ww7, ww8, ww9, ty_HugsException, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, :%(ww70, ww71), ww8, ww9, app(ty_Ratio, bg), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_Maybe, cc), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bh), ca), cb), h) -> new_showListShowl(ww8, ww9, h) new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_[], ba), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (23) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_HugsException, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException)) ---------------------------------------- (24) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww6, :%(ww70, ww71), ww8, ww9, app(ty_Ratio, bg), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_Maybe, cc), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bh), ca), cb), h) -> new_showListShowl(ww8, ww9, h) new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_[], ba), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (25) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, :%(ww70, ww71), ww8, ww9, app(ty_Ratio, bg), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5))) ---------------------------------------- (26) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww6, ww7, ww8, ww9, app(ty_Maybe, cc), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bh), ca), cb), h) -> new_showListShowl(ww8, ww9, h) new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_[], ba), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (27) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, app(ty_Maybe, cc), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4))) ---------------------------------------- (28) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bh), ca), cb), h) -> new_showListShowl(ww8, ww9, h) new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_[], ba), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (29) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_IOErrorKind, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind)) ---------------------------------------- (30) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt1(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bh), ca), cb), h) -> new_showListShowl(ww8, ww9, h) new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_[], ba), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (31) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, app(app(app(ty_@3, bh), ca), cb), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6))) ---------------------------------------- (32) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_[], ba), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (33) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Integer, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer)) ---------------------------------------- (34) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_[], ba), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (35) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_@0, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0)) ---------------------------------------- (36) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_[], ba), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (37) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Float, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float)) ---------------------------------------- (38) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_[], ba), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (39) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, app(app(ty_@2, bc), bd), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5))) ---------------------------------------- (40) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_[], ba), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (41) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Bool, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool)) ---------------------------------------- (42) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_[], ba), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (43) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, app(ty_[], ba), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4))) ---------------------------------------- (44) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (45) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Char, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char)) ---------------------------------------- (46) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (47) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Ordering, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering)) ---------------------------------------- (48) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (49) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Double, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double)) ---------------------------------------- (50) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (51) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, app(app(ty_Either, be), bf), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5)),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5))) ---------------------------------------- (52) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (53) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, app(ty_IO, bb), h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4))) ---------------------------------------- (54) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (55) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_Int, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, ty_Int),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, ty_Int)) ---------------------------------------- (56) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, ty_Int) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (57) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_pt1(ww6, ww7, ww8, ww9, ty_IOError, h) -> new_showListShowl(ww8, ww9, h) we obtained the following new rules [LPAR04]: (new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError),new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError)) ---------------------------------------- (58) Obligation: Q DP problem: The TRS P consists of the following rules: new_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, ty_Int) new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (59) 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_showListShowl(:(ww80, ww81), ww9, h) -> new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), ww80, ww81, ww9, h, h) The graph contains the following edges 1 > 2, 1 > 3, 2 >= 4, 3 >= 5, 3 >= 6 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_HugsException, ty_HugsException) -> new_showListShowl(z1, z2, ty_HugsException) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), :%(x1, x2), z1, z2, app(ty_Ratio, x5), app(ty_Ratio, x5)) -> new_showListShowl(z1, z2, app(ty_Ratio, x5)) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_Maybe, x4), app(ty_Maybe, x4)) -> new_showListShowl(z1, z2, app(ty_Maybe, x4)) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOErrorKind, ty_IOErrorKind) -> new_showListShowl(z1, z2, ty_IOErrorKind) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(app(ty_@3, x4), x5), x6), app(app(app(ty_@3, x4), x5), x6)) -> new_showListShowl(z1, z2, app(app(app(ty_@3, x4), x5), x6)) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Integer, ty_Integer) -> new_showListShowl(z1, z2, ty_Integer) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_@0, ty_@0) -> new_showListShowl(z1, z2, ty_@0) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Float, ty_Float) -> new_showListShowl(z1, z2, ty_Float) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_@2, x4), x5), app(app(ty_@2, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_@2, x4), x5)) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Bool, ty_Bool) -> new_showListShowl(z1, z2, ty_Bool) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_[], x4), app(ty_[], x4)) -> new_showListShowl(z1, z2, app(ty_[], x4)) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Char, ty_Char) -> new_showListShowl(z1, z2, ty_Char) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Ordering, ty_Ordering) -> new_showListShowl(z1, z2, ty_Ordering) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Double, ty_Double) -> new_showListShowl(z1, z2, ty_Double) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(app(ty_Either, x4), x5), app(app(ty_Either, x4), x5)) -> new_showListShowl(z1, z2, app(app(ty_Either, x4), x5)) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, app(ty_IO, x4), app(ty_IO, x4)) -> new_showListShowl(z1, z2, app(ty_IO, x4)) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_Int, ty_Int) -> new_showListShowl(z1, z2, ty_Int) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 *new_pt1(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))), z0, z1, z2, ty_IOError, ty_IOError) -> new_showListShowl(z1, z2, ty_IOError) The graph contains the following edges 3 >= 1, 4 >= 2, 5 >= 3, 6 >= 3 ---------------------------------------- (60) YES ---------------------------------------- (61) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(:(ww1260, ww1261), ww106) -> new_psPs(ww1261, ww106) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (62) 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_psPs(:(ww1260, ww1261), ww106) -> new_psPs(ww1261, ww106) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (63) YES ---------------------------------------- (64) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, :%(ww1420, ww1421), ww148, ty_Ordering, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (65) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (66) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (67) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) at position [5] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bh)), bh, bh),new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bh)), bh, bh)) ---------------------------------------- (68) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bh)), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (69) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bh)), bh, bh) at position [5] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), new_psPs0(:(Char(Succ(ww140)), :(Char(Succ(ww141)), [])), new_showsPrec(ww142, ww148, bh))), bh, bh),new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), new_psPs0(:(Char(Succ(ww140)), :(Char(Succ(ww141)), [])), new_showsPrec(ww142, ww148, bh))), bh, bh)) ---------------------------------------- (70) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), new_psPs0(:(Char(Succ(ww140)), :(Char(Succ(ww141)), [])), new_showsPrec(ww142, ww148, bh))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (71) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), new_psPs0(:(Char(Succ(ww140)), :(Char(Succ(ww141)), [])), new_showsPrec(ww142, ww148, bh))), bh, bh) at position [5,1] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), new_psPs0(:(Char(Succ(ww141)), []), new_showsPrec(ww142, ww148, bh)))), bh, bh),new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), new_psPs0(:(Char(Succ(ww141)), []), new_showsPrec(ww142, ww148, bh)))), bh, bh)) ---------------------------------------- (72) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), new_psPs0(:(Char(Succ(ww141)), []), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (73) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), new_psPs0(:(Char(Succ(ww141)), []), new_showsPrec(ww142, ww148, bh)))), bh, bh) at position [5,1,1] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_psPs0([], new_showsPrec(ww142, ww148, bh))))), bh, bh),new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_psPs0([], new_showsPrec(ww142, ww148, bh))))), bh, bh)) ---------------------------------------- (74) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_psPs0([], new_showsPrec(ww142, ww148, bh))))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (75) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_psPs0([], new_showsPrec(ww142, ww148, bh))))), bh, bh) at position [5,1,1,1] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh),new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh)) ---------------------------------------- (76) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (77) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError)) ---------------------------------------- (78) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOError) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (79) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (80) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (81) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6))) ---------------------------------------- (82) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6)) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6)) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (83) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (84) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (85) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int)) ---------------------------------------- (86) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (87) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (88) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (89) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6))) ---------------------------------------- (90) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6)) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6)) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (91) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (92) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (93) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool)) ---------------------------------------- (94) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (95) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (96) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (97) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double)) ---------------------------------------- (98) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (99) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (100) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (101) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char)) ---------------------------------------- (102) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (103) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (104) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (105) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7))) ---------------------------------------- (106) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7)) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7)) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (107) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (108) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (109) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6))) ---------------------------------------- (110) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6)) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6)) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (111) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (112) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (113) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float)) ---------------------------------------- (114) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (115) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (116) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (117) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException)) ---------------------------------------- (118) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (119) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (120) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (121) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7))) ---------------------------------------- (122) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7)) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7)) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (123) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (124) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (125) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)),new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7))) (new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)),new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7))) ---------------------------------------- (126) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (127) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer)) ---------------------------------------- (128) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (129) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (130) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (131) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0)) ---------------------------------------- (132) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (133) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (134) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (135) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind)) ---------------------------------------- (136) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (137) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (138) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (139) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_pt(ww139, ww140, ww141, ww142, ww148, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8))) ---------------------------------------- (140) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8)) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8)) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (141) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (142) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (143) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, :(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), new_showsPrec(ww142, ww148, bh)))), bh, bh) we