/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) IFR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4)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) NumRed [SOUND, 0 ms] (8) HASKELL (9) Narrow [SOUND, 0 ms] (10) AND (11) QDP (12) NonTerminationLoopProof [COMPLETE, 0 ms] (13) NO (14) QDP (15) NonTerminationLoopProof [COMPLETE, 0 ms] (16) NO (17) QDP (18) NonTerminationLoopProof [COMPLETE, 0 ms] (19) NO (20) QDP (21) NonTerminationLoopProof [COMPLETE, 0 ms] (22) NO (23) QDP (24) NonTerminationLoopProof [COMPLETE, 0 ms] (25) NO (26) QDP (27) QDPSizeChangeProof [EQUIVALENT, 0 ms] (28) YES (29) QDP (30) NonTerminationLoopProof [COMPLETE, 0 ms] (31) NO (32) QDP (33) NonTerminationLoopProof [COMPLETE, 0 ms] (34) NO (35) QDP (36) DependencyGraphProof [EQUIVALENT, 0 ms] (37) QDP (38) QDPOrderProof [EQUIVALENT, 40 ms] (39) QDP (40) DependencyGraphProof [EQUIVALENT, 0 ms] (41) QDP (42) QDPSizeChangeProof [EQUIVALENT, 0 ms] (43) YES (44) QDP (45) NonTerminationLoopProof [COMPLETE, 0 ms] (46) NO (47) QDP (48) NonTerminationLoopProof [COMPLETE, 0 ms] (49) NO (50) QDP (51) NonTerminationLoopProof [COMPLETE, 0 ms] (52) NO (53) QDP (54) TransformationProof [EQUIVALENT, 7 ms] (55) QDP (56) TransformationProof [EQUIVALENT, 0 ms] (57) QDP (58) TransformationProof [EQUIVALENT, 8 ms] (59) QDP (60) TransformationProof [EQUIVALENT, 0 ms] (61) QDP (62) TransformationProof [EQUIVALENT, 0 ms] (63) QDP (64) TransformationProof [EQUIVALENT, 0 ms] (65) QDP (66) DependencyGraphProof [EQUIVALENT, 0 ms] (67) QDP (68) TransformationProof [EQUIVALENT, 0 ms] (69) QDP (70) DependencyGraphProof [EQUIVALENT, 0 ms] (71) QDP (72) TransformationProof [EQUIVALENT, 0 ms] (73) QDP (74) DependencyGraphProof [EQUIVALENT, 0 ms] (75) QDP (76) TransformationProof [EQUIVALENT, 0 ms] (77) QDP (78) DependencyGraphProof [EQUIVALENT, 0 ms] (79) QDP (80) TransformationProof [EQUIVALENT, 0 ms] (81) QDP (82) DependencyGraphProof [EQUIVALENT, 0 ms] (83) QDP (84) TransformationProof [EQUIVALENT, 0 ms] (85) QDP (86) DependencyGraphProof [EQUIVALENT, 0 ms] (87) QDP (88) TransformationProof [EQUIVALENT, 5 ms] (89) QDP (90) DependencyGraphProof [EQUIVALENT, 0 ms] (91) QDP (92) TransformationProof [EQUIVALENT, 0 ms] (93) QDP (94) DependencyGraphProof [EQUIVALENT, 0 ms] (95) QDP (96) TransformationProof [EQUIVALENT, 0 ms] (97) QDP (98) TransformationProof [EQUIVALENT, 0 ms] (99) QDP (100) DependencyGraphProof [EQUIVALENT, 0 ms] (101) QDP (102) TransformationProof [EQUIVALENT, 0 ms] (103) QDP (104) DependencyGraphProof [EQUIVALENT, 0 ms] (105) QDP (106) TransformationProof [EQUIVALENT, 0 ms] (107) QDP (108) DependencyGraphProof [EQUIVALENT, 0 ms] (109) QDP (110) TransformationProof [EQUIVALENT, 0 ms] (111) QDP (112) DependencyGraphProof [EQUIVALENT, 0 ms] (113) QDP (114) TransformationProof [EQUIVALENT, 0 ms] (115) QDP (116) DependencyGraphProof [EQUIVALENT, 0 ms] (117) QDP (118) TransformationProof [EQUIVALENT, 2 ms] (119) QDP (120) DependencyGraphProof [EQUIVALENT, 0 ms] (121) QDP (122) TransformationProof [EQUIVALENT, 0 ms] (123) QDP (124) DependencyGraphProof [EQUIVALENT, 0 ms] (125) QDP (126) TransformationProof [EQUIVALENT, 0 ms] (127) QDP (128) DependencyGraphProof [EQUIVALENT, 0 ms] (129) QDP (130) TransformationProof [EQUIVALENT, 0 ms] (131) QDP (132) DependencyGraphProof [EQUIVALENT, 0 ms] (133) QDP (134) TransformationProof [EQUIVALENT, 0 ms] (135) QDP (136) QDPSizeChangeProof [EQUIVALENT, 0 ms] (137) YES (138) QDP (139) NonTerminationLoopProof [COMPLETE, 0 ms] (140) NO (141) QDP (142) NonTerminationLoopProof [COMPLETE, 0 ms] (143) NO (144) QDP (145) NonTerminationLoopProof [COMPLETE, 0 ms] (146) NO (147) QDP (148) NonTerminationLoopProof [COMPLETE, 0 ms] (149) NO (150) QDP (151) DependencyGraphProof [EQUIVALENT, 0 ms] (152) QDP (153) QDPOrderProof [EQUIVALENT, 0 ms] (154) QDP (155) DependencyGraphProof [EQUIVALENT, 0 ms] (156) QDP (157) QDPSizeChangeProof [EQUIVALENT, 0 ms] (158) YES (159) QDP (160) NonTerminationLoopProof [COMPLETE, 0 ms] (161) NO (162) QDP (163) DependencyGraphProof [EQUIVALENT, 0 ms] (164) QDP (165) TransformationProof [EQUIVALENT, 0 ms] (166) QDP (167) UsableRulesProof [EQUIVALENT, 0 ms] (168) QDP (169) QReductionProof [EQUIVALENT, 2 ms] (170) QDP (171) MNOCProof [EQUIVALENT, 0 ms] (172) QDP (173) InductionCalculusProof [EQUIVALENT, 0 ms] (174) QDP (175) TransformationProof [EQUIVALENT, 0 ms] (176) QDP (177) DependencyGraphProof [EQUIVALENT, 0 ms] (178) QDP (179) TransformationProof [EQUIVALENT, 0 ms] (180) QDP (181) DependencyGraphProof [EQUIVALENT, 0 ms] (182) QDP (183) TransformationProof [EQUIVALENT, 0 ms] (184) QDP (185) DependencyGraphProof [EQUIVALENT, 0 ms] (186) QDP (187) TransformationProof [EQUIVALENT, 0 ms] (188) QDP (189) DependencyGraphProof [EQUIVALENT, 0 ms] (190) QDP (191) MNOCProof [EQUIVALENT, 0 ms] (192) QDP (193) InductionCalculusProof [EQUIVALENT, 0 ms] (194) QDP (195) QDP (196) NonTerminationLoopProof [COMPLETE, 0 ms] (197) NO (198) Narrow [COMPLETE, 0 ms] (199) 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) NumRed (SOUND) Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. ---------------------------------------- (8) Obligation: mainModule Main module Main where { import qualified Prelude; } ---------------------------------------- (9) Narrow (SOUND) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="show",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="show ww3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="showsPrec (Pos Zero) ww3 []",fontsize=16,color="burlywood",shape="box"];3001[label="ww3/ww30 :% ww31",fontsize=10,color="white",style="solid",shape="box"];4 -> 3001[label="",style="solid", color="burlywood", weight=9]; 3001 -> 5[label="",style="solid", color="burlywood", weight=3]; 5[label="showsPrec (Pos Zero) (ww30 :% ww31) []",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6 -> 1529[label="",style="dashed", color="red", weight=0]; 6[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww30) . (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 ww31) []",fontsize=16,color="magenta"];6 -> 1530[label="",style="dashed", color="magenta", weight=3]; 6 -> 1531[label="",style="dashed", color="magenta", weight=3]; 6 -> 1532[label="",style="dashed", color="magenta", weight=3]; 6 -> 1533[label="",style="dashed", color="magenta", weight=3]; 6 -> 1534[label="",style="dashed", color="magenta", weight=3]; 6 -> 1535[label="",style="dashed", color="magenta", weight=3]; 1530[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"];1531[label="[]",fontsize=16,color="green",shape="box"];1532[label="ww31",fontsize=16,color="green",shape="box"];1533[label="ww30",fontsize=16,color="green",shape="box"];1534[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"];1535[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"];1529[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) ww196",fontsize=16,color="black",shape="triangle"];1529 -> 1542[label="",style="solid", color="black", weight=3]; 1542[label="showParen0 ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww196",fontsize=16,color="black",shape="box"];1542 -> 1543[label="",style="solid", color="black", weight=3]; 1543[label="showParen0 ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww196",fontsize=16,color="black",shape="box"];1543 -> 1544[label="",style="solid", color="black", weight=3]; 1544[label="showParen0 ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww196",fontsize=16,color="black",shape="box"];1544 -> 1545[label="",style="solid", color="black", weight=3]; 1545[label="showParen0 ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww196",fontsize=16,color="black",shape="box"];1545 -> 1546[label="",style="solid", color="black", weight=3]; 1546[label="showParen0 ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) (LT == GT) ww196",fontsize=16,color="black",shape="box"];1546 -> 1547[label="",style="solid", color="black", weight=3]; 1547[label="showParen0 ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) False ww196",fontsize=16,color="black",shape="box"];1547 -> 1548[label="",style="solid", color="black", weight=3]; 1548[label="(shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="black",shape="box"];1548 -> 1549[label="",style="solid", color="black", weight=3]; 1549[label="shows ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1549 -> 1550[label="",style="solid", color="black", weight=3]; 1550[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="blue",shape="box"];3002[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3002[label="",style="solid", color="blue", weight=9]; 3002 -> 1551[label="",style="solid", color="blue", weight=3]; 3003[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3003[label="",style="solid", color="blue", weight=9]; 3003 -> 1552[label="",style="solid", color="blue", weight=3]; 3004[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3004[label="",style="solid", color="blue", weight=9]; 3004 -> 1553[label="",style="solid", color="blue", weight=3]; 3005[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3005[label="",style="solid", color="blue", weight=9]; 3005 -> 1554[label="",style="solid", color="blue", weight=3]; 3006[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3006[label="",style="solid", color="blue", weight=9]; 3006 -> 1555[label="",style="solid", color="blue", weight=3]; 3007[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3007[label="",style="solid", color="blue", weight=9]; 3007 -> 1556[label="",style="solid", color="blue", weight=3]; 3008[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3008[label="",style="solid", color="blue", weight=9]; 3008 -> 1557[label="",style="solid", color="blue", weight=3]; 3009[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3009[label="",style="solid", color="blue", weight=9]; 3009 -> 1558[label="",style="solid", color="blue", weight=3]; 3010[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3010[label="",style="solid", color="blue", weight=9]; 3010 -> 1559[label="",style="solid", color="blue", weight=3]; 3011[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3011[label="",style="solid", color="blue", weight=9]; 3011 -> 1560[label="",style="solid", color="blue", weight=3]; 3012[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3012[label="",style="solid", color="blue", weight=9]; 3012 -> 1561[label="",style="solid", color="blue", weight=3]; 3013[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3013[label="",style="solid", color="blue", weight=9]; 3013 -> 1562[label="",style="solid", color="blue", weight=3]; 3014[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3014[label="",style="solid", color="blue", weight=9]; 3014 -> 1563[label="",style="solid", color="blue", weight=3]; 3015[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3015[label="",style="solid", color="blue", weight=9]; 3015 -> 1564[label="",style="solid", color="blue", weight=3]; 3016[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3016[label="",style="solid", color="blue", weight=9]; 3016 -> 1565[label="",style="solid", color="blue", weight=3]; 3017[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3017[label="",style="solid", color="blue", weight=9]; 3017 -> 1566[label="",style="solid", color="blue", weight=3]; 3018[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3018[label="",style="solid", color="blue", weight=9]; 3018 -> 1567[label="",style="solid", color="blue", weight=3]; 3019[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3019[label="",style="solid", color="blue", weight=9]; 3019 -> 1568[label="",style="solid", color="blue", weight=3]; 1551[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1551 -> 1569[label="",style="solid", color="black", weight=3]; 1552[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1552 -> 1570[label="",style="solid", color="black", weight=3]; 1553[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1553 -> 1571[label="",style="solid", color="black", weight=3]; 1554[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1554 -> 1572[label="",style="solid", color="black", weight=3]; 1555[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1555 -> 1573[label="",style="solid", color="black", weight=3]; 1556[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1556 -> 1574[label="",style="solid", color="black", weight=3]; 1557[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1557 -> 1575[label="",style="solid", color="black", weight=3]; 1558[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1558 -> 1576[label="",style="solid", color="black", weight=3]; 1559[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1559 -> 1577[label="",style="solid", color="black", weight=3]; 1560[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1560 -> 1578[label="",style="solid", color="black", weight=3]; 1561[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="burlywood",shape="box"];3020[label="ww191/ww1910 :% ww1911",fontsize=10,color="white",style="solid",shape="box"];1561 -> 3020[label="",style="solid", color="burlywood", weight=9]; 3020 -> 1579[label="",style="solid", color="burlywood", weight=3]; 1562[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1562 -> 1580[label="",style="solid", color="black", weight=3]; 1563[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1563 -> 1581[label="",style="solid", color="black", weight=3]; 1564[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1564 -> 1582[label="",style="solid", color="black", weight=3]; 1565[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1565 -> 1583[label="",style="solid", color="black", weight=3]; 1566[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1566 -> 1584[label="",style="solid", color="black", weight=3]; 1567[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1567 -> 1585[label="",style="solid", color="black", weight=3]; 1568[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1568 -> 1586[label="",style="solid", color="black", weight=3]; 1569 -> 1741[label="",style="dashed", color="red", weight=0]; 1569[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1569 -> 1742[label="",style="dashed", color="magenta", weight=3]; 1569 -> 1743[label="",style="dashed", color="magenta", weight=3]; 1570 -> 1741[label="",style="dashed", color="red", weight=0]; 1570[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1570 -> 1744[label="",style="dashed", color="magenta", weight=3]; 1570 -> 1745[label="",style="dashed", color="magenta", weight=3]; 1571 -> 1741[label="",style="dashed", color="red", weight=0]; 1571[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1571 -> 1746[label="",style="dashed", color="magenta", weight=3]; 1571 -> 1747[label="",style="dashed", color="magenta", weight=3]; 1572 -> 1741[label="",style="dashed", color="red", weight=0]; 1572[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1572 -> 1748[label="",style="dashed", color="magenta", weight=3]; 1572 -> 1749[label="",style="dashed", color="magenta", weight=3]; 1573 -> 1741[label="",style="dashed", color="red", weight=0]; 1573[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1573 -> 1750[label="",style="dashed", color="magenta", weight=3]; 1573 -> 1751[label="",style="dashed", color="magenta", weight=3]; 1574 -> 1741[label="",style="dashed", color="red", weight=0]; 1574[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1574 -> 1752[label="",style="dashed", color="magenta", weight=3]; 1574 -> 1753[label="",style="dashed", color="magenta", weight=3]; 1575 -> 1741[label="",style="dashed", color="red", weight=0]; 1575[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1575 -> 1754[label="",style="dashed", color="magenta", weight=3]; 1575 -> 1755[label="",style="dashed", color="magenta", weight=3]; 1576 -> 1741[label="",style="dashed", color="red", weight=0]; 1576[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1576 -> 1756[label="",style="dashed", color="magenta", weight=3]; 1576 -> 1757[label="",style="dashed", color="magenta", weight=3]; 1577 -> 1741[label="",style="dashed", color="red", weight=0]; 1577[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1577 -> 1758[label="",style="dashed", color="magenta", weight=3]; 1577 -> 