obtained the following new rules [LPAR04]: (new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x7)))), x7, x7),new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x7)))), x7, x7)) (new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z4, z5, x7)))), x7, x7),new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z4, z5, x7)))), x7, x7)) ---------------------------------------- (144) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) new_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x7)))), x7, x7) new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z4, z5, x7)))), x7, x7) The TRS R consists of the following rules: new_primModNatS2(Zero, Succ(ww2110), ww212) -> new_primModNatS4(ww212) new_show6(ww7, df) -> error([]) new_show3(ww7, cg, da, db) -> error([]) new_show7(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_HugsException, bb) -> new_psPs0(new_show9(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, app(app(ty_Either, ec), ed)) -> new_psPs0(new_show1(ww142, ec, ed), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_[], ba), bb) -> new_psPs0(new_show6(ww138, ba), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show10(ww7) -> error([]) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primShowInt0(Neg(ww70)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww70))) new_showsPrec(ww142, ww148, ty_Float) -> new_psPs0(new_show10(ww142), ww148) new_show(ww7) -> error([]) new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Int, bb) -> new_psPs0(new_show2(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show14(ww7) -> error([]) new_primModNatS3(Succ(ww1560), Zero) -> new_primModNatS2(Succ(ww1560), Zero, Zero) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Bool, bb) -> new_psPs0(new_show14(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_show2(ww7) -> new_primShowInt0(ww7) new_show12(ww7, dd, de) -> error([]) new_primModNatS2(Zero, Zero, ww212) -> new_primModNatS4(ww212) new_primModNatS2(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS2(ww2100, ww2110, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Float, bb) -> new_psPs0(new_show10(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primModNatS4(ww212) -> Zero new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Ordering, bb) -> new_psPs0(new_show5(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_psPs0(:(ww1260, ww1261), ww106) -> :(ww1260, new_psPs0(ww1261, ww106)) new_primModNatS3(Zero, Succ(ww1570)) -> Succ(Zero) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_show0(ww7) -> error([]) new_showsPrec(ww142, ww148, app(app(app(ty_@3, ee), ef), eg)) -> new_psPs0(new_show3(ww142, ee, ef, eg), ww148) new_primIntToChar(ww156, ww157) -> Char(new_primModNatS3(ww156, ww157)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_@0, bb) -> new_psPs0(new_show0(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS01(ww205, ww206, ww2070, ww2080) new_showsPrec(ww142, ww148, app(app(ty_@2, ea), eb)) -> new_psPs0(new_show12(ww142, ea, eb), ww148) new_show9(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_IOError) -> new_psPs0(new_show(ww142), ww148) new_showsPrec(ww142, ww148, ty_Bool) -> new_psPs0(new_show14(ww142), ww148) new_show4(ww7, dc) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_Either, bf), bg), bb) -> new_psPs0(new_show1(ww138, bf, bg), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_Maybe, cd), bb) -> new_psPs0(new_show4(ww138, cd), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(:%(ww1380, ww1381), ww139, ww140, ww141, ww142, ww148, app(ty_Ratio, bh), bb) -> new_showParen0(ww1380, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1381, new_pt0(ww139, ww140, ww141, ww142, ww148, bh), bh, bh) new_show13(ww7) -> error([]) new_showsPrec(ww142, ww148, ty_Char) -> new_psPs0(new_show15(ww142), ww148) new_showsPrec(ww142, ww148, ty_Integer) -> new_psPs0(new_show7(ww142), ww148) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_psPs0([], ww106) -> ww106 new_primModNatS01(ww205, ww206, Zero, Succ(ww2080)) -> Succ(Succ(ww205)) new_showsPrec(ww142, ww148, ty_Double) -> new_psPs0(new_show13(ww142), ww148) new_show8(ww7, fa) -> error([]) new_showsPrec(ww142, ww148, app(ty_Maybe, eh)) -> new_psPs0(new_show4(ww142, eh), ww148) new_showsPrec(ww142, ww148, ty_@0) -> new_psPs0(new_show0(ww142), ww148) new_showsPrec(ww142, ww148, ty_Ordering) -> new_psPs0(new_show5(ww142), ww148) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(ty_IO, bc), bb) -> new_psPs0(new_show8(ww138, bc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_showsPrec(ww142, ww148, ty_IOErrorKind) -> new_psPs0(new_show11(ww142), ww148) new_show5(ww7) -> error([]) new_pt0(ww139, ww140, ww141, ww142, ww148, bb) -> new_psPs0(:(Char(Succ(ww139)), :(Char(Succ(ww140)), :(Char(Succ(ww141)), []))), new_showsPrec(ww142, ww148, bb)) new_primModNatS2(Succ(ww2100), Zero, ww212) -> new_primModNatS3(ww2100, ww212) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(app(ty_@3, ca), cb), cc), bb) -> new_psPs0(new_show3(ww138, ca, cb, cc), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_showsPrec(ww142, ww148, app(ty_IO, dh)) -> new_psPs0(new_show8(ww142, dh), ww148) new_primModNatS02(ww205, ww206) -> new_primModNatS2(Succ(ww205), Succ(ww206), Succ(ww206)) new_show1(ww7, ce, cf) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOError, bb) -> new_psPs0(new_show(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Char, bb) -> new_psPs0(new_show15(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primShowInt0(Pos(Succ(ww700))) -> new_psPs0(new_primShowInt0(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) new_primShowInt0(Pos(Zero)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))))))))))))))))))), []) new_primModNatS01(ww205, ww206, Zero, Zero) -> new_primModNatS02(ww205, ww206) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_IOErrorKind, bb) -> new_psPs0(new_show11(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS01(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS02(ww205, ww206) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_showsPrec(ww142, ww148, app(ty_[], dg)) -> new_psPs0(new_show6(ww142, dg), ww148) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Integer, bb) -> new_psPs0(new_show7(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_showsPrec(ww142, ww148, ty_HugsException) -> new_psPs0(new_show9(ww142), ww148) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, app(app(ty_@2, bd), be), bb) -> new_psPs0(new_show12(ww138, bd, be), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(:%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen0(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) new_show11(ww7) -> error([]) new_showParen0(ww138, ww139, ww140, ww141, ww142, ww148, ty_Double, bb) -> new_psPs0(new_show13(ww138), new_pt0(ww139, ww140, ww141, ww142, ww148, bb)) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_showsPrec(ww142, ww148, ty_Int) -> new_psPs0(new_show2(ww142), ww148) new_show15(ww7) -> error([]) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primModNatS3(Succ(ww1560), Succ(ww1570)) -> new_primModNatS01(ww1560, ww1570, ww1560, ww1570) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_showsPrec(x0, x1, ty_Ordering) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(ty_IO, x2)) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_IOError) new_show15(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_show10(x0) new_primModNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS3(Zero, Succ(x0), x1) new_primModNatS2(Zero, Succ(x0), x1) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_showsPrec(x0, x1, ty_Int) new_primDivNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS3(Zero, Zero) new_show13(x0) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_show9(x0) new_primModNatS02(x0, x1) new_primIntToChar(x0, x1) new_show(x0) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS2(Succ(x0), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS3(Succ(x0), Succ(x1)) new_show4(x0, x1) new_showsPrec(x0, x1, ty_@0) new_primShowInt0(Pos(Zero)) new_primModNatS2(Succ(x0), Succ(x1), x2) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Char) new_show11(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Zero) new_show6(x0, x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_show12(x0, x1, x2) new_primDivNatS3(Zero, Zero, x0) new_show1(x0, x1, x2) new_primModNatS2(Zero, Zero, x0) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showsPrec(x0, x1, app(ty_[], x2)) new_show3(x0, x1, x2, x3) new_psPs0(:(x0, x1), x2) new_showsPrec(x0, x1, ty_Float) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_psPs0([], x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS3(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Bool) new_show8(x0, x1) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show7(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_show2(x0) new_showsPrec(x0, x1, ty_Double) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primModNatS01(x0, x1, Zero, Zero) new_show14(x0) new_show0(x0) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_show5(x0) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_showsPrec(x0, x1, ty_Integer) new_primModNatS3(Succ(x0), Zero) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_pt0(x0, x1, x2, x3, x4, x5) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (145) 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_pt(ww139, ww140, ww141, :%(ww1420, ww1421), ww148, app(ty_Ratio, h)) -> new_showParen(ww1420, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1421, ww148, h, h) The graph contains the following edges 4 > 1, 4 > 5, 5 >= 6, 6 > 7, 6 > 8 *new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x7)))), x7, x7) The graph contains the following edges 1 > 1, 2 >= 2, 3 > 2, 4 >= 2, 3 >= 3, 2 >= 4, 3 > 4, 4 >= 4, 1 > 5, 7 > 7, 8 > 7, 7 > 8, 8 > 8 *new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_showParen(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x1, :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))), :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))))), new_showsPrec(z4, z5, x7)))), x7, x7) The graph contains the following edges 1 > 1, 2 >= 2, 3 > 2, 4 >= 2, 3 >= 3, 2 >= 4, 3 > 4, 4 >= 4, 1 > 5, 7 > 7, 8 > 7, 7 > 8, 8 > 8 *new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Ratio, x7)) The graph contains the following edges 2 >= 1, 3 > 1, 4 >= 1, 3 >= 2, 2 >= 3, 3 > 3, 4 >= 3, 5 >= 4, 6 >= 5, 7 >= 6, 8 >= 6 *new_showParen(:%(x0, x1), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7), app(ty_Ratio, x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x7)) The graph contains the following edges 2 >= 1, 3 > 1, 4 >= 1, 3 >= 2, 2 >= 3, 3 > 3, 4 >= 3, 5 >= 4, 6 >= 5, 7 >= 6, 8 >= 6 ---------------------------------------- (146) YES ---------------------------------------- (147) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(ww2100), Zero, ww212) -> new_primModNatS1(ww2100, ww212) new_primModNatS1(Zero, Zero) -> new_primModNatS(Zero, Zero, Zero) new_primModNatS00(ww205, ww206) -> new_primModNatS(Succ(ww205), Succ(ww206), Succ(ww206)) new_primModNatS0(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS(Succ(ww205), Succ(ww206), Succ(ww206)) new_primModNatS(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS(ww2100, ww2110, ww212) new_primModNatS0(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS0(ww205, ww206, ww2070, ww2080) new_primModNatS1(Succ(ww1560), Succ(ww1570)) -> new_primModNatS0(ww1560, ww1570, ww1560, ww1570) new_primModNatS0(ww205, ww206, Zero, Zero) -> new_primModNatS00(ww205, ww206) new_primModNatS1(Succ(ww1560), Zero) -> new_primModNatS(Succ(ww1560), Zero, Zero) R is empty. Q is empty. 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_primModNatS1(Succ(ww1560), Succ(ww1570)) -> new_primModNatS0(ww1560, ww1570, ww1560, ww1570) new_primModNatS0(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS(Succ(ww205), Succ(ww206), Succ(ww206)) new_primModNatS(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS(ww2100, ww2110, ww212) new_primModNatS(Succ(ww2100), Zero, ww212) -> new_primModNatS1(ww2100, ww212) new_primModNatS1(Succ(ww1560), Zero) -> new_primModNatS(Succ(ww1560), Zero, Zero) new_primModNatS0(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS0(ww205, ww206, ww2070, ww2080) new_primModNatS0(ww205, ww206, Zero, Zero) -> new_primModNatS00(ww205, ww206) new_primModNatS00(ww205, ww206) -> new_primModNatS(Succ(ww205), Succ(ww206), Succ(ww206)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (150) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_primModNatS1(Succ(ww1560), Succ(ww1570)) -> new_primModNatS0(ww1560, ww1570, ww1560, ww1570) new_primModNatS(Succ(ww2100), Succ(ww2110), ww212) -> new_primModNatS(ww2100, ww2110, ww212) new_primModNatS1(Succ(ww1560), Zero) -> new_primModNatS(Succ(ww1560), Zero, Zero) The remaining pairs can at least be oriented weakly. Used ordering: Polynomial interpretation [POLO]: POL(Succ(x_1)) = 1 + x_1 POL(Zero) = 0 POL(new_primModNatS(x_1, x_2, x_3)) = x_1 POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 POL(new_primModNatS00(x_1, x_2)) = 1 + x_1 POL(new_primModNatS1(x_1, x_2)) = 1 + x_1 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: none ---------------------------------------- (151) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS0(ww205, ww206, Succ(ww2070), Zero) -> new_primModNatS(Succ(ww205), Succ(ww206), Succ(ww206)) new_primModNatS(Succ(ww2100), Zero, ww212) -> new_primModNatS1(ww2100, ww212) new_primModNatS0(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS0(ww205, ww206, ww2070, ww2080) new_primModNatS0(ww205, ww206, Zero, Zero) -> new_primModNatS00(ww205, ww206) new_primModNatS00(ww205, ww206) -> new_primModNatS(Succ(ww205), Succ(ww206), Succ(ww206)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (152) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. ---------------------------------------- (153) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS0(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS0(ww205, ww206, ww2070, ww2080) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (154) 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_primModNatS0(ww205, ww206, Succ(ww2070), Succ(ww2080)) -> new_primModNatS0(ww205, ww206, ww2070, ww2080) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (155) YES ---------------------------------------- (156) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Neg(ww70)) -> new_primShowInt(Pos(ww70)) new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) The TRS R consists of the following rules: new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (157) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (158) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) The TRS R consists of the following rules: new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (159) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(new_div(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS2(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))),new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS2(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ---------------------------------------- (160) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS2(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_div(ww153, ww154) -> Pos(new_primDivNatS2(ww153, ww154)) new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (161) 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. ---------------------------------------- (162) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS2(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_div(x0, x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (163) 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_div(x0, x1) ---------------------------------------- (164) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS2(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (165) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (166) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS2(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (167) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS2(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) the following chains were created: *We consider the chain new_primShowInt(Pos(Succ(x0))) -> new_primShowInt(Pos(new_primDivNatS2(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), new_primShowInt(Pos(Succ(x1))) -> new_primShowInt(Pos(new_primDivNatS2(x1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) which results in the following constraint: (1) (new_primShowInt(Pos(new_primDivNatS2(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))=new_primShowInt(Pos(Succ(x1))) ==> new_primShowInt(Pos(Succ(x0)))_>=_new_primShowInt(Pos(new_primDivNatS2(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint: (2) (Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=x2 & new_primDivNatS2(x0, x2)=Succ(x1) ==> new_primShowInt(Pos(Succ(x0)))_>=_new_primShowInt(Pos(new_primDivNatS2(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS2(x0, x2)=Succ(x1) which results in the following new constraints: (3) (new_primDivNatS01(x4, x3, x4, x3)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Succ(x3) ==> new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS2(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) (4) (Succ(new_primDivNatS3(Succ(x6), Zero, Zero))=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Zero ==> new_primShowInt(Pos(Succ(Succ(x6))))_>=_new_primShowInt(Pos(new_primDivNatS2(Succ(x6), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) (5) (Succ(new_primDivNatS3(Zero, Zero, Zero))=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Zero ==> new_primShowInt(Pos(Succ(Zero)))_>=_new_primShowInt(Pos(new_primDivNatS2(Zero, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint: (6) (x4=x7 & x3=x8 & new_primDivNatS01(x4, x3, x7, x8)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 ==> new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS2(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x4, x3, x7, x8)=Succ(x1) which results in the following new constraints: (7) (new_primDivNatS02(x10, x9)=Succ(x1) & x10=Zero & x9=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x9 ==> new_primShowInt(Pos(Succ(Succ(x10))))_>=_new_primShowInt(Pos(new_primDivNatS2(Succ(x10), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) (8) (new_primDivNatS02(x16, x15)=Succ(x1) & x16=Succ(x14) & x15=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 ==> new_primShowInt(Pos(Succ(Succ(x16))))_>=_new_primShowInt(Pos(new_primDivNatS2(Succ(x16), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) (9) (new_primDivNatS01(x20, x19, x18, x17)=Succ(x1) & x20=Succ(x18) & x19=Succ(x17) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x19 & (\/x21:new_primDivNatS01(x20, x19, x18, x17)=Succ(x21) & x20=x18 & x19=x17 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x19 ==> new_primShowInt(Pos(Succ(Succ(x20))))_>=_new_primShowInt(Pos(new_primDivNatS2(Succ(x20), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ==> new_primShowInt(Pos(Succ(Succ(x20))))_>=_new_primShowInt(Pos(new_primDivNatS2(Succ(x20), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) We solved constraint (7) using rules (I), (II), (III).We solved constraint (8) using rules (I), (II), (III).We simplified constraint (9) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint: (10) (new_primShowInt(Pos(Succ(Succ(Succ(x18)))))_>=_new_primShowInt(Pos(new_primDivNatS2(Succ(Succ(x18)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) To summarize, we get the following constraints P__>=_ for the following pairs. *new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS2(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) *(new_primShowInt(Pos(Succ(Succ(Succ(x18)))))_>=_new_primShowInt(Pos(new_primDivNatS2(Succ(Succ(x18)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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. ---------------------------------------- (168) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS2(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (169) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(ww700))) -> new_primShowInt(Pos(new_primDivNatS2(ww700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))),new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) (new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero))) ---------------------------------------- (170) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (171) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (172) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (173) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero))) (new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))),new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) ---------------------------------------- (174) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)) new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (175) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (176) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (177) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) at position [0,0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero))) (new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))),new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) ---------------------------------------- (178) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)) new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (179) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (180) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (181) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) at position [0,0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero))) (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))) ---------------------------------------- (182) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)) new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (183) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (184) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (185) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (186) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (187) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) the following chains were created: *We consider the chain new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero)))))))), new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x1))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x1))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x1, Succ(Succ(Succ(Succ(Succ(Zero)))))))) which results in the following constraint: (1) (new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))=new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x1))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))) We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint: (2) (Succ(Succ(Succ(x0)))=x2 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x4 & new_primDivNatS01(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))) We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints: (3) (new_primDivNatS02(x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Zero)))=x6 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x5 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Zero, Succ(Succ(Succ(Succ(Succ(Zero))))))))) (4) (new_primDivNatS02(x12, x11)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x10))))=x12 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x11 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x10))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x10)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x10), Succ(Succ(Succ(Succ(Succ(Zero))))))))) (5) (new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x14))))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Succ(x13) & (\/x17:new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x17))))) & Succ(Succ(Succ(x14)))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x13 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x14)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x14))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x14, Succ(Succ(Succ(Succ(Succ(Zero))))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x14))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x14)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x14), Succ(Succ(Succ(Succ(Succ(Zero))))))))) We solved constraint (3) using rules (I), (II).We solved constraint (4) using rules (I), (II).We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint: (6) (new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x14))))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Zero))))=x13 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x14))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x14)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x14), Succ(Succ(Succ(Succ(Succ(Zero))))))))) We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints: (7) (new_primDivNatS02(x19, x18)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Zero))))=x19 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x18 & Succ(Succ(Succ(Succ(Zero))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))))))) (8) (new_primDivNatS02(x25, x24)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x23)))))=x25 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x24 & Succ(Succ(Succ(Succ(Zero))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x23)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x23))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x23)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) (9) (new_primDivNatS01(x29, x28, x27, x26)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x27)))))=x29 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x28 & Succ(Succ(Succ(Succ(Zero))))=Succ(x26) & (\/x30:new_primDivNatS01(x29, x28, x27, x26)=Succ(Succ(Succ(Succ(Succ(x30))))) & Succ(Succ(Succ(Succ(x27))))=x29 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x28 & Succ(Succ(Succ(Succ(Zero))))=x26 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x27)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x27), Succ(Succ(Succ(Succ(Succ(Zero))))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) We solved constraint (7) using rules (I), (II).We solved constraint (8) using rules (I), (II).We simplified constraint (9) using rules (I), (II), (III), (IV) which results in the following new constraint: (10) (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) To summarize, we get the following constraints P__>=_ for the following pairs. *new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) *(new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(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. ---------------------------------------- (188) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1530), Succ(ww1540)) -> new_primDivNatS01(ww1530, ww1540, ww1530, ww1540) new_primDivNatS2(Zero, Succ(ww1540)) -> Zero new_primDivNatS01(ww200, ww201, Zero, Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Zero, Succ(ww2030)) -> Zero new_primDivNatS01(ww200, ww201, Succ(ww2020), Zero) -> new_primDivNatS02(ww200, ww201) new_primDivNatS01(ww200, ww201, Succ(ww2020), Succ(ww2030)) -> new_primDivNatS01(ww200, ww201, ww2020, ww2030) new_primDivNatS02(ww200, ww201) -> Succ(new_primDivNatS3(Succ(ww200), Succ(ww201), Succ(ww201))) new_primDivNatS3(Succ(ww2140), Succ(ww2150), ww216) -> new_primDivNatS3(ww2140, ww2150, ww216) new_primDivNatS3(Zero, Zero, ww216) -> new_primDivNatS4(ww216) new_primDivNatS3(Succ(ww2140), Zero, ww216) -> new_primDivNatS2(ww2140, ww216) new_primDivNatS3(Zero, Succ(ww2150), ww216) -> new_primDivNatS4(ww216) new_primDivNatS4(ww216) -> Zero new_primDivNatS2(Succ(ww1530), Zero) -> Succ(new_primDivNatS3(Succ(ww1530), Zero, Zero)) new_primDivNatS2(Zero, Zero) -> Succ(new_primDivNatS3(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1)) new_primDivNatS3(Succ(x0), Zero, x1) new_primDivNatS2(Zero, Succ(x0)) new_primDivNatS2(Succ(x0), Zero) new_primDivNatS2(Zero, Zero) new_primDivNatS3(Zero, Succ(x0), x1) new_primDivNatS3(Succ(x0), Succ(x1), x2) new_primDivNatS3(Zero, Zero, x0) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS4(x0) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (189) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="showList",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="showList ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="showList ww3 ww4",fontsize=16,color="burlywood",shape="triangle"];1769[label="ww3/ww30 : ww31",fontsize=10,color="white",style="solid",shape="box"];4 -> 1769[label="",style="solid", color="burlywood", weight=9]; 1769 -> 5[label="",style="solid", color="burlywood", weight=3]; 1770[label="ww3/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 1770[label="",style="solid", color="burlywood", weight=9]; 1770 -> 6[label="",style="solid", color="burlywood", weight=3]; 5[label="showList (ww30 : ww31) ww4",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3]; 6[label="showList [] ww4",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3]; 7 -> 9[label="",style="dashed", color="red", weight=0]; 7[label="(showChar (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) . (shows ww30) . showListShowl ww31",fontsize=16,color="magenta"];7 -> 10[label="",style="dashed", color="magenta", weight=3]; 7 -> 11[label="",style="dashed", color="magenta", weight=3]; 7 -> 12[label="",style="dashed", color="magenta", weight=3]; 7 -> 13[label="",style="dashed", color="magenta", weight=3]; 8 -> 18[label="",style="dashed", color="red", weight=0]; 8[label="showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) : []) ww4",fontsize=16,color="magenta"];8 -> 19[label="",style="dashed", color="magenta", weight=3]; 8 -> 20[label="",style="dashed", color="magenta", weight=3]; 8 -> 21[label="",style="dashed", color="magenta", weight=3]; 10[label="ww31",fontsize=16,color="green",shape="box"];11[label="ww4",fontsize=16,color="green",shape="box"];12[label="ww30",fontsize=16,color="green",shape="box"];13[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];9[label="(showChar (Char (Succ ww6))) . (shows ww7) . showListShowl ww8",fontsize=16,color="black",shape="triangle"];9 -> 17[label="",style="solid", color="black", weight=3]; 19[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];20[label="ww4",fontsize=16,color="green",shape="box"];21[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];18[label="showString (Char (Succ ww14) : Char (Succ ww15) : []) ww16",fontsize=16,color="black",shape="triangle"];18 -> 25[label="",style="solid", color="black", weight=3]; 17 -> 180[label="",style="dashed", color="red", weight=0]; 17[label="showChar (Char (Succ ww6)) ((shows ww7) . showListShowl ww8)",fontsize=16,color="magenta"];17 -> 181[label="",style="dashed", color="magenta", weight=3]; 17 -> 182[label="",style="dashed", color="magenta", weight=3]; 25 -> 461[label="",style="dashed", color="red", weight=0]; 25[label="(++) (Char (Succ ww14) : Char (Succ ww15) : []) ww16",fontsize=16,color="magenta"];25 -> 462[label="",style="dashed", color="magenta", weight=3]; 25 -> 463[label="",style="dashed", color="magenta", weight=3]; 181[label="(shows ww7) . showListShowl ww8",fontsize=16,color="black",shape="box"];181 -> 185[label="",style="solid", color="black", weight=3]; 182[label="ww6",fontsize=16,color="green",shape="box"];180[label="showChar (Char (Succ ww57)) ww58",fontsize=16,color="black",shape="triangle"];180 -> 186[label="",style="solid", color="black", weight=3]; 462[label="ww16",fontsize=16,color="green",shape="box"];463[label="Char (Succ ww14) : Char (Succ ww15) : []",fontsize=16,color="green",shape="box"];461[label="ww126 ++ ww106",fontsize=16,color="burlywood",shape="triangle"];1771[label="ww126/ww1260 : ww1261",fontsize=10,color="white",style="solid",shape="box"];461 -> 1771[label="",style="solid", color="burlywood", weight=9]; 1771 -> 601[label="",style="solid", color="burlywood", weight=3]; 1772[label="ww126/[]",fontsize=10,color="white",style="solid",shape="box"];461 -> 1772[label="",style="solid", color="burlywood", weight=9]; 1772 -> 602[label="",style="solid", color="burlywood", weight=3]; 185[label="shows ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];185 -> 187[label="",style="solid", color="black", weight=3]; 186[label="(:) Char (Succ ww57) ww58",fontsize=16,color="green",shape="box"];601[label="(ww1260 : ww1261) ++ ww106",fontsize=16,color="black",shape="box"];601 -> 657[label="",style="solid", color="black", weight=3]; 602[label="[] ++ ww106",fontsize=16,color="black",shape="box"];602 -> 658[label="",style="solid", color="black", weight=3]; 187[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="blue",shape="box"];1773[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1773[label="",style="solid", color="blue", weight=9]; 1773 -> 188[label="",style="solid", color="blue", weight=3]; 1774[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1774[label="",style="solid", color="blue", weight=9]; 1774 -> 189[label="",style="solid", color="blue", weight=3]; 1775[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1775[label="",style="solid", color="blue", weight=9]; 1775 -> 190[label="",style="solid", color="blue", weight=3]; 1776[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1776[label="",style="solid", color="blue", weight=9]; 1776 -> 191[label="",style="solid", color="blue", weight=3]; 1777[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1777[label="",style="solid", color="blue", weight=9]; 1777 -> 192[label="",style="solid", color="blue", weight=3]; 1778[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1778[label="",style="solid", color="blue", weight=9]; 1778 -> 193[label="",style="solid", color="blue", weight=3]; 1779[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1779[label="",style="solid", color="blue", weight=9]; 1779 -> 194[label="",style="solid", color="blue", weight=3]; 1780[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1780[label="",style="solid", color="blue", weight=9]; 1780 -> 195[label="",style="solid", color="blue", weight=3]; 1781[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1781[label="",style="solid", color="blue", weight=9]; 1781 -> 196[label="",style="solid", color="blue", weight=3]; 1782[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1782[label="",style="solid", color="blue", weight=9]; 1782 -> 197[label="",style="solid", color="blue", weight=3]; 1783[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1783[label="",style="solid", color="blue", weight=9]; 1783 -> 198[label="",style="solid", color="blue", weight=3]; 1784[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1784[label="",style="solid", color="blue", weight=9]; 1784 -> 199[label="",style="solid", color="blue", weight=3]; 1785[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1785[label="",style="solid", color="blue", weight=9]; 1785 -> 200[label="",style="solid", color="blue", weight=3]; 1786[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1786[label="",style="solid", color="blue", weight=9]; 1786 -> 201[label="",style="solid", color="blue", weight=3]; 1787[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1787[label="",style="solid", color="blue", weight=9]; 1787 -> 202[label="",style="solid", color="blue", weight=3]; 1788[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1788[label="",style="solid", color="blue", weight=9]; 1788 -> 203[label="",style="solid", color="blue", weight=3]; 1789[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1789[label="",style="solid", color="blue", weight=9]; 1789 -> 204[label="",style="solid", color="blue", weight=3]; 1790[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];187 -> 1790[label="",style="solid", color="blue", weight=9]; 1790 -> 205[label="",style="solid", color="blue", weight=3]; 657[label="ww1260 : ww1261 ++ ww106",fontsize=16,color="green",shape="box"];657 -> 683[label="",style="dashed", color="green", weight=3]; 658[label="ww106",fontsize=16,color="green",shape="box"];188[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];188 -> 206[label="",style="solid", color="black", weight=3]; 189[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];189 -> 207[label="",style="solid", color="black", weight=3]; 190[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];190 -> 208[label="",style="solid", color="black", weight=3]; 191[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];191 -> 209[label="",style="solid", color="black", weight=3]; 192[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];192 -> 210[label="",style="solid", color="black", weight=3]; 193[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];193 -> 211[label="",style="solid", color="black", weight=3]; 194[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];194 -> 212[label="",style="solid", color="black", weight=3]; 195[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];195 -> 213[label="",style="solid", color="black", weight=3]; 196[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];196 -> 214[label="",style="solid", color="black", weight=3]; 197[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];197 -> 215[label="",style="solid", color="black", weight=3]; 198[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="burlywood",shape="box"];1791[label="ww7/ww70 :% ww71",fontsize=10,color="white",style="solid",shape="box"];198 -> 1791[label="",style="solid", color="burlywood", weight=9]; 1791 -> 216[label="",style="solid", color="burlywood", weight=3]; 199[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];199 -> 217[label="",style="solid", color="black", weight=3]; 200[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];200 -> 218[label="",style="solid", color="black", weight=3]; 201[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];201 -> 219[label="",style="solid", color="black", weight=3]; 202[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];202 -> 220[label="",style="solid", color="black", weight=3]; 203[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];203 -> 221[label="",style="solid", color="black", weight=3]; 204[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];204 -> 222[label="",style="solid", color="black", weight=3]; 205[label="showsPrec (Pos Zero) ww7 (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];205 -> 223[label="",style="solid", color="black", weight=3]; 683 -> 461[label="",style="dashed", color="red", weight=0]; 683[label="ww1261 ++ ww106",fontsize=16,color="magenta"];683 -> 707[label="",style="dashed", color="magenta", weight=3]; 206 -> 461[label="",style="dashed", color="red", weight=0]; 206[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];206 -> 468[label="",style="dashed", color="magenta", weight=3]; 206 -> 469[label="",style="dashed", color="magenta", weight=3]; 207 -> 461[label="",style="dashed", color="red", weight=0]; 207[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];207 -> 470[label="",style="dashed", color="magenta", weight=3]; 207 -> 471[label="",style="dashed", color="magenta", weight=3]; 208 -> 461[label="",style="dashed", color="red", weight=0]; 208[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];208 -> 472[label="",style="dashed", color="magenta", weight=3]; 208 -> 473[label="",style="dashed", color="magenta", weight=3]; 209 -> 461[label="",style="dashed", color="red", weight=0]; 209[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];209 -> 474[label="",style="dashed", color="magenta", weight=3]; 209 -> 475[label="",style="dashed", color="magenta", weight=3]; 210 -> 461[label="",style="dashed", color="red", weight=0]; 210[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];210 -> 476[label="",style="dashed", color="magenta", weight=3]; 210 -> 477[label="",style="dashed", color="magenta", weight=3]; 211 -> 461[label="",style="dashed", color="red", weight=0]; 211[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];211 -> 478[label="",style="dashed", color="magenta", weight=3]; 211 -> 479[label="",style="dashed", color="magenta", weight=3]; 212 -> 461[label="",style="dashed", color="red", weight=0]; 212[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];212 -> 480[label="",style="dashed", color="magenta", weight=3]; 212 -> 481[label="",style="dashed", color="magenta", weight=3]; 213 -> 461[label="",style="dashed", color="red", weight=0]; 213[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];213 -> 482[label="",style="dashed", color="magenta", weight=3]; 213 -> 483[label="",style="dashed", color="magenta", weight=3]; 214 -> 461[label="",style="dashed", color="red", weight=0]; 214[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];214 -> 484[label="",style="dashed", color="magenta", weight=3]; 214 -> 485[label="",style="dashed", color="magenta", weight=3]; 215 -> 461[label="",style="dashed", color="red", weight=0]; 215[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];215 -> 486[label="",style="dashed", color="magenta", weight=3]; 215 -> 487[label="",style="dashed", color="magenta", weight=3]; 216[label="showsPrec (Pos Zero) (ww70 :% ww71) (showListShowl ww8 ww9)",fontsize=16,color="black",shape="box"];216 -> 234[label="",style="solid", color="black", weight=3]; 217 -> 461[label="",style="dashed", color="red", weight=0]; 217[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];217 -> 488[label="",style="dashed", color="magenta", weight=3]; 217 -> 489[label="",style="dashed", color="magenta", weight=3]; 218 -> 461[label="",style="dashed", color="red", weight=0]; 218[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];218 -> 490[label="",style="dashed", color="magenta", weight=3]; 218 -> 491[label="",style="dashed", color="magenta", weight=3]; 219 -> 461[label="",style="dashed", color="red", weight=0]; 219[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];219 -> 492[label="",style="dashed", color="magenta", weight=3]; 219 -> 493[label="",style="dashed", color="magenta", weight=3]; 220 -> 461[label="",style="dashed", color="red", weight=0]; 220[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];220 -> 494[label="",style="dashed", color="magenta", weight=3]; 220 -> 495[label="",style="dashed", color="magenta", weight=3]; 221 -> 461[label="",style="dashed", color="red", weight=0]; 221[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];221 -> 496[label="",style="dashed", color="magenta", weight=3]; 221 -> 497[label="",style="dashed", color="magenta", weight=3]; 222 -> 461[label="",style="dashed", color="red", weight=0]; 222[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];222 -> 498[label="",style="dashed", color="magenta", weight=3]; 222 -> 499[label="",style="dashed", color="magenta", weight=3]; 223 -> 461[label="",style="dashed", color="red", weight=0]; 223[label="show ww7 ++ showListShowl ww8 ww9",fontsize=16,color="magenta"];223 -> 500[label="",style="dashed", color="magenta", weight=3]; 223 -> 501[label="",style="dashed", color="magenta", weight=3]; 707[label="ww1261",fontsize=16,color="green",shape="box"];468 -> 296[label="",style="dashed", color="red", weight=0]; 468[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];469[label="show ww7",fontsize=16,color="black",shape="triangle"];469 -> 603[label="",style="solid", color="black", weight=3]; 470 -> 296[label="",style="dashed", color="red", weight=0]; 470[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];471[label="show ww7",fontsize=16,color="black",shape="triangle"];471 -> 604[label="",style="solid", color="black", weight=3]; 472 -> 296[label="",style="dashed", color="red", weight=0]; 472[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];473[label="show ww7",fontsize=16,color="black",shape="triangle"];473 -> 605[label="",style="solid", color="black", weight=3]; 474 -> 296[label="",style="dashed", color="red", weight=0]; 474[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];475[label="show ww7",fontsize=16,color="black",shape="triangle"];475 -> 606[label="",style="solid", color="black", weight=3]; 476 -> 296[label="",style="dashed", color="red", weight=0]; 476[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];477[label="show ww7",fontsize=16,color="black",shape="triangle"];477 -> 607[label="",style="solid", color="black", weight=3]; 478 -> 296[label="",style="dashed", color="red", weight=0]; 478[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];479[label="show ww7",fontsize=16,color="black",shape="triangle"];479 -> 608[label="",style="solid", color="black", weight=3]; 480 -> 296[label="",style="dashed", color="red", weight=0]; 480[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];481[label="show ww7",fontsize=16,color="black",shape="triangle"];481 -> 609[label="",style="solid", color="black", weight=3]; 482 -> 296[label="",style="dashed", color="red", weight=0]; 482[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];483[label="show ww7",fontsize=16,color="black",shape="triangle"];483 -> 610[label="",style="solid", color="black", weight=3]; 484 -> 296[label="",style="dashed", color="red", weight=0]; 484[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];485[label="show ww7",fontsize=16,color="black",shape="triangle"];485 -> 611[label="",style="solid", color="black", weight=3]; 486 -> 296[label="",style="dashed", color="red", weight=0]; 486[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];487[label="show ww7",fontsize=16,color="black",shape="triangle"];487 -> 612[label="",style="solid", color="black", weight=3]; 234 -> 687[label="",style="dashed", color="red", weight=0]; 234[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww70) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww71) (showListShowl ww8 ww9)",fontsize=16,color="magenta"];234 -> 688[label="",style="dashed", color="magenta", weight=3]; 234 -> 689[label="",style="dashed", color="magenta", weight=3]; 234 -> 690[label="",style="dashed", color="magenta", weight=3]; 234 -> 691[label="",style="dashed", color="magenta", weight=3]; 234 -> 692[label="",style="dashed", color="magenta", weight=3]; 234 -> 693[label="",style="dashed", color="magenta", weight=3]; 488 -> 296[label="",style="dashed", color="red", weight=0]; 488[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];489[label="show ww7",fontsize=16,color="black",shape="triangle"];489 -> 613[label="",style="solid", color="black", weight=3]; 490 -> 296[label="",style="dashed", color="red", weight=0]; 490[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];491[label="show ww7",fontsize=16,color="black",shape="triangle"];491 -> 614[label="",style="solid", color="black", weight=3]; 492 -> 296[label="",style="dashed", color="red", weight=0]; 492[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];493[label="show ww7",fontsize=16,color="black",shape="triangle"];493 -> 615[label="",style="solid", color="black", weight=3]; 494 -> 296[label="",style="dashed", color="red", weight=0]; 494[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];495[label="show ww7",fontsize=16,color="black",shape="triangle"];495 -> 616[label="",style="solid", color="black", weight=3]; 496 -> 296[label="",style="dashed", color="red", weight=0]; 496[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];497[label="show ww7",fontsize=16,color="black",shape="triangle"];497 -> 617[label="",style="solid", color="black", weight=3]; 498 -> 296[label="",style="dashed", color="red", weight=0]; 498[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];499[label="show ww7",fontsize=16,color="black",shape="triangle"];499 -> 618[label="",style="solid", color="black", weight=3]; 500 -> 296[label="",style="dashed", color="red", weight=0]; 500[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];501[label="show ww7",fontsize=16,color="black",shape="triangle"];501 -> 619[label="",style="solid", color="black", weight=3]; 296[label="showListShowl ww8 ww9",fontsize=16,color="burlywood",shape="triangle"];1792[label="ww8/ww80 : ww81",fontsize=10,color="white",style="solid",shape="box"];296 -> 1792[label="",style="solid", color="burlywood", weight=9]; 1792 -> 312[label="",style="solid", color="burlywood", weight=3]; 1793[label="ww8/[]",fontsize=10,color="white",style="solid",shape="box"];296 -> 1793[label="",style="solid", color="burlywood", weight=9]; 1793 -> 313[label="",style="solid", color="burlywood", weight=3]; 603[label="error []",fontsize=16,color="red",shape="box"];604[label="error []",fontsize=16,color="red",shape="box"];605[label="error []",fontsize=16,color="red",shape="box"];606[label="error []",fontsize=16,color="red",shape="box"];607[label="error []",fontsize=16,color="red",shape="box"];608[label="error []",fontsize=16,color="red",shape="box"];609[label="error []",fontsize=16,color="red",shape="box"];610[label="error []",fontsize=16,color="red",shape="box"];611[label="error []",fontsize=16,color="red",shape="box"];612[label="error []",fontsize=16,color="red",shape="box"];688[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];689[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];690[label="ww71",fontsize=16,color="green",shape="box"];691[label="ww70",fontsize=16,color="green",shape="box"];692[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];693 -> 296[label="",style="dashed", color="red", weight=0]; 693[label="showListShowl ww8 ww9",fontsize=16,color="magenta"];687[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) ww148",fontsize=16,color="black",shape="triangle"];687 -> 708[label="",style="solid", color="black", weight=3]; 613[label="error []",fontsize=16,color="red",shape="box"];614[label="error []",fontsize=16,color="red",shape="box"];615[label="error []",fontsize=16,color="red",shape="box"];616[label="error []",fontsize=16,color="red",shape="box"];617[label="error []",fontsize=16,color="red",shape="box"];618[label="error []",fontsize=16,color="red",shape="box"];619[label="primShowInt ww7",fontsize=16,color="burlywood",shape="triangle"];1794[label="ww7/Pos ww70",fontsize=10,color="white",style="solid",shape="box"];619 -> 1794[label="",style="solid", color="burlywood", weight=9]; 1794 -> 659[label="",style="solid", color="burlywood", weight=3]; 1795[label="ww7/Neg ww70",fontsize=10,color="white",style="solid",shape="box"];619 -> 1795[label="",style="solid", color="burlywood", weight=9]; 1795 -> 660[label="",style="solid", color="burlywood", weight=3]; 312[label="showListShowl (ww80 : ww81) ww9",fontsize=16,color="black",shape="box"];312 -> 319[label="",style="solid", color="black", weight=3]; 313[label="showListShowl [] ww9",fontsize=16,color="black",shape="box"];313 -> 320[label="",style="solid", color="black", weight=3]; 708[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww148",fontsize=16,color="black",shape="box"];708 -> 712[label="",style="solid", color="black", weight=3]; 659[label="primShowInt (Pos ww70)",fontsize=16,color="burlywood",shape="box"];1796[label="ww70/Succ ww700",fontsize=10,color="white",style="solid",shape="box"];659 -> 1796[label="",style="solid", color="burlywood", weight=9]; 1796 -> 684[label="",style="solid", color="burlywood", weight=3]; 1797[label="ww70/Zero",fontsize=10,color="white",style="solid",shape="box"];659 -> 1797[label="",style="solid", color="burlywood", weight=9]; 1797 -> 685[label="",style="solid", color="burlywood", weight=3]; 660[label="primShowInt (Neg ww70)",fontsize=16,color="black",shape="box"];660 -> 686[label="",style="solid", color="black", weight=3]; 319 -> 9[label="",style="dashed", color="red", weight=0]; 319[label="(showChar (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))) . (shows ww80) . showListShowl ww81",fontsize=16,color="magenta"];319 -> 330[label="",style="dashed", color="magenta", weight=3]; 319 -> 331[label="",style="dashed", color="magenta", weight=3]; 319 -> 332[label="",style="dashed", color="magenta", weight=3]; 320 -> 180[label="",style="dashed", color="red", weight=0]; 320[label="showChar (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ww9",fontsize=16,color="magenta"];320 -> 333[label="",style="dashed", color="magenta", weight=3]; 320 -> 334[label="",style="dashed", color="magenta", weight=3]; 712[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww148",fontsize=16,color="black",shape="box"];712 -> 716[label="",style="solid", color="black", weight=3]; 684[label="primShowInt (Pos (Succ ww700))",fontsize=16,color="black",shape="box"];684 -> 709[label="",style="solid", color="black", weight=3]; 685[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];685 -> 710[label="",style="solid", color="black", weight=3]; 686[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))) : primShowInt (Pos ww70)",fontsize=16,color="green",shape="box"];686 -> 711[label="",style="dashed", color="green", weight=3]; 330[label="ww81",fontsize=16,color="green",shape="box"];331[label="ww80",fontsize=16,color="green",shape="box"];332[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];333[label="ww9",fontsize=16,color="green",shape="box"];334[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];716[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww148",fontsize=16,color="black",shape="box"];716 -> 719[label="",style="solid", color="black", weight=3]; 709 -> 461[label="",style="dashed", color="red", weight=0]; 709[label="primShowInt (div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];709 -> 713[label="",style="dashed", color="magenta", weight=3]; 709 -> 714[label="",style="dashed", color="magenta", weight=3]; 710[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))) : []",fontsize=16,color="green",shape="box"];711 -> 619[label="",style="dashed", color="red", weight=0]; 711[label="primShowInt (Pos ww70)",fontsize=16,color="magenta"];711 -> 715[label="",style="dashed", color="magenta", weight=3]; 719[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww148",fontsize=16,color="black",shape="box"];719 -> 723[label="",style="solid", color="black", weight=3]; 713[label="toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];713 -> 717[label="",style="dashed", color="green", weight=3]; 714 -> 619[label="",style="dashed", color="red", weight=0]; 714[label="primShowInt (div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];714 -> 718[label="",style="dashed", color="magenta", weight=3]; 715[label="Pos ww70",fontsize=16,color="green",shape="box"];723[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) (LT == GT) ww148",fontsize=16,color="black",shape="box"];723 -> 727[label="",style="solid", color="black", weight=3]; 717[label="toEnum (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];717 -> 739[label="",style="solid", color="black", weight=3]; 718 -> 724[label="",style="dashed", color="red", weight=0]; 718[label="div Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];718 -> 725[label="",style="dashed", color="magenta", weight=3]; 718 -> 726[label="",style="dashed", color="magenta", weight=3]; 727[label="showParen0 ((shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142) False ww148",fontsize=16,color="black",shape="box"];727 -> 738[label="",style="solid", color="black", weight=3]; 739 -> 751[label="",style="dashed", color="red", weight=0]; 739[label="primIntToChar (mod Pos (Succ ww700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];739 -> 752[label="",style="dashed", color="magenta", weight=3]; 739 -> 753[label="",style="dashed", color="magenta", weight=3]; 725[label="ww700",fontsize=16,color="green",shape="box"];726[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];724[label="div Pos (Succ ww153) Pos (Succ ww154)",fontsize=16,color="black",shape="triangle"];724 -> 737[label="",style="solid", color="black", weight=3]; 738[label="(shows ww138) . (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="black",shape="box"];738 -> 750[label="",style="solid", color="black", weight=3]; 752[label="ww700",fontsize=16,color="green",shape="box"];753[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];751[label="primIntToChar (mod Pos (Succ ww156) Pos (Succ ww157))",fontsize=16,color="black",shape="triangle"];751 -> 754[label="",style="solid", color="black", weight=3]; 737[label="primDivInt (Pos (Succ ww153)) (Pos (Succ ww154))",fontsize=16,color="black",shape="box"];737 -> 749[label="",style="solid", color="black", weight=3]; 750[label="shows ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];750 -> 755[label="",style="solid", color="black", weight=3]; 754[label="primIntToChar (primModInt (Pos (Succ ww156)) (Pos (Succ ww157)))",fontsize=16,color="black",shape="box"];754 -> 757[label="",style="solid", color="black", weight=3]; 749[label="Pos (primDivNatS (Succ ww153) (Succ ww154))",fontsize=16,color="green",shape="box"];749 -> 756[label="",style="dashed", color="green", weight=3]; 755[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="blue",shape="box"];1798[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1798[label="",style="solid", color="blue", weight=9]; 1798 -> 758[label="",style="solid", color="blue", weight=3]; 1799[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1799[label="",style="solid", color="blue", weight=9]; 1799 -> 759[label="",style="solid", color="blue", weight=3]; 1800[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1800[label="",style="solid", color="blue", weight=9]; 1800 -> 760[label="",style="solid", color="blue", weight=3]; 1801[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1801[label="",style="solid", color="blue", weight=9]; 1801 -> 761[label="",style="solid", color="blue", weight=3]; 1802[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1802[label="",style="solid", color="blue", weight=9]; 1802 -> 762[label="",style="solid", color="blue", weight=3]; 1803[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1803[label="",style="solid", color="blue", weight=9]; 1803 -> 763[label="",style="solid", color="blue", weight=3]; 1804[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1804[label="",style="solid", color="blue", weight=9]; 1804 -> 764[label="",style="solid", color="blue", weight=3]; 1805[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1805[label="",style="solid", color="blue", weight=9]; 1805 -> 765[label="",style="solid", color="blue", weight=3]; 1806[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1806[label="",style="solid", color="blue", weight=9]; 1806 -> 766[label="",style="solid", color="blue", weight=3]; 1807[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1807[label="",style="solid", color="blue", weight=9]; 1807 -> 767[label="",style="solid", color="blue", weight=3]; 1808[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1808[label="",style="solid", color="blue", weight=9]; 1808 -> 768[label="",style="solid", color="blue", weight=3]; 1809[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1809[label="",style="solid", color="blue", weight=9]; 1809 -> 769[label="",style="solid", color="blue", weight=3]; 1810[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1810[label="",style="solid", color="blue", weight=9]; 1810 -> 770[label="",style="solid", color="blue", weight=3]; 1811[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1811[label="",style="solid", color="blue", weight=9]; 1811 -> 771[label="",style="solid", color="blue", weight=3]; 1812[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1812[label="",style="solid", color="blue", weight=9]; 1812 -> 772[label="",style="solid", color="blue", weight=3]; 1813[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1813[label="",style="solid", color="blue", weight=9]; 1813 -> 773[label="",style="solid", color="blue", weight=3]; 1814[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1814[label="",style="solid", color="blue", weight=9]; 1814 -> 774[label="",style="solid", color="blue", weight=3]; 1815[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];755 -> 1815[label="",style="solid", color="blue", weight=9]; 1815 -> 775[label="",style="solid", color="blue", weight=3]; 757[label="primIntToChar (Pos (primModNatS (Succ ww156) (Succ ww157)))",fontsize=16,color="black",shape="box"];757 -> 777[label="",style="solid", color="black", weight=3]; 756[label="primDivNatS (Succ ww153) (Succ ww154)",fontsize=16,color="black",shape="triangle"];756 -> 776[label="",style="solid", color="black", weight=3]; 758[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];758 -> 778[label="",style="solid", color="black", weight=3]; 759[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];759 -> 779[label="",style="solid", color="black", weight=3]; 760[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];760 -> 780[label="",style="solid", color="black", weight=3]; 761[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];761 -> 781[label="",style="solid", color="black", weight=3]; 762[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];762 -> 782[label="",style="solid", color="black", weight=3]; 763[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];763 -> 783[label="",style="solid", color="black", weight=3]; 764[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];764 -> 784[label="",style="solid", color="black", weight=3]; 765[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];765 -> 785[label="",style="solid", color="black", weight=3]; 766[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];766 -> 786[label="",style="solid", color="black", weight=3]; 767[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];767 -> 787[label="",style="solid", color="black", weight=3]; 768[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="burlywood",shape="box"];1816[label="ww138/ww1380 :% ww1381",fontsize=10,color="white",style="solid",shape="box"];768 -> 1816[label="",style="solid", color="burlywood", weight=9]; 1816 -> 788[label="",style="solid", color="burlywood", weight=3]; 769[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];769 -> 789[label="",style="solid", color="black", weight=3]; 770[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];770 -> 790[label="",style="solid", color="black", weight=3]; 771[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];771 -> 791[label="",style="solid", color="black", weight=3]; 772[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];772 -> 792[label="",style="solid", color="black", weight=3]; 773[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];773 -> 793[label="",style="solid", color="black", weight=3]; 774[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];774 -> 794[label="",style="solid", color="black", weight=3]; 775[label="showsPrec (Pos Zero) ww138 ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];775 -> 795[label="",style="solid", color="black", weight=3]; 777[label="Char (primModNatS (Succ ww156) (Succ ww157))",fontsize=16,color="green",shape="box"];777 -> 798[label="",style="dashed", color="green", weight=3]; 776[label="primDivNatS0 ww153 ww154 (primGEqNatS ww153 ww154)",fontsize=16,color="burlywood",shape="box"];1817[label="ww153/Succ ww1530",fontsize=10,color="white",style="solid",shape="box"];776 -> 1817[label="",style="solid", color="burlywood", weight=9]; 1817 -> 796[label="",style="solid", color="burlywood", weight=3]; 1818[label="ww153/Zero",fontsize=10,color="white",style="solid",shape="box"];776 -> 1818[label="",style="solid", color="burlywood", weight=9]; 1818 -> 797[label="",style="solid", color="burlywood", weight=3]; 778 -> 461[label="",style="dashed", color="red", weight=0]; 778[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];778 -> 799[label="",style="dashed", color="magenta", weight=3]; 778 -> 800[label="",style="dashed", color="magenta", weight=3]; 779 -> 461[label="",style="dashed", color="red", weight=0]; 779[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];779 -> 801[label="",style="dashed", color="magenta", weight=3]; 779 -> 802[label="",style="dashed", color="magenta", weight=3]; 780 -> 461[label="",style="dashed", color="red", weight=0]; 780[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];780 -> 803[label="",style="dashed", color="magenta", weight=3]; 780 -> 804[label="",style="dashed", color="magenta", weight=3]; 781 -> 461[label="",style="dashed", color="red", weight=0]; 781[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];781 -> 805[label="",style="dashed", color="magenta", weight=3]; 781 -> 806[label="",style="dashed", color="magenta", weight=3]; 782 -> 461[label="",style="dashed", color="red", weight=0]; 782[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];782 -> 807[label="",style="dashed", color="magenta", weight=3]; 782 -> 808[label="",style="dashed", color="magenta", weight=3]; 783 -> 461[label="",style="dashed", color="red", weight=0]; 783[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];783 -> 809[label="",style="dashed", color="magenta", weight=3]; 783 -> 810[label="",style="dashed", color="magenta", weight=3]; 784 -> 461[label="",style="dashed", color="red", weight=0]; 784[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];784 -> 811[label="",style="dashed", color="magenta", weight=3]; 784 -> 812[label="",style="dashed", color="magenta", weight=3]; 785 -> 