1759[label="",style="dashed", color="magenta", weight=3]; 1578 -> 1741[label="",style="dashed", color="red", weight=0]; 1578[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1578 -> 1760[label="",style="dashed", color="magenta", weight=3]; 1578 -> 1761[label="",style="dashed", color="magenta", weight=3]; 1579[label="showsPrec (Pos Zero) (ww1910 :% ww1911) ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1579 -> 1597[label="",style="solid", color="black", weight=3]; 1580 -> 1741[label="",style="dashed", color="red", weight=0]; 1580[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1580 -> 1762[label="",style="dashed", color="magenta", weight=3]; 1580 -> 1763[label="",style="dashed", color="magenta", weight=3]; 1581 -> 1741[label="",style="dashed", color="red", weight=0]; 1581[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1581 -> 1764[label="",style="dashed", color="magenta", weight=3]; 1581 -> 1765[label="",style="dashed", color="magenta", weight=3]; 1582 -> 1741[label="",style="dashed", color="red", weight=0]; 1582[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1582 -> 1766[label="",style="dashed", color="magenta", weight=3]; 1582 -> 1767[label="",style="dashed", color="magenta", weight=3]; 1583 -> 1741[label="",style="dashed", color="red", weight=0]; 1583[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1583 -> 1768[label="",style="dashed", color="magenta", weight=3]; 1583 -> 1769[label="",style="dashed", color="magenta", weight=3]; 1584 -> 1741[label="",style="dashed", color="red", weight=0]; 1584[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1584 -> 1770[label="",style="dashed", color="magenta", weight=3]; 1584 -> 1771[label="",style="dashed", color="magenta", weight=3]; 1585 -> 1741[label="",style="dashed", color="red", weight=0]; 1585[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1585 -> 1772[label="",style="dashed", color="magenta", weight=3]; 1585 -> 1773[label="",style="dashed", color="magenta", weight=3]; 1586 -> 1741[label="",style="dashed", color="red", weight=0]; 1586[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1586 -> 1774[label="",style="dashed", color="magenta", weight=3]; 1586 -> 1775[label="",style="dashed", color="magenta", weight=3]; 1742[label="show ww191",fontsize=16,color="black",shape="triangle"];1742 -> 1971[label="",style="solid", color="black", weight=3]; 1743 -> 1616[label="",style="dashed", color="red", weight=0]; 1743[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1741[label="ww237 ++ ww197",fontsize=16,color="burlywood",shape="triangle"];3021[label="ww237/ww2370 : ww2371",fontsize=10,color="white",style="solid",shape="box"];1741 -> 3021[label="",style="solid", color="burlywood", weight=9]; 3021 -> 1972[label="",style="solid", color="burlywood", weight=3]; 3022[label="ww237/[]",fontsize=10,color="white",style="solid",shape="box"];1741 -> 3022[label="",style="solid", color="burlywood", weight=9]; 3022 -> 1973[label="",style="solid", color="burlywood", weight=3]; 1744[label="show ww191",fontsize=16,color="black",shape="triangle"];1744 -> 1974[label="",style="solid", color="black", weight=3]; 1745 -> 1616[label="",style="dashed", color="red", weight=0]; 1745[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1746[label="show ww191",fontsize=16,color="black",shape="triangle"];1746 -> 1975[label="",style="solid", color="black", weight=3]; 1747 -> 1616[label="",style="dashed", color="red", weight=0]; 1747[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1748[label="show ww191",fontsize=16,color="black",shape="triangle"];1748 -> 1976[label="",style="solid", color="black", weight=3]; 1749 -> 1616[label="",style="dashed", color="red", weight=0]; 1749[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1750[label="show ww191",fontsize=16,color="black",shape="triangle"];1750 -> 1977[label="",style="solid", color="black", weight=3]; 1751 -> 1616[label="",style="dashed", color="red", weight=0]; 1751[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1752[label="show ww191",fontsize=16,color="black",shape="triangle"];1752 -> 1978[label="",style="solid", color="black", weight=3]; 1753 -> 1616[label="",style="dashed", color="red", weight=0]; 1753[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1754[label="show ww191",fontsize=16,color="black",shape="triangle"];1754 -> 1979[label="",style="solid", color="black", weight=3]; 1755 -> 1616[label="",style="dashed", color="red", weight=0]; 1755[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1756[label="show ww191",fontsize=16,color="black",shape="triangle"];1756 -> 1980[label="",style="solid", color="black", weight=3]; 1757 -> 1616[label="",style="dashed", color="red", weight=0]; 1757[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1758[label="show ww191",fontsize=16,color="black",shape="triangle"];1758 -> 1981[label="",style="solid", color="black", weight=3]; 1759 -> 1616[label="",style="dashed", color="red", weight=0]; 1759[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1760[label="show ww191",fontsize=16,color="black",shape="triangle"];1760 -> 1982[label="",style="solid", color="black", weight=3]; 1761 -> 1616[label="",style="dashed", color="red", weight=0]; 1761[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1597 -> 1529[label="",style="dashed", color="red", weight=0]; 1597[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1910) . (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 ww1911) ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="magenta"];1597 -> 1615[label="",style="dashed", color="magenta", weight=3]; 1597 -> 1616[label="",style="dashed", color="magenta", weight=3]; 1597 -> 1617[label="",style="dashed", color="magenta", weight=3]; 1597 -> 1618[label="",style="dashed", color="magenta", weight=3]; 1597 -> 1619[label="",style="dashed", color="magenta", weight=3]; 1597 -> 1620[label="",style="dashed", color="magenta", weight=3]; 1762[label="show ww191",fontsize=16,color="black",shape="triangle"];1762 -> 1983[label="",style="solid", color="black", weight=3]; 1763 -> 1616[label="",style="dashed", color="red", weight=0]; 1763[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1764[label="show ww191",fontsize=16,color="black",shape="triangle"];1764 -> 1984[label="",style="solid", color="black", weight=3]; 1765 -> 1616[label="",style="dashed", color="red", weight=0]; 1765[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1766[label="show ww191",fontsize=16,color="black",shape="triangle"];1766 -> 1985[label="",style="solid", color="black", weight=3]; 1767 -> 1616[label="",style="dashed", color="red", weight=0]; 1767[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1768[label="show ww191",fontsize=16,color="black",shape="triangle"];1768 -> 1986[label="",style="solid", color="black", weight=3]; 1769 -> 1616[label="",style="dashed", color="red", weight=0]; 1769[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1770[label="show ww191",fontsize=16,color="black",shape="triangle"];1770 -> 1987[label="",style="solid", color="black", weight=3]; 1771 -> 1616[label="",style="dashed", color="red", weight=0]; 1771[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1772[label="show ww191",fontsize=16,color="black",shape="triangle"];1772 -> 1988[label="",style="solid", color="black", weight=3]; 1773 -> 1616[label="",style="dashed", color="red", weight=0]; 1773[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1774[label="show ww191",fontsize=16,color="black",shape="triangle"];1774 -> 1989[label="",style="solid", color="black", weight=3]; 1775 -> 1616[label="",style="dashed", color="red", weight=0]; 1775[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1971[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1971 -> 1991[label="",style="solid", color="black", weight=3]; 1616[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="black",shape="triangle"];1616 -> 1639[label="",style="solid", color="black", weight=3]; 1972[label="(ww2370 : ww2371) ++ ww197",fontsize=16,color="black",shape="box"];1972 -> 1992[label="",style="solid", color="black", weight=3]; 1973[label="[] ++ ww197",fontsize=16,color="black",shape="box"];1973 -> 1993[label="",style="solid", color="black", weight=3]; 1974[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1974 -> 1994[label="",style="solid", color="black", weight=3]; 1975[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1975 -> 1995[label="",style="solid", color="black", weight=3]; 1976[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1976 -> 1996[label="",style="solid", color="black", weight=3]; 1977[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1977 -> 1997[label="",style="solid", color="black", weight=3]; 1978[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1978 -> 1998[label="",style="solid", color="black", weight=3]; 1979[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1979 -> 1999[label="",style="solid", color="black", weight=3]; 1980[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1980 -> 2000[label="",style="solid", color="black", weight=3]; 1981[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1981 -> 2001[label="",style="solid", color="black", weight=3]; 1982[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1982 -> 2002[label="",style="solid", color="black", weight=3]; 1615[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"];1617[label="ww1911",fontsize=16,color="green",shape="box"];1618[label="ww1910",fontsize=16,color="green",shape="box"];1619[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"];1620[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"];1983[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1983 -> 2003[label="",style="solid", color="black", weight=3]; 1984[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1984 -> 2004[label="",style="solid", color="black", weight=3]; 1985[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1985 -> 2005[label="",style="solid", color="black", weight=3]; 1986[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1986 -> 2006[label="",style="solid", color="black", weight=3]; 1987[label="primShowInt ww191",fontsize=16,color="burlywood",shape="triangle"];3023[label="ww191/Pos ww1910",fontsize=10,color="white",style="solid",shape="box"];1987 -> 3023[label="",style="solid", color="burlywood", weight=9]; 3023 -> 2007[label="",style="solid", color="burlywood", weight=3]; 3024[label="ww191/Neg ww1910",fontsize=10,color="white",style="solid",shape="box"];1987 -> 3024[label="",style="solid", color="burlywood", weight=9]; 3024 -> 2008[label="",style="solid", color="burlywood", weight=3]; 1988[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1988 -> 2009[label="",style="solid", color="black", weight=3]; 1989[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1989 -> 2010[label="",style="solid", color="black", weight=3]; 1991 -> 1741[label="",style="dashed", color="red", weight=0]; 1991[label="show ww191 ++ []",fontsize=16,color="magenta"];1991 -> 2029[label="",style="dashed", color="magenta", weight=3]; 1991 -> 2030[label="",style="dashed", color="magenta", weight=3]; 1639[label="showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : []) (shows ww195 ww196)",fontsize=16,color="black",shape="box"];1639 -> 1675[label="",style="solid", color="black", weight=3]; 1992[label="ww2370 : ww2371 ++ ww197",fontsize=16,color="green",shape="box"];1992 -> 2031[label="",style="dashed", color="green", weight=3]; 1993[label="ww197",fontsize=16,color="green",shape="box"];1994 -> 1741[label="",style="dashed", color="red", weight=0]; 1994[label="show ww191 ++ []",fontsize=16,color="magenta"];1994 -> 2032[label="",style="dashed", color="magenta", weight=3]; 1994 -> 2033[label="",style="dashed", color="magenta", weight=3]; 1995 -> 1741[label="",style="dashed", color="red", weight=0]; 1995[label="show ww191 ++ []",fontsize=16,color="magenta"];1995 -> 2034[label="",style="dashed", color="magenta", weight=3]; 1995 -> 2035[label="",style="dashed", color="magenta", weight=3]; 1996 -> 1741[label="",style="dashed", color="red", weight=0]; 1996[label="show ww191 ++ []",fontsize=16,color="magenta"];1996 -> 2036[label="",style="dashed", color="magenta", weight=3]; 1996 -> 2037[label="",style="dashed", color="magenta", weight=3]; 1997 -> 1741[label="",style="dashed", color="red", weight=0]; 1997[label="show ww191 ++ []",fontsize=16,color="magenta"];1997 -> 2038[label="",style="dashed", color="magenta", weight=3]; 1997 -> 2039[label="",style="dashed", color="magenta", weight=3]; 1998 -> 1741[label="",style="dashed", color="red", weight=0]; 1998[label="show ww191 ++ []",fontsize=16,color="magenta"];1998 -> 2040[label="",style="dashed", color="magenta", weight=3]; 1998 -> 2041[label="",style="dashed", color="magenta", weight=3]; 1999 -> 1741[label="",style="dashed", color="red", weight=0]; 1999[label="show ww191 ++ []",fontsize=16,color="magenta"];1999 -> 2042[label="",style="dashed", color="magenta", weight=3]; 1999 -> 2043[label="",style="dashed", color="magenta", weight=3]; 2000 -> 1741[label="",style="dashed", color="red", weight=0]; 2000[label="show ww191 ++ []",fontsize=16,color="magenta"];2000 -> 2044[label="",style="dashed", color="magenta", weight=3]; 2000 -> 2045[label="",style="dashed", color="magenta", weight=3]; 2001 -> 1741[label="",style="dashed", color="red", weight=0]; 2001[label="show ww191 ++ []",fontsize=16,color="magenta"];2001 -> 2046[label="",style="dashed", color="magenta", weight=3]; 2001 -> 2047[label="",style="dashed", color="magenta", weight=3]; 2002 -> 1741[label="",style="dashed", color="red", weight=0]; 2002[label="show ww191 ++ []",fontsize=16,color="magenta"];2002 -> 2048[label="",style="dashed", color="magenta", weight=3]; 2002 -> 2049[label="",style="dashed", color="magenta", weight=3]; 2003 -> 1741[label="",style="dashed", color="red", weight=0]; 2003[label="show ww191 ++ []",fontsize=16,color="magenta"];2003 -> 2050[label="",style="dashed", color="magenta", weight=3]; 2003 -> 2051[label="",style="dashed", color="magenta", weight=3]; 2004 -> 1741[label="",style="dashed", color="red", weight=0]; 2004[label="show ww191 ++ []",fontsize=16,color="magenta"];2004 -> 2052[label="",style="dashed", color="magenta", weight=3]; 2004 -> 2053[label="",style="dashed", color="magenta", weight=3]; 2005 -> 1741[label="",style="dashed", color="red", weight=0]; 2005[label="show ww191 ++ []",fontsize=16,color="magenta"];2005 -> 2054[label="",style="dashed", color="magenta", weight=3]; 2005 -> 2055[label="",style="dashed", color="magenta", weight=3]; 2006 -> 1741[label="",style="dashed", color="red", weight=0]; 2006[label="show ww191 ++ []",fontsize=16,color="magenta"];2006 -> 2056[label="",style="dashed", color="magenta", weight=3]; 2006 -> 2057[label="",style="dashed", color="magenta", weight=3]; 2007[label="primShowInt (Pos ww1910)",fontsize=16,color="burlywood",shape="box"];3025[label="ww1910/Succ ww19100",fontsize=10,color="white",style="solid",shape="box"];2007 -> 3025[label="",style="solid", color="burlywood", weight=9]; 3025 -> 2058[label="",style="solid", color="burlywood", weight=3]; 3026[label="ww1910/Zero",fontsize=10,color="white",style="solid",shape="box"];2007 -> 3026[label="",style="solid", color="burlywood", weight=9]; 3026 -> 2059[label="",style="solid", color="burlywood", weight=3]; 2008[label="primShowInt (Neg ww1910)",fontsize=16,color="black",shape="box"];2008 -> 2060[label="",style="solid", color="black", weight=3]; 2009 -> 1741[label="",style="dashed", color="red", weight=0]; 2009[label="show ww191 ++ []",fontsize=16,color="magenta"];2009 -> 2061[label="",style="dashed", color="magenta", weight=3]; 2009 -> 2062[label="",style="dashed", color="magenta", weight=3]; 2010 -> 1741[label="",style="dashed", color="red", weight=0]; 2010[label="show ww191 ++ []",fontsize=16,color="magenta"];2010 -> 2063[label="",style="dashed", color="magenta", weight=3]; 2010 -> 2064[label="",style="dashed", color="magenta", weight=3]; 2029 -> 1742[label="",style="dashed", color="red", weight=0]; 2029[label="show ww191",fontsize=16,color="magenta"];2030[label="[]",fontsize=16,color="green",shape="box"];1675 -> 1741[label="",style="dashed", color="red", weight=0]; 1675[label="(++) (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : []) shows ww195 ww196",fontsize=16,color="magenta"];1675 -> 1895[label="",style="dashed", color="magenta", weight=3]; 1675 -> 1896[label="",style="dashed", color="magenta", weight=3]; 2031 -> 1741[label="",style="dashed", color="red", weight=0]; 2031[label="ww2371 ++ ww197",fontsize=16,color="magenta"];2031 -> 2083[label="",style="dashed", color="magenta", weight=3]; 2032 -> 1744[label="",style="dashed", color="red", weight=0]; 2032[label="show ww191",fontsize=16,color="magenta"];2033[label="[]",fontsize=16,color="green",shape="box"];2034 -> 1746[label="",style="dashed", color="red", weight=0]; 2034[label="show ww191",fontsize=16,color="magenta"];2035[label="[]",fontsize=16,color="green",shape="box"];2036 -> 1748[label="",style="dashed", color="red", weight=0]; 2036[label="show ww191",fontsize=16,color="magenta"];2037[label="[]",fontsize=16,color="green",shape="box"];2038 -> 1750[label="",style="dashed", color="red", weight=0]; 2038[label="show ww191",fontsize=16,color="magenta"];2039[label="[]",fontsize=16,color="green",shape="box"];2040 -> 1752[label="",style="dashed", color="red", weight=0]; 2040[label="show ww191",fontsize=16,color="magenta"];2041[label="[]",fontsize=16,color="green",shape="box"];2042 -> 1754[label="",style="dashed", color="red", weight=0]; 2042[label="show ww191",fontsize=16,color="magenta"];2043[label="[]",fontsize=16,color="green",shape="box"];2044 -> 1756[label="",style="dashed", color="red", weight=0]; 2044[label="show ww191",fontsize=16,color="magenta"];2045[label="[]",fontsize=16,color="green",shape="box"];2046 -> 1758[label="",style="dashed", color="red", weight=0]; 2046[label="show ww191",fontsize=16,color="magenta"];2047[label="[]",fontsize=16,color="green",shape="box"];2048 -> 1760[label="",style="dashed", color="red", weight=0]; 2048[label="show ww191",fontsize=16,color="magenta"];2049[label="[]",fontsize=16,color="green",shape="box"];2050 -> 1762[label="",style="dashed", color="red", weight=0]; 2050[label="show ww191",fontsize=16,color="magenta"];2051[label="[]",fontsize=16,color="green",shape="box"];2052 -> 1764[label="",style="dashed", color="red", weight=0]; 2052[label="show ww191",fontsize=16,color="magenta"];2053[label="[]",fontsize=16,color="green",shape="box"];2054 -> 1766[label="",style="dashed", color="red", weight=0]; 2054[label="show ww191",fontsize=16,color="magenta"];2055[label="[]",fontsize=16,color="green",shape="box"];2056 -> 1768[label="",style="dashed", color="red", weight=0]; 2056[label="show ww191",fontsize=16,color="magenta"];2057[label="[]",fontsize=16,color="green",shape="box"];2058[label="primShowInt (Pos (Succ ww19100))",fontsize=16,color="black",shape="box"];2058 -> 2084[label="",style="solid", color="black", weight=3]; 2059[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];2059 -> 2085[label="",style="solid", color="black", weight=3]; 2060[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 ww1910)",fontsize=16,color="green",shape="box"];2060 -> 2086[label="",style="dashed", color="green", weight=3]; 2061 -> 1772[label="",style="dashed", color="red", weight=0]; 2061[label="show ww191",fontsize=16,color="magenta"];2062[label="[]",fontsize=16,color="green",shape="box"];2063 -> 1774[label="",style="dashed", color="red", weight=0]; 2063[label="show ww191",fontsize=16,color="magenta"];2064[label="[]",fontsize=16,color="green",shape="box"];1895[label="Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : []",fontsize=16,color="green",shape="box"];1896[label="shows ww195 ww196",fontsize=16,color="black",shape="box"];1896 -> 1990[label="",style="solid", color="black", weight=3]; 2083[label="ww2371",fontsize=16,color="green",shape="box"];2084 -> 1741[label="",style="dashed", color="red", weight=0]; 2084[label="primShowInt (div Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];2084 -> 2122[label="",style="dashed", color="magenta", weight=3]; 2084 -> 2123[label="",style="dashed", color="magenta", weight=3]; 2085[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"];2086 -> 1987[label="",style="dashed", color="red", weight=0]; 2086[label="primShowInt (Pos ww1910)",fontsize=16,color="magenta"];2086 -> 2124[label="",style="dashed", color="magenta", weight=3]; 1990[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="blue",shape="box"];3027[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3027[label="",style="solid", color="blue", weight=9]; 3027 -> 2011[label="",style="solid", color="blue", weight=3]; 3028[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3028[label="",style="solid", color="blue", weight=9]; 3028 -> 2012[label="",style="solid", color="blue", weight=3]; 3029[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3029[label="",style="solid", color="blue", weight=9]; 3029 -> 2013[label="",style="solid", color="blue", weight=3]; 3030[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3030[label="",style="solid", color="blue", weight=9]; 3030 -> 2014[label="",style="solid", color="blue", weight=3]; 3031[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3031[label="",style="solid", color="blue", weight=9]; 3031 -> 2015[label="",style="solid", color="blue", weight=3]; 3032[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3032[label="",style="solid", color="blue", weight=9]; 3032 -> 2016[label="",style="solid", color="blue", weight=3]; 3033[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3033[label="",style="solid", color="blue", weight=9]; 3033 -> 2017[label="",style="solid", color="blue", weight=3]; 3034[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3034[label="",style="solid", color="blue", weight=9]; 3034 -> 2018[label="",style="solid", color="blue", weight=3]; 3035[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3035[label="",style="solid", color="blue", weight=9]; 3035 -> 2019[label="",style="solid", color="blue", weight=3]; 3036[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3036[label="",style="solid", color="blue", weight=9]; 3036 -> 2020[label="",style="solid", color="blue", weight=3]; 3037[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3037[label="",style="solid", color="blue", weight=9]; 3037 -> 2021[label="",style="solid", color="blue", weight=3]; 3038[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3038[label="",style="solid", color="blue", weight=9]; 3038 -> 2022[label="",style="solid", color="blue", weight=3]; 3039[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3039[label="",style="solid", color="blue", weight=9]; 3039 -> 2023[label="",style="solid", color="blue", weight=3]; 3040[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3040[label="",style="solid", color="blue", weight=9]; 3040 -> 2024[label="",style="solid", color="blue", weight=3]; 3041[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3041[label="",style="solid", color="blue", weight=9]; 3041 -> 2025[label="",style="solid", color="blue", weight=3]; 3042[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3042[label="",style="solid", color="blue", weight=9]; 3042 -> 2026[label="",style="solid", color="blue", weight=3]; 3043[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3043[label="",style="solid", color="blue", weight=9]; 3043 -> 2027[label="",style="solid", color="blue", weight=3]; 3044[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3044[label="",style="solid", color="blue", weight=9]; 3044 -> 2028[label="",style="solid", color="blue", weight=3]; 2122 -> 1987[label="",style="dashed", color="red", weight=0]; 2122[label="primShowInt (div Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];2122 -> 2147[label="",style="dashed", color="magenta", weight=3]; 2123[label="toEnum (mod Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];2123 -> 2148[label="",style="dashed", color="green", weight=3]; 2124[label="Pos ww1910",fontsize=16,color="green",shape="box"];2011[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2011 -> 2065[label="",style="solid", color="black", weight=3]; 2012[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2012 -> 