461[label="",style="dashed", color="red", weight=0]; 785[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];785 -> 813[label="",style="dashed", color="magenta", weight=3]; 785 -> 814[label="",style="dashed", color="magenta", weight=3]; 786 -> 461[label="",style="dashed", color="red", weight=0]; 786[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];786 -> 815[label="",style="dashed", color="magenta", weight=3]; 786 -> 816[label="",style="dashed", color="magenta", weight=3]; 787 -> 461[label="",style="dashed", color="red", weight=0]; 787[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];787 -> 817[label="",style="dashed", color="magenta", weight=3]; 787 -> 818[label="",style="dashed", color="magenta", weight=3]; 788[label="showsPrec (Pos Zero) (ww1380 :% ww1381) ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="black",shape="box"];788 -> 819[label="",style="solid", color="black", weight=3]; 789 -> 461[label="",style="dashed", color="red", weight=0]; 789[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];789 -> 820[label="",style="dashed", color="magenta", weight=3]; 789 -> 821[label="",style="dashed", color="magenta", weight=3]; 790 -> 461[label="",style="dashed", color="red", weight=0]; 790[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];790 -> 822[label="",style="dashed", color="magenta", weight=3]; 790 -> 823[label="",style="dashed", color="magenta", weight=3]; 791 -> 461[label="",style="dashed", color="red", weight=0]; 791[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];791 -> 824[label="",style="dashed", color="magenta", weight=3]; 791 -> 825[label="",style="dashed", color="magenta", weight=3]; 792 -> 461[label="",style="dashed", color="red", weight=0]; 792[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];792 -> 826[label="",style="dashed", color="magenta", weight=3]; 792 -> 827[label="",style="dashed", color="magenta", weight=3]; 793 -> 461[label="",style="dashed", color="red", weight=0]; 793[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];793 -> 828[label="",style="dashed", color="magenta", weight=3]; 793 -> 829[label="",style="dashed", color="magenta", weight=3]; 794 -> 461[label="",style="dashed", color="red", weight=0]; 794[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];794 -> 830[label="",style="dashed", color="magenta", weight=3]; 794 -> 831[label="",style="dashed", color="magenta", weight=3]; 795 -> 461[label="",style="dashed", color="red", weight=0]; 795[label="show ww138 ++ (showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];795 -> 832[label="",style="dashed", color="magenta", weight=3]; 795 -> 833[label="",style="dashed", color="magenta", weight=3]; 798[label="primModNatS (Succ ww156) (Succ ww157)",fontsize=16,color="black",shape="triangle"];798 -> 838[label="",style="solid", color="black", weight=3]; 796[label="primDivNatS0 (Succ ww1530) ww154 (primGEqNatS (Succ ww1530) ww154)",fontsize=16,color="burlywood",shape="box"];1819[label="ww154/Succ ww1540",fontsize=10,color="white",style="solid",shape="box"];796 -> 1819[label="",style="solid", color="burlywood", weight=9]; 1819 -> 834[label="",style="solid", color="burlywood", weight=3]; 1820[label="ww154/Zero",fontsize=10,color="white",style="solid",shape="box"];796 -> 1820[label="",style="solid", color="burlywood", weight=9]; 1820 -> 835[label="",style="solid", color="burlywood", weight=3]; 797[label="primDivNatS0 Zero ww154 (primGEqNatS Zero ww154)",fontsize=16,color="burlywood",shape="box"];1821[label="ww154/Succ ww1540",fontsize=10,color="white",style="solid",shape="box"];797 -> 1821[label="",style="solid", color="burlywood", weight=9]; 1821 -> 836[label="",style="solid", color="burlywood", weight=3]; 1822[label="ww154/Zero",fontsize=10,color="white",style="solid",shape="box"];797 -> 1822[label="",style="solid", color="burlywood", weight=9]; 1822 -> 837[label="",style="solid", color="burlywood", weight=3]; 799[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="black",shape="triangle"];799 -> 839[label="",style="solid", color="black", weight=3]; 800 -> 469[label="",style="dashed", color="red", weight=0]; 800[label="show ww138",fontsize=16,color="magenta"];800 -> 840[label="",style="dashed", color="magenta", weight=3]; 801 -> 799[label="",style="dashed", color="red", weight=0]; 801[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];802 -> 471[label="",style="dashed", color="red", weight=0]; 802[label="show ww138",fontsize=16,color="magenta"];802 -> 841[label="",style="dashed", color="magenta", weight=3]; 803 -> 799[label="",style="dashed", color="red", weight=0]; 803[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];804 -> 473[label="",style="dashed", color="red", weight=0]; 804[label="show ww138",fontsize=16,color="magenta"];804 -> 842[label="",style="dashed", color="magenta", weight=3]; 805 -> 799[label="",style="dashed", color="red", weight=0]; 805[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];806 -> 475[label="",style="dashed", color="red", weight=0]; 806[label="show ww138",fontsize=16,color="magenta"];806 -> 843[label="",style="dashed", color="magenta", weight=3]; 807 -> 799[label="",style="dashed", color="red", weight=0]; 807[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];808 -> 477[label="",style="dashed", color="red", weight=0]; 808[label="show ww138",fontsize=16,color="magenta"];808 -> 844[label="",style="dashed", color="magenta", weight=3]; 809 -> 799[label="",style="dashed", color="red", weight=0]; 809[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];810 -> 479[label="",style="dashed", color="red", weight=0]; 810[label="show ww138",fontsize=16,color="magenta"];810 -> 845[label="",style="dashed", color="magenta", weight=3]; 811 -> 799[label="",style="dashed", color="red", weight=0]; 811[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];812 -> 481[label="",style="dashed", color="red", weight=0]; 812[label="show ww138",fontsize=16,color="magenta"];812 -> 846[label="",style="dashed", color="magenta", weight=3]; 813 -> 799[label="",style="dashed", color="red", weight=0]; 813[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];814 -> 483[label="",style="dashed", color="red", weight=0]; 814[label="show ww138",fontsize=16,color="magenta"];814 -> 847[label="",style="dashed", color="magenta", weight=3]; 815 -> 799[label="",style="dashed", color="red", weight=0]; 815[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];816 -> 485[label="",style="dashed", color="red", weight=0]; 816[label="show ww138",fontsize=16,color="magenta"];816 -> 848[label="",style="dashed", color="magenta", weight=3]; 817 -> 799[label="",style="dashed", color="red", weight=0]; 817[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];818 -> 487[label="",style="dashed", color="red", weight=0]; 818[label="show ww138",fontsize=16,color="magenta"];818 -> 849[label="",style="dashed", color="magenta", weight=3]; 819 -> 687[label="",style="dashed", color="red", weight=0]; 819[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1380) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww1381) ((showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142)",fontsize=16,color="magenta"];819 -> 850[label="",style="dashed", color="magenta", weight=3]; 819 -> 851[label="",style="dashed", color="magenta", weight=3]; 819 -> 852[label="",style="dashed", color="magenta", weight=3]; 819 -> 853[label="",style="dashed", color="magenta", weight=3]; 819 -> 854[label="",style="dashed", color="magenta", weight=3]; 819 -> 855[label="",style="dashed", color="magenta", weight=3]; 820 -> 799[label="",style="dashed", color="red", weight=0]; 820[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];821 -> 489[label="",style="dashed", color="red", weight=0]; 821[label="show ww138",fontsize=16,color="magenta"];821 -> 856[label="",style="dashed", color="magenta", weight=3]; 822 -> 799[label="",style="dashed", color="red", weight=0]; 822[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];823 -> 491[label="",style="dashed", color="red", weight=0]; 823[label="show ww138",fontsize=16,color="magenta"];823 -> 857[label="",style="dashed", color="magenta", weight=3]; 824 -> 799[label="",style="dashed", color="red", weight=0]; 824[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];825 -> 493[label="",style="dashed", color="red", weight=0]; 825[label="show ww138",fontsize=16,color="magenta"];825 -> 858[label="",style="dashed", color="magenta", weight=3]; 826 -> 799[label="",style="dashed", color="red", weight=0]; 826[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];827 -> 495[label="",style="dashed", color="red", weight=0]; 827[label="show ww138",fontsize=16,color="magenta"];827 -> 859[label="",style="dashed", color="magenta", weight=3]; 828 -> 799[label="",style="dashed", color="red", weight=0]; 828[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];829 -> 497[label="",style="dashed", color="red", weight=0]; 829[label="show ww138",fontsize=16,color="magenta"];829 -> 860[label="",style="dashed", color="magenta", weight=3]; 830 -> 799[label="",style="dashed", color="red", weight=0]; 830[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];831 -> 499[label="",style="dashed", color="red", weight=0]; 831[label="show ww138",fontsize=16,color="magenta"];831 -> 861[label="",style="dashed", color="magenta", weight=3]; 832 -> 799[label="",style="dashed", color="red", weight=0]; 832[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];833 -> 501[label="",style="dashed", color="red", weight=0]; 833[label="show ww138",fontsize=16,color="magenta"];833 -> 862[label="",style="dashed", color="magenta", weight=3]; 838[label="primModNatS0 ww156 ww157 (primGEqNatS ww156 ww157)",fontsize=16,color="burlywood",shape="box"];1823[label="ww156/Succ ww1560",fontsize=10,color="white",style="solid",shape="box"];838 -> 1823[label="",style="solid", color="burlywood", weight=9]; 1823 -> 867[label="",style="solid", color="burlywood", weight=3]; 1824[label="ww156/Zero",fontsize=10,color="white",style="solid",shape="box"];838 -> 1824[label="",style="solid", color="burlywood", weight=9]; 1824 -> 868[label="",style="solid", color="burlywood", weight=3]; 834[label="primDivNatS0 (Succ ww1530) (Succ ww1540) (primGEqNatS (Succ ww1530) (Succ ww1540))",fontsize=16,color="black",shape="box"];834 -> 863[label="",style="solid", color="black", weight=3]; 835[label="primDivNatS0 (Succ ww1530) Zero (primGEqNatS (Succ ww1530) Zero)",fontsize=16,color="black",shape="box"];835 -> 864[label="",style="solid", color="black", weight=3]; 836[label="primDivNatS0 Zero (Succ ww1540) (primGEqNatS Zero (Succ ww1540))",fontsize=16,color="black",shape="box"];836 -> 865[label="",style="solid", color="black", weight=3]; 837[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];837 -> 866[label="",style="solid", color="black", weight=3]; 839[label="showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : []) (shows ww142 ww148)",fontsize=16,color="black",shape="box"];839 -> 869[label="",style="solid", color="black", weight=3]; 840[label="ww138",fontsize=16,color="green",shape="box"];841[label="ww138",fontsize=16,color="green",shape="box"];842[label="ww138",fontsize=16,color="green",shape="box"];843[label="ww138",fontsize=16,color="green",shape="box"];844[label="ww138",fontsize=16,color="green",shape="box"];845[label="ww138",fontsize=16,color="green",shape="box"];846[label="ww138",fontsize=16,color="green",shape="box"];847[label="ww138",fontsize=16,color="green",shape="box"];848[label="ww138",fontsize=16,color="green",shape="box"];849[label="ww138",fontsize=16,color="green",shape="box"];850[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];851[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];852[label="ww1381",fontsize=16,color="green",shape="box"];853[label="ww1380",fontsize=16,color="green",shape="box"];854[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];855 -> 799[label="",style="dashed", color="red", weight=0]; 855[label="(showString (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : [])) . shows ww142",fontsize=16,color="magenta"];856[label="ww138",fontsize=16,color="green",shape="box"];857[label="ww138",fontsize=16,color="green",shape="box"];858[label="ww138",fontsize=16,color="green",shape="box"];859[label="ww138",fontsize=16,color="green",shape="box"];860[label="ww138",fontsize=16,color="green",shape="box"];861[label="ww138",fontsize=16,color="green",shape="box"];862[label="ww138",fontsize=16,color="green",shape="box"];867[label="primModNatS0 (Succ ww1560) ww157 (primGEqNatS (Succ ww1560) ww157)",fontsize=16,color="burlywood",shape="box"];1825[label="ww157/Succ ww1570",fontsize=10,color="white",style="solid",shape="box"];867 -> 1825[label="",style="solid", color="burlywood", weight=9]; 1825 -> 875[label="",style="solid", color="burlywood", weight=3]; 1826[label="ww157/Zero",fontsize=10,color="white",style="solid",shape="box"];867 -> 1826[label="",style="solid", color="burlywood", weight=9]; 1826 -> 876[label="",style="solid", color="burlywood", weight=3]; 868[label="primModNatS0 Zero ww157 (primGEqNatS Zero ww157)",fontsize=16,color="burlywood",shape="box"];1827[label="ww157/Succ ww1570",fontsize=10,color="white",style="solid",shape="box"];868 -> 1827[label="",style="solid", color="burlywood", weight=9]; 1827 -> 877[label="",style="solid", color="burlywood", weight=3]; 1828[label="ww157/Zero",fontsize=10,color="white",style="solid",shape="box"];868 -> 1828[label="",style="solid", color="burlywood", weight=9]; 1828 -> 878[label="",style="solid", color="burlywood", weight=3]; 863 -> 1485[label="",style="dashed", color="red", weight=0]; 863[label="primDivNatS0 (Succ ww1530) (Succ ww1540) (primGEqNatS ww1530 ww1540)",fontsize=16,color="magenta"];863 -> 1486[label="",style="dashed", color="magenta", weight=3]; 863 -> 1487[label="",style="dashed", color="magenta", weight=3]; 863 -> 1488[label="",style="dashed", color="magenta", weight=3]; 863 -> 1489[label="",style="dashed", color="magenta", weight=3]; 864[label="primDivNatS0 (Succ ww1530) Zero True",fontsize=16,color="black",shape="box"];864 -> 872[label="",style="solid", color="black", weight=3]; 865[label="primDivNatS0 Zero (Succ ww1540) False",fontsize=16,color="black",shape="box"];865 -> 873[label="",style="solid", color="black", weight=3]; 866[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];866 -> 874[label="",style="solid", color="black", weight=3]; 869 -> 461[label="",style="dashed", color="red", weight=0]; 869[label="(++) (Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : []) shows ww142 ww148",fontsize=16,color="magenta"];869 -> 879[label="",style="dashed", color="magenta", weight=3]; 869 -> 880[label="",style="dashed", color="magenta", weight=3]; 875[label="primModNatS0 (Succ ww1560) (Succ ww1570) (primGEqNatS (Succ ww1560) (Succ ww1570))",fontsize=16,color="black",shape="box"];875 -> 887[label="",style="solid", color="black", weight=3]; 876[label="primModNatS0 (Succ ww1560) Zero (primGEqNatS (Succ ww1560) Zero)",fontsize=16,color="black",shape="box"];876 -> 888[label="",style="solid", color="black", weight=3]; 877[label="primModNatS0 Zero (Succ ww1570) (primGEqNatS Zero (Succ ww1570))",fontsize=16,color="black",shape="box"];877 -> 889[label="",style="solid", color="black", weight=3]; 878[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];878 -> 890[label="",style="solid", color="black", weight=3]; 1486[label="ww1540",fontsize=16,color="green",shape="box"];1487[label="ww1540",fontsize=16,color="green",shape="box"];1488[label="ww1530",fontsize=16,color="green",shape="box"];1489[label="ww1530",fontsize=16,color="green",shape="box"];1485[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS ww202 ww203)",fontsize=16,color="burlywood",shape="triangle"];1829[label="ww202/Succ ww2020",fontsize=10,color="white",style="solid",shape="box"];1485 -> 1829[label="",style="solid", color="burlywood", weight=9]; 1829 -> 1526[label="",style="solid", color="burlywood", weight=3]; 1830[label="ww202/Zero",fontsize=10,color="white",style="solid",shape="box"];1485 -> 1830[label="",style="solid", color="burlywood", weight=9]; 1830 -> 1527[label="",style="solid", color="burlywood", weight=3]; 872[label="Succ (primDivNatS (primMinusNatS (Succ ww1530) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];872 -> 885[label="",style="dashed", color="green", weight=3]; 873[label="Zero",fontsize=16,color="green",shape="box"];874[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];874 -> 886[label="",style="dashed", color="green", weight=3]; 879[label="shows ww142 ww148",fontsize=16,color="black",shape="box"];879 -> 891[label="",style="solid", color="black", weight=3]; 880[label="Char (Succ ww139) : Char (Succ ww140) : Char (Succ ww141) : []",fontsize=16,color="green",shape="box"];887 -> 1546[label="",style="dashed", color="red", weight=0]; 887[label="primModNatS0 (Succ ww1560) (Succ ww1570) (primGEqNatS ww1560 ww1570)",fontsize=16,color="magenta"];887 -> 1547[label="",style="dashed", color="magenta", weight=3]; 887 -> 1548[label="",style="dashed", color="magenta", weight=3]; 887 -> 1549[label="",style="dashed", color="magenta", weight=3]; 887 -> 1550[label="",style="dashed", color="magenta", weight=3]; 888[label="primModNatS0 (Succ ww1560) Zero True",fontsize=16,color="black",shape="box"];888 -> 900[label="",style="solid", color="black", weight=3]; 889[label="primModNatS0 Zero (Succ ww1570) False",fontsize=16,color="black",shape="box"];889 -> 901[label="",style="solid", color="black", weight=3]; 890[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];890 -> 902[label="",style="solid", color="black", weight=3]; 1526[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS (Succ ww2020) ww203)",fontsize=16,color="burlywood",shape="box"];1831[label="ww203/Succ ww2030",fontsize=10,color="white",style="solid",shape="box"];1526 -> 1831[label="",style="solid", color="burlywood", weight=9]; 1831 -> 1538[label="",style="solid", color="burlywood", weight=3]; 1832[label="ww203/Zero",fontsize=10,color="white",style="solid",shape="box"];1526 -> 1832[label="",style="solid", color="burlywood", weight=9]; 1832 -> 1539[label="",style="solid", color="burlywood", weight=3]; 1527[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS Zero ww203)",fontsize=16,color="burlywood",shape="box"];1833[label="ww203/Succ ww2030",fontsize=10,color="white",style="solid",shape="box"];1527 -> 1833[label="",style="solid", color="burlywood", weight=9]; 1833 -> 1540[label="",style="solid", color="burlywood", weight=3]; 1834[label="ww203/Zero",fontsize=10,color="white",style="solid",shape="box"];1527 -> 1834[label="",style="solid", color="burlywood", weight=9]; 1834 -> 1541[label="",style="solid", color="burlywood", weight=3]; 885 -> 1729[label="",style="dashed", color="red", weight=0]; 885[label="primDivNatS (primMinusNatS (Succ ww1530) Zero) (Succ Zero)",fontsize=16,color="magenta"];885 -> 1730[label="",style="dashed", color="magenta", weight=3]; 885 -> 1731[label="",style="dashed", color="magenta", weight=3]; 885 -> 1732[label="",style="dashed", color="magenta", weight=3]; 886 -> 1729[label="",style="dashed", color="red", weight=0]; 886[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];886 -> 1733[label="",style="dashed", color="magenta", weight=3]; 886 -> 1734[label="",style="dashed", color="magenta", weight=3]; 886 -> 1735[label="",style="dashed", color="magenta", weight=3]; 891[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="blue",shape="box"];1835[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1835[label="",style="solid", color="blue", weight=9]; 1835 -> 903[label="",style="solid", color="blue", weight=3]; 1836[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1836[label="",style="solid", color="blue", weight=9]; 1836 -> 904[label="",style="solid", color="blue", weight=3]; 1837[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1837[label="",style="solid", color="blue", weight=9]; 1837 -> 905[label="",style="solid", color="blue", weight=3]; 1838[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1838[label="",style="solid", color="blue", weight=9]; 1838 -> 906[label="",style="solid", color="blue", weight=3]; 1839[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1839[label="",style="solid", color="blue", weight=9]; 1839 -> 907[label="",style="solid", color="blue", weight=3]; 1840[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1840[label="",style="solid", color="blue", weight=9]; 1840 -> 908[label="",style="solid", color="blue", weight=3]; 1841[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1841[label="",style="solid", color="blue", weight=9]; 1841 -> 909[label="",style="solid", color="blue", weight=3]; 1842[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1842[label="",style="solid", color="blue", weight=9]; 1842 -> 910[label="",style="solid", color="blue", weight=3]; 1843[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1843[label="",style="solid", color="blue", weight=9]; 1843 -> 911[label="",style="solid", color="blue", weight=3]; 1844[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1844[label="",style="solid", color="blue", weight=9]; 1844 -> 912[label="",style="solid", color="blue", weight=3]; 1845[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1845[label="",style="solid", color="blue", weight=9]; 1845 -> 913[label="",style="solid", color="blue", weight=3]; 1846[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1846[label="",style="solid", color="blue", weight=9]; 1846 -> 914[label="",style="solid", color="blue", weight=3]; 1847[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1847[label="",style="solid", color="blue", weight=9]; 1847 -> 915[label="",style="solid", color="blue", weight=3]; 1848[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1848[label="",style="solid", color="blue", weight=9]; 1848 -> 916[label="",style="solid", color="blue", weight=3]; 1849[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1849[label="",style="solid", color="blue", weight=9]; 1849 -> 917[label="",style="solid", color="blue", weight=3]; 1850[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1850[label="",style="solid", color="blue", weight=9]; 1850 -> 918[label="",style="solid", color="blue", weight=3]; 1851[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1851[label="",style="solid", color="blue", weight=9]; 1851 -> 919[label="",style="solid", color="blue", weight=3]; 1852[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];891 -> 1852[label="",style="solid", color="blue", weight=9]; 1852 -> 920[label="",style="solid", color="blue", weight=3]; 1547[label="ww1570",fontsize=16,color="green",shape="box"];1548[label="ww1560",fontsize=16,color="green",shape="box"];1549[label="ww1570",fontsize=16,color="green",shape="box"];1550[label="ww1560",fontsize=16,color="green",shape="box"];1546[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS ww207 ww208)",fontsize=16,color="burlywood",shape="triangle"];1853[label="ww207/Succ ww2070",fontsize=10,color="white",style="solid",shape="box"];1546 -> 1853[label="",style="solid", color="burlywood", weight=9]; 1853 -> 1587[label="",style="solid", color="burlywood", weight=3]; 1854[label="ww207/Zero",fontsize=10,color="white",style="solid",shape="box"];1546 -> 1854[label="",style="solid", color="burlywood", weight=9]; 1854 -> 1588[label="",style="solid", color="burlywood", weight=3]; 900 -> 1633[label="",style="dashed", color="red", weight=0]; 900[label="primModNatS (primMinusNatS (Succ ww1560) Zero) (Succ Zero)",fontsize=16,color="magenta"];900 -> 1634[label="",style="dashed", color="magenta", weight=3]; 900 -> 1635[label="",style="dashed", color="magenta", weight=3]; 900 -> 1636[label="",style="dashed", color="magenta", weight=3]; 901[label="Succ Zero",fontsize=16,color="green",shape="box"];902 -> 1633[label="",style="dashed", color="red", weight=0]; 902[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];902 -> 1637[label="",style="dashed", color="magenta", weight=3]; 902 -> 1638[label="",style="dashed", color="magenta", weight=3]; 902 -> 1639[label="",style="dashed", color="magenta", weight=3]; 1538[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS (Succ ww2020) (Succ ww2030))",fontsize=16,color="black",shape="box"];1538 -> 1589[label="",style="solid", color="black", weight=3]; 1539[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS (Succ ww2020) Zero)",fontsize=16,color="black",shape="box"];1539 -> 1590[label="",style="solid", color="black", weight=3]; 1540[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS Zero (Succ ww2030))",fontsize=16,color="black",shape="box"];1540 -> 1591[label="",style="solid", color="black", weight=3]; 1541[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1541 -> 1592[label="",style="solid", color="black", weight=3]; 1730[label="Succ ww1530",fontsize=16,color="green",shape="box"];1731[label="Zero",fontsize=16,color="green",shape="box"];1732[label="Zero",fontsize=16,color="green",shape="box"];1729[label="primDivNatS (primMinusNatS ww214 ww215) (Succ ww216)",fontsize=16,color="burlywood",shape="triangle"];1855[label="ww214/Succ ww2140",fontsize=10,color="white",style="solid",shape="box"];1729 -> 1855[label="",style="solid", color="burlywood", weight=9]; 1855 -> 1754[label="",style="solid", color="burlywood", weight=3]; 1856[label="ww214/Zero",fontsize=10,color="white",style="solid",shape="box"];1729 -> 1856[label="",style="solid", color="burlywood", weight=9]; 1856 -> 1755[label="",style="solid", color="burlywood", weight=3]; 1733[label="Zero",fontsize=16,color="green",shape="box"];1734[label="Zero",fontsize=16,color="green",shape="box"];1735[label="Zero",fontsize=16,color="green",shape="box"];903[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];903 -> 935[label="",style="solid", color="black", weight=3]; 904[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];904 -> 936[label="",style="solid", color="black", weight=3]; 905[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];905 -> 937[label="",style="solid", color="black", weight=3]; 906[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];906 -> 938[label="",style="solid", color="black", weight=3]; 907[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];907 -> 939[label="",style="solid", color="black", weight=3]; 908[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];908 -> 940[label="",style="solid", color="black", weight=3]; 909[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];909 -> 941[label="",style="solid", color="black", weight=3]; 910[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];910 -> 942[label="",style="solid", color="black", weight=3]; 911[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];911 -> 943[label="",style="solid", color="black", weight=3]; 912[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];912 -> 944[label="",style="solid", color="black", weight=3]; 913[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="burlywood",shape="box"];1857[label="ww142/ww1420 :% ww1421",fontsize=10,color="white",style="solid",shape="box"];913 -> 1857[label="",style="solid", color="burlywood", weight=9]; 1857 -> 945[label="",style="solid", color="burlywood", weight=3]; 914[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];914 -> 946[label="",style="solid", color="black", weight=3]; 915[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];915 -> 947[label="",style="solid", color="black", weight=3]; 916[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];916 -> 948[label="",style="solid", color="black", weight=3]; 917[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];917 -> 949[label="",style="solid", color="black", weight=3]; 918[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];918 -> 950[label="",style="solid", color="black", weight=3]; 919[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];919 -> 951[label="",style="solid", color="black", weight=3]; 920[label="showsPrec (Pos Zero) ww142 ww148",fontsize=16,color="black",shape="box"];920 -> 952[label="",style="solid", color="black", weight=3]; 1587[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS (Succ ww2070) ww208)",fontsize=16,color="burlywood",shape="box"];1858[label="ww208/Succ ww2080",fontsize=10,color="white",style="solid",shape="box"];1587 -> 1858[label="",style="solid", color="burlywood", weight=9]; 1858 -> 1597[label="",style="solid", color="burlywood", weight=3]; 1859[label="ww208/Zero",fontsize=10,color="white",style="solid",shape="box"];1587 -> 1859[label="",style="solid", color="burlywood", weight=9]; 1859 -> 1598[label="",style="solid", color="burlywood", weight=3]; 1588[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS Zero ww208)",fontsize=16,color="burlywood",shape="box"];1860[label="ww208/Succ ww2080",fontsize=10,color="white",style="solid",shape="box"];1588 -> 1860[label="",style="solid", color="burlywood", weight=9]; 1860 -> 1599[label="",style="solid", color="burlywood", weight=3]; 1861[label="ww208/Zero",fontsize=10,color="white",style="solid",shape="box"];1588 -> 1861[label="",style="solid", color="burlywood", weight=9]; 1861 -> 1600[label="",style="solid", color="burlywood", weight=3]; 1634[label="Zero",fontsize=16,color="green",shape="box"];1635[label="Succ ww1560",fontsize=16,color="green",shape="box"];1636[label="Zero",fontsize=16,color="green",shape="box"];1633[label="primModNatS (primMinusNatS ww210 ww211) (Succ ww212)",fontsize=16,color="burlywood",shape="triangle"];1862[label="ww210/Succ ww2100",fontsize=10,color="white",style="solid",shape="box"];1633 -> 1862[label="",style="solid", color="burlywood", weight=9]; 1862 -> 1664[label="",style="solid", color="burlywood", weight=3]; 1863[label="ww210/Zero",fontsize=10,color="white",style="solid",shape="box"];1633 -> 1863[label="",style="solid", color="burlywood", weight=9]; 1863 -> 1665[label="",style="solid", color="burlywood", weight=3]; 1637[label="Zero",fontsize=16,color="green",shape="box"];1638[label="Zero",fontsize=16,color="green",shape="box"];1639[label="Zero",fontsize=16,color="green",shape="box"];1589 -> 1485[label="",style="dashed", color="red", weight=0]; 1589[label="primDivNatS0 (Succ ww200) (Succ ww201) (primGEqNatS ww2020 ww2030)",fontsize=16,color="magenta"];1589 -> 1601[label="",style="dashed", color="magenta", weight=3]; 1589 -> 1602[label="",style="dashed", color="magenta", weight=3]; 1590[label="primDivNatS0 (Succ ww200) (Succ ww201) True",fontsize=16,color="black",shape="triangle"];1590 -> 1603[label="",style="solid", color="black", weight=3]; 1591[label="primDivNatS0 (Succ ww200) (Succ ww201) False",fontsize=16,color="black",shape="box"];1591 -> 1604[label="",style="solid", color="black", weight=3]; 1592 -> 1590[label="",style="dashed", color="red", weight=0]; 1592[label="primDivNatS0 (Succ ww200) (Succ ww201) True",fontsize=16,color="magenta"];1754[label="primDivNatS (primMinusNatS (Succ ww2140) ww215) (Succ ww216)",fontsize=16,color="burlywood",shape="box"];1864[label="ww215/Succ ww2150",fontsize=10,color="white",style="solid",shape="box"];1754 -> 1864[label="",style="solid", color="burlywood", weight=9]; 1864 -> 1756[label="",style="solid", color="burlywood", weight=3]; 1865[label="ww215/Zero",fontsize=10,color="white",style="solid",shape="box"];1754 -> 1865[label="",style="solid", color="burlywood", weight=9]; 1865 -> 1757[label="",style="solid", color="burlywood", weight=3]; 1755[label="primDivNatS (primMinusNatS Zero ww215) (Succ ww216)",fontsize=16,color="burlywood",shape="box"];1866[label="ww215/Succ ww2150",fontsize=10,color="white",style="solid",shape="box"];1755 -> 1866[label="",style="solid", color="burlywood", weight=9]; 1866 -> 1758[label="",style="solid", color="burlywood", weight=3]; 1867[label="ww215/Zero",fontsize=10,color="white",style="solid",shape="box"];1755 -> 1867[label="",style="solid", color="burlywood", weight=9]; 1867 -> 1759[label="",style="solid", color="burlywood", weight=3]; 935 -> 461[label="",style="dashed", color="red", weight=0]; 935[label="show ww142 ++ ww148",fontsize=16,color="magenta"];935 -> 966[label="",style="dashed", color="magenta", weight=3]; 935 -> 967[label="",style="dashed", color="magenta", weight=3]; 936 -> 461[label="",style="dashed", color="red", weight=0]; 936[label="show ww142 ++ ww148",fontsize=16,color="magenta"];936 -> 968[label="",style="dashed", color="magenta", weight=3]; 936 -> 969[label="",style="dashed", color="magenta", weight=3]; 937 -> 461[label="",style="dashed", color="red", weight=0]; 937[label="show ww142 ++ ww148",fontsize=16,color="magenta"];937 -> 970[label="",style="dashed", color="magenta", weight=3]; 937 -> 971[label="",style="dashed", color="magenta", weight=3]; 938 -> 461[label="",style="dashed", color="red", weight=0]; 938[label="show ww142 ++ ww148",fontsize=16,color="magenta"];938 -> 972[label="",style="dashed", color="magenta", weight=3]; 938 -> 973[label="",style="dashed", color="magenta", weight=3]; 939 -> 461[label="",style="dashed", color="red", weight=0]; 939[label="show ww142 ++ ww148",fontsize=16,color="magenta"];939 -> 974[label="",style="dashed", color="magenta", weight=3]; 939 -> 975[label="",style="dashed", color="magenta", weight=3]; 940 -> 461[label="",style="dashed", color="red", weight=0]; 940[label="show ww142 ++ ww148",fontsize=16,color="magenta"];940 -> 976[label="",style="dashed", color="magenta", weight=3]; 940 -> 977[label="",style="dashed", color="magenta", weight=3]; 