2066[label="",style="solid", color="black", weight=3]; 2013[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2013 -> 2067[label="",style="solid", color="black", weight=3]; 2014[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2014 -> 2068[label="",style="solid", color="black", weight=3]; 2015[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2015 -> 2069[label="",style="solid", color="black", weight=3]; 2016[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2016 -> 2070[label="",style="solid", color="black", weight=3]; 2017[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2017 -> 2071[label="",style="solid", color="black", weight=3]; 2018[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2018 -> 2072[label="",style="solid", color="black", weight=3]; 2019[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2019 -> 2073[label="",style="solid", color="black", weight=3]; 2020[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2020 -> 2074[label="",style="solid", color="black", weight=3]; 2021[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="burlywood",shape="box"];3045[label="ww195/ww1950 :% ww1951",fontsize=10,color="white",style="solid",shape="box"];2021 -> 3045[label="",style="solid", color="burlywood", weight=9]; 3045 -> 2075[label="",style="solid", color="burlywood", weight=3]; 2022[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2022 -> 2076[label="",style="solid", color="black", weight=3]; 2023[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2023 -> 2077[label="",style="solid", color="black", weight=3]; 2024[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2024 -> 2078[label="",style="solid", color="black", weight=3]; 2025[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2025 -> 2079[label="",style="solid", color="black", weight=3]; 2026[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2026 -> 2080[label="",style="solid", color="black", weight=3]; 2027[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2027 -> 2081[label="",style="solid", color="black", weight=3]; 2028[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2028 -> 2082[label="",style="solid", color="black", weight=3]; 2147 -> 2149[label="",style="dashed", color="red", weight=0]; 2147[label="div Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];2147 -> 2150[label="",style="dashed", color="magenta", weight=3]; 2147 -> 2151[label="",style="dashed", color="magenta", weight=3]; 2148[label="toEnum (mod Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];2148 -> 2166[label="",style="solid", color="black", weight=3]; 2065 -> 1741[label="",style="dashed", color="red", weight=0]; 2065[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2065 -> 2087[label="",style="dashed", color="magenta", weight=3]; 2065 -> 2088[label="",style="dashed", color="magenta", weight=3]; 2066 -> 1741[label="",style="dashed", color="red", weight=0]; 2066[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2066 -> 2089[label="",style="dashed", color="magenta", weight=3]; 2066 -> 2090[label="",style="dashed", color="magenta", weight=3]; 2067 -> 1741[label="",style="dashed", color="red", weight=0]; 2067[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2067 -> 2091[label="",style="dashed", color="magenta", weight=3]; 2067 -> 2092[label="",style="dashed", color="magenta", weight=3]; 2068 -> 1741[label="",style="dashed", color="red", weight=0]; 2068[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2068 -> 2093[label="",style="dashed", color="magenta", weight=3]; 2068 -> 2094[label="",style="dashed", color="magenta", weight=3]; 2069 -> 1741[label="",style="dashed", color="red", weight=0]; 2069[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2069 -> 2095[label="",style="dashed", color="magenta", weight=3]; 2069 -> 2096[label="",style="dashed", color="magenta", weight=3]; 2070 -> 1741[label="",style="dashed", color="red", weight=0]; 2070[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2070 -> 2097[label="",style="dashed", color="magenta", weight=3]; 2070 -> 2098[label="",style="dashed", color="magenta", weight=3]; 2071 -> 1741[label="",style="dashed", color="red", weight=0]; 2071[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2071 -> 2099[label="",style="dashed", color="magenta", weight=3]; 2071 -> 2100[label="",style="dashed", color="magenta", weight=3]; 2072 -> 1741[label="",style="dashed", color="red", weight=0]; 2072[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2072 -> 2101[label="",style="dashed", color="magenta", weight=3]; 2072 -> 2102[label="",style="dashed", color="magenta", weight=3]; 2073 -> 1741[label="",style="dashed", color="red", weight=0]; 2073[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2073 -> 2103[label="",style="dashed", color="magenta", weight=3]; 2073 -> 2104[label="",style="dashed", color="magenta", weight=3]; 2074 -> 1741[label="",style="dashed", color="red", weight=0]; 2074[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2074 -> 2105[label="",style="dashed", color="magenta", weight=3]; 2074 -> 2106[label="",style="dashed", color="magenta", weight=3]; 2075[label="showsPrec (Pos Zero) (ww1950 :% ww1951) ww196",fontsize=16,color="black",shape="box"];2075 -> 2107[label="",style="solid", color="black", weight=3]; 2076 -> 1741[label="",style="dashed", color="red", weight=0]; 2076[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2076 -> 2108[label="",style="dashed", color="magenta", weight=3]; 2076 -> 2109[label="",style="dashed", color="magenta", weight=3]; 2077 -> 1741[label="",style="dashed", color="red", weight=0]; 2077[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2077 -> 2110[label="",style="dashed", color="magenta", weight=3]; 2077 -> 2111[label="",style="dashed", color="magenta", weight=3]; 2078 -> 1741[label="",style="dashed", color="red", weight=0]; 2078[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2078 -> 2112[label="",style="dashed", color="magenta", weight=3]; 2078 -> 2113[label="",style="dashed", color="magenta", weight=3]; 2079 -> 1741[label="",style="dashed", color="red", weight=0]; 2079[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2079 -> 2114[label="",style="dashed", color="magenta", weight=3]; 2079 -> 2115[label="",style="dashed", color="magenta", weight=3]; 2080 -> 1741[label="",style="dashed", color="red", weight=0]; 2080[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2080 -> 2116[label="",style="dashed", color="magenta", weight=3]; 2080 -> 2117[label="",style="dashed", color="magenta", weight=3]; 2081 -> 1741[label="",style="dashed", color="red", weight=0]; 2081[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2081 -> 2118[label="",style="dashed", color="magenta", weight=3]; 2081 -> 2119[label="",style="dashed", color="magenta", weight=3]; 2082 -> 1741[label="",style="dashed", color="red", weight=0]; 2082[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2082 -> 2120[label="",style="dashed", color="magenta", weight=3]; 2082 -> 2121[label="",style="dashed", color="magenta", weight=3]; 2150[label="ww19100",fontsize=16,color="green",shape="box"];2151[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];2149[label="div Pos (Succ ww239) Pos (Succ ww240)",fontsize=16,color="black",shape="triangle"];2149 -> 2155[label="",style="solid", color="black", weight=3]; 2166 -> 2177[label="",style="dashed", color="red", weight=0]; 2166[label="primIntToChar (mod Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];2166 -> 2178[label="",style="dashed", color="magenta", weight=3]; 2166 -> 2179[label="",style="dashed", color="magenta", weight=3]; 2087 -> 1742[label="",style="dashed", color="red", weight=0]; 2087[label="show ww195",fontsize=16,color="magenta"];2087 -> 2125[label="",style="dashed", color="magenta", weight=3]; 2088[label="ww196",fontsize=16,color="green",shape="box"];2089 -> 1744[label="",style="dashed", color="red", weight=0]; 2089[label="show ww195",fontsize=16,color="magenta"];2089 -> 2126[label="",style="dashed", color="magenta", weight=3]; 2090[label="ww196",fontsize=16,color="green",shape="box"];2091 -> 1746[label="",style="dashed", color="red", weight=0]; 2091[label="show ww195",fontsize=16,color="magenta"];2091 -> 2127[label="",style="dashed", color="magenta", weight=3]; 2092[label="ww196",fontsize=16,color="green",shape="box"];2093 -> 1748[label="",style="dashed", color="red", weight=0]; 2093[label="show ww195",fontsize=16,color="magenta"];2093 -> 2128[label="",style="dashed", color="magenta", weight=3]; 2094[label="ww196",fontsize=16,color="green",shape="box"];2095 -> 1750[label="",style="dashed", color="red", weight=0]; 2095[label="show ww195",fontsize=16,color="magenta"];2095 -> 2129[label="",style="dashed", color="magenta", weight=3]; 2096[label="ww196",fontsize=16,color="green",shape="box"];2097 -> 1752[label="",style="dashed", color="red", weight=0]; 2097[label="show ww195",fontsize=16,color="magenta"];2097 -> 2130[label="",style="dashed", color="magenta", weight=3]; 2098[label="ww196",fontsize=16,color="green",shape="box"];2099 -> 1754[label="",style="dashed", color="red", weight=0]; 2099[label="show ww195",fontsize=16,color="magenta"];2099 -> 2131[label="",style="dashed", color="magenta", weight=3]; 2100[label="ww196",fontsize=16,color="green",shape="box"];2101 -> 1756[label="",style="dashed", color="red", weight=0]; 2101[label="show ww195",fontsize=16,color="magenta"];2101 -> 2132[label="",style="dashed", color="magenta", weight=3]; 2102[label="ww196",fontsize=16,color="green",shape="box"];2103 -> 1758[label="",style="dashed", color="red", weight=0]; 2103[label="show ww195",fontsize=16,color="magenta"];2103 -> 2133[label="",style="dashed", color="magenta", weight=3]; 2104[label="ww196",fontsize=16,color="green",shape="box"];2105 -> 1760[label="",style="dashed", color="red", weight=0]; 2105[label="show ww195",fontsize=16,color="magenta"];2105 -> 2134[label="",style="dashed", color="magenta", weight=3]; 2106[label="ww196",fontsize=16,color="green",shape="box"];2107 -> 1529[label="",style="dashed", color="red", weight=0]; 2107[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1950) . (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 ww1951) ww196",fontsize=16,color="magenta"];2107 -> 2135[label="",style="dashed", color="magenta", weight=3]; 2107 -> 2136[label="",style="dashed", color="magenta", weight=3]; 2107 -> 2137[label="",style="dashed", color="magenta", weight=3]; 2107 -> 2138[label="",style="dashed", color="magenta", weight=3]; 2107 -> 2139[label="",style="dashed", color="magenta", weight=3]; 2108 -> 1762[label="",style="dashed", color="red", weight=0]; 2108[label="show ww195",fontsize=16,color="magenta"];2108 -> 2140[label="",style="dashed", color="magenta", weight=3]; 2109[label="ww196",fontsize=16,color="green",shape="box"];2110 -> 1764[label="",style="dashed", color="red", weight=0]; 2110[label="show ww195",fontsize=16,color="magenta"];2110 -> 2141[label="",style="dashed", color="magenta", weight=3]; 2111[label="ww196",fontsize=16,color="green",shape="box"];2112 -> 1766[label="",style="dashed", color="red", weight=0]; 2112[label="show ww195",fontsize=16,color="magenta"];2112 -> 2142[label="",style="dashed", color="magenta", weight=3]; 2113[label="ww196",fontsize=16,color="green",shape="box"];2114 -> 1768[label="",style="dashed", color="red", weight=0]; 2114[label="show ww195",fontsize=16,color="magenta"];2114 -> 2143[label="",style="dashed", color="magenta", weight=3]; 2115[label="ww196",fontsize=16,color="green",shape="box"];2116 -> 1770[label="",style="dashed", color="red", weight=0]; 2116[label="show ww195",fontsize=16,color="magenta"];2116 -> 2144[label="",style="dashed", color="magenta", weight=3]; 2117[label="ww196",fontsize=16,color="green",shape="box"];2118 -> 1772[label="",style="dashed", color="red", weight=0]; 2118[label="show ww195",fontsize=16,color="magenta"];2118 -> 2145[label="",style="dashed", color="magenta", weight=3]; 2119[label="ww196",fontsize=16,color="green",shape="box"];2120 -> 1774[label="",style="dashed", color="red", weight=0]; 2120[label="show ww195",fontsize=16,color="magenta"];2120 -> 2146[label="",style="dashed", color="magenta", weight=3]; 2121[label="ww196",fontsize=16,color="green",shape="box"];2155[label="primDivInt (Pos (Succ ww239)) (Pos (Succ ww240))",fontsize=16,color="black",shape="box"];2155 -> 2165[label="",style="solid", color="black", weight=3]; 2178[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];2179[label="ww19100",fontsize=16,color="green",shape="box"];2177[label="primIntToChar (mod Pos (Succ ww245) Pos (Succ ww246))",fontsize=16,color="black",shape="triangle"];2177 -> 2180[label="",style="solid", color="black", weight=3]; 2125[label="ww195",fontsize=16,color="green",shape="box"];2126[label="ww195",fontsize=16,color="green",shape="box"];2127[label="ww195",fontsize=16,color="green",shape="box"];2128[label="ww195",fontsize=16,color="green",shape="box"];2129[label="ww195",fontsize=16,color="green",shape="box"];2130[label="ww195",fontsize=16,color="green",shape="box"];2131[label="ww195",fontsize=16,color="green",shape="box"];2132[label="ww195",fontsize=16,color="green",shape="box"];2133[label="ww195",fontsize=16,color="green",shape="box"];2134[label="ww195",fontsize=16,color="green",shape="box"];2135[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"];2136[label="ww1951",fontsize=16,color="green",shape="box"];2137[label="ww1950",fontsize=16,color="green",shape="box"];2138[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"];2139[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"];2140[label="ww195",fontsize=16,color="green",shape="box"];2141[label="ww195",fontsize=16,color="green",shape="box"];2142[label="ww195",fontsize=16,color="green",shape="box"];2143[label="ww195",fontsize=16,color="green",shape="box"];2144[label="ww195",fontsize=16,color="green",shape="box"];2145[label="ww195",fontsize=16,color="green",shape="box"];2146[label="ww195",fontsize=16,color="green",shape="box"];2165[label="Pos (primDivNatS (Succ ww239) (Succ ww240))",fontsize=16,color="green",shape="box"];2165 -> 2176[label="",style="dashed", color="green", weight=3]; 2180[label="primIntToChar (primModInt (Pos (Succ ww245)) (Pos (Succ ww246)))",fontsize=16,color="black",shape="box"];2180 -> 2182[label="",style="solid", color="black", weight=3]; 2176[label="primDivNatS (Succ ww239) (Succ ww240)",fontsize=16,color="black",shape="triangle"];2176 -> 2181[label="",style="solid", color="black", weight=3]; 2182[label="primIntToChar (Pos (primModNatS (Succ ww245) (Succ ww246)))",fontsize=16,color="black",shape="box"];2182 -> 2185[label="",style="solid", color="black", weight=3]; 2181[label="primDivNatS0 ww239 ww240 (primGEqNatS ww239 ww240)",fontsize=16,color="burlywood",shape="box"];3046[label="ww239/Succ ww2390",fontsize=10,color="white",style="solid",shape="box"];2181 -> 3046[label="",style="solid", color="burlywood", weight=9]; 3046 -> 2183[label="",style="solid", color="burlywood", weight=3]; 3047[label="ww239/Zero",fontsize=10,color="white",style="solid",shape="box"];2181 -> 3047[label="",style="solid", color="burlywood", weight=9]; 3047 -> 2184[label="",style="solid", color="burlywood", weight=3]; 2185[label="Char (primModNatS (Succ ww245) (Succ ww246))",fontsize=16,color="green",shape="box"];2185 -> 2190[label="",style="dashed", color="green", weight=3]; 2183[label="primDivNatS0 (Succ ww2390) ww240 (primGEqNatS (Succ ww2390) ww240)",fontsize=16,color="burlywood",shape="box"];3048[label="ww240/Succ ww2400",fontsize=10,color="white",style="solid",shape="box"];2183 -> 3048[label="",style="solid", color="burlywood", weight=9]; 3048 -> 2186[label="",style="solid", color="burlywood", weight=3]; 3049[label="ww240/Zero",fontsize=10,color="white",style="solid",shape="box"];2183 -> 3049[label="",style="solid", color="burlywood", weight=9]; 3049 -> 2187[label="",style="solid", color="burlywood", weight=3]; 2184[label="primDivNatS0 Zero ww240 (primGEqNatS Zero ww240)",fontsize=16,color="burlywood",shape="box"];3050[label="ww240/Succ ww2400",fontsize=10,color="white",style="solid",shape="box"];2184 -> 3050[label="",style="solid", color="burlywood", weight=9]; 3050 -> 2188[label="",style="solid", color="burlywood", weight=3]; 