941 -> 461[label="",style="dashed", color="red", weight=0]; 941[label="show ww142 ++ ww148",fontsize=16,color="magenta"];941 -> 978[label="",style="dashed", color="magenta", weight=3]; 941 -> 979[label="",style="dashed", color="magenta", weight=3]; 942 -> 461[label="",style="dashed", color="red", weight=0]; 942[label="show ww142 ++ ww148",fontsize=16,color="magenta"];942 -> 980[label="",style="dashed", color="magenta", weight=3]; 942 -> 981[label="",style="dashed", color="magenta", weight=3]; 943 -> 461[label="",style="dashed", color="red", weight=0]; 943[label="show ww142 ++ ww148",fontsize=16,color="magenta"];943 -> 982[label="",style="dashed", color="magenta", weight=3]; 943 -> 983[label="",style="dashed", color="magenta", weight=3]; 944 -> 461[label="",style="dashed", color="red", weight=0]; 944[label="show ww142 ++ ww148",fontsize=16,color="magenta"];944 -> 984[label="",style="dashed", color="magenta", weight=3]; 944 -> 985[label="",style="dashed", color="magenta", weight=3]; 945[label="showsPrec (Pos Zero) (ww1420 :% ww1421) ww148",fontsize=16,color="black",shape="box"];945 -> 986[label="",style="solid", color="black", weight=3]; 946 -> 461[label="",style="dashed", color="red", weight=0]; 946[label="show ww142 ++ ww148",fontsize=16,color="magenta"];946 -> 987[label="",style="dashed", color="magenta", weight=3]; 946 -> 988[label="",style="dashed", color="magenta", weight=3]; 947 -> 461[label="",style="dashed", color="red", weight=0]; 947[label="show ww142 ++ ww148",fontsize=16,color="magenta"];947 -> 989[label="",style="dashed", color="magenta", weight=3]; 947 -> 990[label="",style="dashed", color="magenta", weight=3]; 948 -> 461[label="",style="dashed", color="red", weight=0]; 948[label="show ww142 ++ ww148",fontsize=16,color="magenta"];948 -> 991[label="",style="dashed", color="magenta", weight=3]; 948 -> 992[label="",style="dashed", color="magenta", weight=3]; 949 -> 461[label="",style="dashed", color="red", weight=0]; 949[label="show ww142 ++ ww148",fontsize=16,color="magenta"];949 -> 993[label="",style="dashed", color="magenta", weight=3]; 949 -> 994[label="",style="dashed", color="magenta", weight=3]; 950 -> 461[label="",style="dashed", color="red", weight=0]; 950[label="show ww142 ++ ww148",fontsize=16,color="magenta"];950 -> 995[label="",style="dashed", color="magenta", weight=3]; 950 -> 996[label="",style="dashed", color="magenta", weight=3]; 951 -> 461[label="",style="dashed", color="red", weight=0]; 951[label="show ww142 ++ ww148",fontsize=16,color="magenta"];951 -> 997[label="",style="dashed", color="magenta", weight=3]; 951 -> 998[label="",style="dashed", color="magenta", weight=3]; 952 -> 461[label="",style="dashed", color="red", weight=0]; 952[label="show ww142 ++ ww148",fontsize=16,color="magenta"];952 -> 999[label="",style="dashed", color="magenta", weight=3]; 952 -> 1000[label="",style="dashed", color="magenta", weight=3]; 1597[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS (Succ ww2070) (Succ ww2080))",fontsize=16,color="black",shape="box"];1597 -> 1611[label="",style="solid", color="black", weight=3]; 1598[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS (Succ ww2070) Zero)",fontsize=16,color="black",shape="box"];1598 -> 1612[label="",style="solid", color="black", weight=3]; 1599[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS Zero (Succ ww2080))",fontsize=16,color="black",shape="box"];1599 -> 1613[label="",style="solid", color="black", weight=3]; 1600[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1600 -> 1614[label="",style="solid", color="black", weight=3]; 1664[label="primModNatS (primMinusNatS (Succ ww2100) ww211) (Succ ww212)",fontsize=16,color="burlywood",shape="box"];1868[label="ww211/Succ ww2110",fontsize=10,color="white",style="solid",shape="box"];1664 -> 1868[label="",style="solid", color="burlywood", weight=9]; 1868 -> 1670[label="",style="solid", color="burlywood", weight=3]; 1869[label="ww211/Zero",fontsize=10,color="white",style="solid",shape="box"];1664 -> 1869[label="",style="solid", color="burlywood", weight=9]; 1869 -> 1671[label="",style="solid", color="burlywood", weight=3]; 1665[label="primModNatS (primMinusNatS Zero ww211) (Succ ww212)",fontsize=16,color="burlywood",shape="box"];1870[label="ww211/Succ ww2110",fontsize=10,color="white",style="solid",shape="box"];1665 -> 1870[label="",style="solid", color="burlywood", weight=9]; 1870 -> 1672[label="",style="solid", color="burlywood", weight=3]; 1871[label="ww211/Zero",fontsize=10,color="white",style="solid",shape="box"];1665 -> 1871[label="",style="solid", color="burlywood", weight=9]; 1871 -> 1673[label="",style="solid", color="burlywood", weight=3]; 1601[label="ww2030",fontsize=16,color="green",shape="box"];1602[label="ww2020",fontsize=16,color="green",shape="box"];1603[label="Succ (primDivNatS (primMinusNatS (Succ ww200) (Succ ww201)) (Succ (Succ ww201)))",fontsize=16,color="green",shape="box"];1603 -> 1615[label="",style="dashed", color="green", weight=3]; 1604[label="Zero",fontsize=16,color="green",shape="box"];1756[label="primDivNatS (primMinusNatS (Succ ww2140) (Succ ww2150)) (Succ ww216)",fontsize=16,color="black",shape="box"];1756 -> 1760[label="",style="solid", color="black", weight=3]; 1757[label="primDivNatS (primMinusNatS (Succ ww2140) Zero) (Succ ww216)",fontsize=16,color="black",shape="box"];1757 -> 1761[label="",style="solid", color="black", weight=3]; 1758[label="primDivNatS (primMinusNatS Zero (Succ ww2150)) (Succ ww216)",fontsize=16,color="black",shape="box"];1758 -> 1762[label="",style="solid", color="black", weight=3]; 1759[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww216)",fontsize=16,color="black",shape="box"];1759 -> 1763[label="",style="solid", color="black", weight=3]; 966[label="ww148",fontsize=16,color="green",shape="box"];967 -> 469[label="",style="dashed", color="red", weight=0]; 967[label="show ww142",fontsize=16,color="magenta"];967 -> 1012[label="",style="dashed", color="magenta", weight=3]; 968[label="ww148",fontsize=16,color="green",shape="box"];969 -> 471[label="",style="dashed", color="red", weight=0]; 969[label="show ww142",fontsize=16,color="magenta"];969 -> 1013[label="",style="dashed", color="magenta", weight=3]; 970[label="ww148",fontsize=16,color="green",shape="box"];971 -> 473[label="",style="dashed", color="red", weight=0]; 971[label="show ww142",fontsize=16,color="magenta"];971 -> 1014[label="",style="dashed", color="magenta", weight=3]; 972[label="ww148",fontsize=16,color="green",shape="box"];973 -> 475[label="",style="dashed", color="red", weight=0]; 973[label="show ww142",fontsize=16,color="magenta"];973 -> 1015[label="",style="dashed", color="magenta", weight=3]; 974[label="ww148",fontsize=16,color="green",shape="box"];975 -> 477[label="",style="dashed", color="red", weight=0]; 975[label="show ww142",fontsize=16,color="magenta"];975 -> 1016[label="",style="dashed", color="magenta", weight=3]; 976[label="ww148",fontsize=16,color="green",shape="box"];977 -> 479[label="",style="dashed", color="red", weight=0]; 977[label="show ww142",fontsize=16,color="magenta"];977 -> 1017[label="",style="dashed", color="magenta", weight=3]; 978[label="ww148",fontsize=16,color="green",shape="box"];979 -> 481[label="",style="dashed", color="red", weight=0]; 979[label="show ww142",fontsize=16,color="magenta"];979 -> 1018[label="",style="dashed", color="magenta", weight=3]; 980[label="ww148",fontsize=16,color="green",shape="box"];981 -> 483[label="",style="dashed", color="red", weight=0]; 981[label="show ww142",fontsize=16,color="magenta"];981 -> 1019[label="",style="dashed", color="magenta", weight=3]; 982[label="ww148",fontsize=16,color="green",shape="box"];983 -> 485[label="",style="dashed", color="red", weight=0]; 983[label="show ww142",fontsize=16,color="magenta"];983 -> 1020[label="",style="dashed", color="magenta", weight=3]; 984[label="ww148",fontsize=16,color="green",shape="box"];985 -> 487[label="",style="dashed", color="red", weight=0]; 985[label="show ww142",fontsize=16,color="magenta"];985 -> 1021[label="",style="dashed", color="magenta", weight=3]; 986 -> 687[label="",style="dashed", color="red", weight=0]; 986[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1420) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww1421) ww148",fontsize=16,color="magenta"];986 -> 1022[label="",style="dashed", color="magenta", weight=3]; 986 -> 1023[label="",style="dashed", color="magenta", weight=3]; 986 -> 1024[label="",style="dashed", color="magenta", weight=3]; 986 -> 1025[label="",style="dashed", color="magenta", weight=3]; 986 -> 1026[label="",style="dashed", color="magenta", weight=3]; 987[label="ww148",fontsize=16,color="green",shape="box"];988 -> 489[label="",style="dashed", color="red", weight=0]; 988[label="show ww142",fontsize=16,color="magenta"];988 -> 1027[label="",style="dashed", color="magenta", weight=3]; 989[label="ww148",fontsize=16,color="green",shape="box"];990 -> 491[label="",style="dashed", color="red", weight=0]; 990[label="show ww142",fontsize=16,color="magenta"];990 -> 1028[label="",style="dashed", color="magenta", weight=3]; 991[label="ww148",fontsize=16,color="green",shape="box"];992 -> 493[label="",style="dashed", color="red", weight=0]; 992[label="show ww142",fontsize=16,color="magenta"];992 -> 1029[label="",style="dashed", color="magenta", weight=3]; 993[label="ww148",fontsize=16,color="green",shape="box"];994 -> 495[label="",style="dashed", color="red", weight=0]; 994[label="show ww142",fontsize=16,color="magenta"];994 -> 1030[label="",style="dashed", color="magenta", weight=3]; 995[label="ww148",fontsize=16,color="green",shape="box"];996 -> 497[label="",style="dashed", color="red", weight=0]; 996[label="show ww142",fontsize=16,color="magenta"];996 -> 1031[label="",style="dashed", color="magenta", weight=3]; 997[label="ww148",fontsize=16,color="green",shape="box"];998 -> 499[label="",style="dashed", color="red", weight=0]; 998[label="show ww142",fontsize=16,color="magenta"];998 -> 1032[label="",style="dashed", color="magenta", weight=3]; 999[label="ww148",fontsize=16,color="green",shape="box"];1000 -> 501[label="",style="dashed", color="red", weight=0]; 1000[label="show ww142",fontsize=16,color="magenta"];1000 -> 1033[label="",style="dashed", color="magenta", weight=3]; 1611 -> 1546[label="",style="dashed", color="red", weight=0]; 1611[label="primModNatS0 (Succ ww205) (Succ ww206) (primGEqNatS ww2070 ww2080)",fontsize=16,color="magenta"];1611 -> 1620[label="",style="dashed", color="magenta", weight=3]; 1611 -> 1621[label="",style="dashed", color="magenta", weight=3]; 1612[label="primModNatS0 (Succ ww205) (Succ ww206) True",fontsize=16,color="black",shape="triangle"];1612 -> 1622[label="",style="solid", color="black", weight=3]; 1613[label="primModNatS0 (Succ ww205) (Succ ww206) False",fontsize=16,color="black",shape="box"];1613 -> 1623[label="",style="solid", color="black", weight=3]; 1614 -> 1612[label="",style="dashed", color="red", weight=0]; 1614[label="primModNatS0 (Succ ww205) (Succ ww206) True",fontsize=16,color="magenta"];1670[label="primModNatS (primMinusNatS (Succ ww2100) (Succ ww2110)) (Succ ww212)",fontsize=16,color="black",shape="box"];1670 -> 1678[label="",style="solid", color="black", weight=3]; 1671[label="primModNatS (primMinusNatS (Succ ww2100) Zero) (Succ ww212)",fontsize=16,color="black",shape="box"];1671 -> 1679[label="",style="solid", color="black", weight=3]; 1672[label="primModNatS (primMinusNatS Zero (Succ ww2110)) (Succ ww212)",fontsize=16,color="black",shape="box"];1672 -> 1680[label="",style="solid", color="black", weight=3]; 1673[label="primModNatS (primMinusNatS Zero Zero) (Succ ww212)",fontsize=16,color="black",shape="box"];1673 -> 1681[label="",style="solid", color="black", weight=3]; 1615 -> 1729[label="",style="dashed", color="red", weight=0]; 1615[label="primDivNatS (primMinusNatS (Succ ww200) (Succ ww201)) (Succ (Succ ww201))",fontsize=16,color="magenta"];1615 -> 1736[label="",style="dashed", color="magenta", weight=3]; 1615 -> 1737[label="",style="dashed", color="magenta", weight=3]; 1615 -> 1738[label="",style="dashed", color="magenta", weight=3]; 1760 -> 1729[label="",style="dashed", color="red", weight=0]; 1760[label="primDivNatS (primMinusNatS ww2140 ww2150) (Succ ww216)",fontsize=16,color="magenta"];1760 -> 1764[label="",style="dashed", color="magenta", weight=3]; 1760 -> 1765[label="",style="dashed", color="magenta", weight=3]; 1761 -> 756[label="",style="dashed", color="red", weight=0]; 1761[label="primDivNatS (Succ ww2140) (Succ ww216)",fontsize=16,color="magenta"];1761 -> 1766[label="",style="dashed", color="magenta", weight=3]; 1761 -> 1767[label="",style="dashed", color="magenta", weight=3]; 1762[label="primDivNatS Zero (Succ ww216)",fontsize=16,color="black",shape="triangle"];1762 -> 1768[label="",style="solid", color="black", weight=3]; 1763 -> 1762[label="",style="dashed", color="red", weight=0]; 1763[label="primDivNatS Zero (Succ ww216)",fontsize=16,color="magenta"];1012[label="ww142",fontsize=16,color="green",shape="box"];1013[label="ww142",fontsize=16,color="green",shape="box"];1014[label="ww142",fontsize=16,color="green",shape="box"];1015[label="ww142",fontsize=16,color="green",shape="box"];1016[label="ww142",fontsize=16,color="green",shape="box"];1017[label="ww142",fontsize=16,color="green",shape="box"];1018[label="ww142",fontsize=16,color="green",shape="box"];1019[label="ww142",fontsize=16,color="green",shape="box"];1020[label="ww142",fontsize=16,color="green",shape="box"];1021[label="ww142",fontsize=16,color="green",shape="box"];1022[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1023[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1024[label="ww1421",fontsize=16,color="green",shape="box"];1025[label="ww1420",fontsize=16,color="green",shape="box"];1026[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1027[label="ww142",fontsize=16,color="green",shape="box"];1028[label="ww142",fontsize=16,color="green",shape="box"];1029[label="ww142",fontsize=16,color="green",shape="box"];1030[label="ww142",fontsize=16,color="green",shape="box"];1031[label="ww142",fontsize=16,color="green",shape="box"];1032[label="ww142",fontsize=16,color="green",shape="box"];1033[label="ww142",fontsize=16,color="green",shape="box"];1620[label="ww2070",fontsize=16,color="green",shape="box"];1621[label="ww2080",fontsize=16,color="green",shape="box"];1622 -> 1633[label="",style="dashed", color="red", weight=0]; 1622[label="primModNatS (primMinusNatS (Succ ww205) (Succ ww206)) (Succ (Succ ww206))",fontsize=16,color="magenta"];1622 -> 1646[label="",style="dashed", color="magenta", weight=3]; 1622 -> 1647[label="",style="dashed", color="magenta", weight=3]; 1622 -> 1648[label="",style="dashed", color="magenta", weight=3]; 1623[label="Succ (Succ ww205)",fontsize=16,color="green",shape="box"];1678 -> 1633[label="",style="dashed", color="red", weight=0]; 1678[label="primModNatS (primMinusNatS ww2100 ww2110) (Succ ww212)",fontsize=16,color="magenta"];1678 -> 1688[label="",style="dashed", color="magenta", weight=3]; 1678 -> 1689[label="",style="dashed", color="magenta", weight=3]; 1679 -> 798[label="",style="dashed", color="red", weight=0]; 1679[label="primModNatS (Succ ww2100) (Succ ww212)",fontsize=16,color="magenta"];1679 -> 1690[label="",style="dashed", color="magenta", weight=3]; 1679 -> 1691[label="",style="dashed", color="magenta", weight=3]; 1680[label="primModNatS Zero (Succ ww212)",fontsize=16,color="black",shape="triangle"];1680 -> 1692[label="",style="solid", color="black", weight=3]; 1681 -> 1680[label="",style="dashed", color="red", weight=0]; 1681[label="primModNatS Zero (Succ ww212)",fontsize=16,color="magenta"];1736[label="Succ ww200",fontsize=16,color="green",shape="box"];1737[label="Succ ww201",fontsize=16,color="green",shape="box"];1738[label="Succ ww201",fontsize=16,color="green",shape="box"];1764[label="ww2140",fontsize=16,color="green",shape="box"];1765[label="ww2150",fontsize=16,color="green",shape="box"];1766[label="ww2140",fontsize=16,color="green",shape="box"];1767[label="ww216",fontsize=16,color="green",shape="box"];1768[label="Zero",fontsize=16,color="green",shape="box"];1646[label="Succ ww206",fontsize=16,color="green",shape="box"];1647[label="Succ ww205",fontsize=16,color="green",shape="box"];1648[label="Succ ww206",fontsize=16,color="green",shape="box"];1688[label="ww2110",fontsize=16,color="green",shape="box"];1689[label="ww2100",fontsize=16,color="green",shape="box"];1690[label="ww2100",fontsize=16,color="green",shape="box"];1691[label="ww212",fontsize=16,color="green",shape="box"];1692[label="Zero",fontsize=16,color="green",shape="box"];} ---------------------------------------- (190) TRUE