3051[label="ww240/Zero",fontsize=10,color="white",style="solid",shape="box"];2184 -> 3051[label="",style="solid", color="burlywood", weight=9]; 3051 -> 2189[label="",style="solid", color="burlywood", weight=3]; 2190[label="primModNatS (Succ ww245) (Succ ww246)",fontsize=16,color="black",shape="triangle"];2190 -> 2195[label="",style="solid", color="black", weight=3]; 2186[label="primDivNatS0 (Succ ww2390) (Succ ww2400) (primGEqNatS (Succ ww2390) (Succ ww2400))",fontsize=16,color="black",shape="box"];2186 -> 2191[label="",style="solid", color="black", weight=3]; 2187[label="primDivNatS0 (Succ ww2390) Zero (primGEqNatS (Succ ww2390) Zero)",fontsize=16,color="black",shape="box"];2187 -> 2192[label="",style="solid", color="black", weight=3]; 2188[label="primDivNatS0 Zero (Succ ww2400) (primGEqNatS Zero (Succ ww2400))",fontsize=16,color="black",shape="box"];2188 -> 2193[label="",style="solid", color="black", weight=3]; 2189[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2189 -> 2194[label="",style="solid", color="black", weight=3]; 2195[label="primModNatS0 ww245 ww246 (primGEqNatS ww245 ww246)",fontsize=16,color="burlywood",shape="box"];3052[label="ww245/Succ ww2450",fontsize=10,color="white",style="solid",shape="box"];2195 -> 3052[label="",style="solid", color="burlywood", weight=9]; 3052 -> 2201[label="",style="solid", color="burlywood", weight=3]; 3053[label="ww245/Zero",fontsize=10,color="white",style="solid",shape="box"];2195 -> 3053[label="",style="solid", color="burlywood", weight=9]; 3053 -> 2202[label="",style="solid", color="burlywood", weight=3]; 2191 -> 2707[label="",style="dashed", color="red", weight=0]; 2191[label="primDivNatS0 (Succ ww2390) (Succ ww2400) (primGEqNatS ww2390 ww2400)",fontsize=16,color="magenta"];2191 -> 2708[label="",style="dashed", color="magenta", weight=3]; 2191 -> 2709[label="",style="dashed", color="magenta", weight=3]; 2191 -> 2710[label="",style="dashed", color="magenta", weight=3]; 2191 -> 2711[label="",style="dashed", color="magenta", weight=3]; 2192[label="primDivNatS0 (Succ ww2390) Zero True",fontsize=16,color="black",shape="box"];2192 -> 2198[label="",style="solid", color="black", weight=3]; 2193[label="primDivNatS0 Zero (Succ ww2400) False",fontsize=16,color="black",shape="box"];2193 -> 2199[label="",style="solid", color="black", weight=3]; 2194[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2194 -> 2200[label="",style="solid", color="black", weight=3]; 2201[label="primModNatS0 (Succ ww2450) ww246 (primGEqNatS (Succ ww2450) ww246)",fontsize=16,color="burlywood",shape="box"];3054[label="ww246/Succ ww2460",fontsize=10,color="white",style="solid",shape="box"];2201 -> 3054[label="",style="solid", color="burlywood", weight=9]; 3054 -> 2209[label="",style="solid", color="burlywood", weight=3]; 3055[label="ww246/Zero",fontsize=10,color="white",style="solid",shape="box"];2201 -> 3055[label="",style="solid", color="burlywood", weight=9]; 3055 -> 2210[label="",style="solid", color="burlywood", weight=3]; 2202[label="primModNatS0 Zero ww246 (primGEqNatS Zero ww246)",fontsize=16,color="burlywood",shape="box"];3056[label="ww246/Succ ww2460",fontsize=10,color="white",style="solid",shape="box"];2202 -> 3056[label="",style="solid", color="burlywood", weight=9]; 3056 -> 2211[label="",style="solid", color="burlywood", weight=3]; 3057[label="ww246/Zero",fontsize=10,color="white",style="solid",shape="box"];2202 -> 3057[label="",style="solid", color="burlywood", weight=9]; 3057 -> 2212[label="",style="solid", color="burlywood", weight=3]; 2708[label="ww2390",fontsize=16,color="green",shape="box"];2709[label="ww2400",fontsize=16,color="green",shape="box"];2710[label="ww2390",fontsize=16,color="green",shape="box"];2711[label="ww2400",fontsize=16,color="green",shape="box"];2707[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS ww291 ww292)",fontsize=16,color="burlywood",shape="triangle"];3058[label="ww291/Succ ww2910",fontsize=10,color="white",style="solid",shape="box"];2707 -> 3058[label="",style="solid", color="burlywood", weight=9]; 3058 -> 2748[label="",style="solid", color="burlywood", weight=3]; 3059[label="ww291/Zero",fontsize=10,color="white",style="solid",shape="box"];2707 -> 3059[label="",style="solid", color="burlywood", weight=9]; 3059 -> 2749[label="",style="solid", color="burlywood", weight=3]; 2198[label="Succ (primDivNatS (primMinusNatS (Succ ww2390) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2198 -> 2207[label="",style="dashed", color="green", weight=3]; 2199[label="Zero",fontsize=16,color="green",shape="box"];2200[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2200 -> 2208[label="",style="dashed", color="green", weight=3]; 2209[label="primModNatS0 (Succ ww2450) (Succ ww2460) (primGEqNatS (Succ ww2450) (Succ ww2460))",fontsize=16,color="black",shape="box"];2209 -> 2219[label="",style="solid", color="black", weight=3]; 2210[label="primModNatS0 (Succ ww2450) Zero (primGEqNatS (Succ ww2450) Zero)",fontsize=16,color="black",shape="box"];2210 -> 2220[label="",style="solid", color="black", weight=3]; 2211[label="primModNatS0 Zero (Succ ww2460) (primGEqNatS Zero (Succ ww2460))",fontsize=16,color="black",shape="box"];2211 -> 2221[label="",style="solid", color="black", weight=3]; 2212[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2212 -> 2222[label="",style="solid", color="black", weight=3]; 2748[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS (Succ ww2910) ww292)",fontsize=16,color="burlywood",shape="box"];3060[label="ww292/Succ ww2920",fontsize=10,color="white",style="solid",shape="box"];2748 -> 3060[label="",style="solid", color="burlywood", weight=9]; 3060 -> 2760[label="",style="solid", color="burlywood", weight=3]; 3061[label="ww292/Zero",fontsize=10,color="white",style="solid",shape="box"];2748 -> 3061[label="",style="solid", color="burlywood", weight=9]; 3061 -> 2761[label="",style="solid", color="burlywood", weight=3]; 2749[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS Zero ww292)",fontsize=16,color="burlywood",shape="box"];3062[label="ww292/Succ ww2920",fontsize=10,color="white",style="solid",shape="box"];2749 -> 3062[label="",style="solid", color="burlywood", weight=9]; 3062 -> 2762[label="",style="solid", color="burlywood", weight=3]; 3063[label="ww292/Zero",fontsize=10,color="white",style="solid",shape="box"];2749 -> 3063[label="",style="solid", color="burlywood", weight=9]; 3063 -> 2763[label="",style="solid", color="burlywood", weight=3]; 2207 -> 2961[label="",style="dashed", color="red", weight=0]; 2207[label="primDivNatS (primMinusNatS (Succ ww2390) Zero) (Succ Zero)",fontsize=16,color="magenta"];2207 -> 2962[label="",style="dashed", color="magenta", weight=3]; 2207 -> 2963[label="",style="dashed", color="magenta", weight=3]; 2207 -> 2964[label="",style="dashed", color="magenta", weight=3]; 2208 -> 2961[label="",style="dashed", color="red", weight=0]; 2208[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2208 -> 2965[label="",style="dashed", color="magenta", weight=3]; 2208 -> 2966[label="",style="dashed", color="magenta", weight=3]; 2208 -> 2967[label="",style="dashed", color="magenta", weight=3]; 2219 -> 2782[label="",style="dashed", color="red", weight=0]; 2219[label="primModNatS0 (Succ ww2450) (Succ ww2460) (primGEqNatS ww2450 ww2460)",fontsize=16,color="magenta"];2219 -> 2783[label="",style="dashed", color="magenta", weight=3]; 2219 -> 2784[label="",style="dashed", color="magenta", weight=3]; 2219 -> 2785[label="",style="dashed", color="magenta", weight=3]; 2219 -> 2786[label="",style="dashed", color="magenta", weight=3]; 2220[label="primModNatS0 (Succ ww2450) Zero True",fontsize=16,color="black",shape="box"];2220 -> 2233[label="",style="solid", color="black", weight=3]; 2221[label="primModNatS0 Zero (Succ ww2460) False",fontsize=16,color="black",shape="box"];2221 -> 2234[label="",style="solid", color="black", weight=3]; 2222[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2222 -> 2235[label="",style="solid", color="black", weight=3]; 2760[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS (Succ ww2910) (Succ ww2920))",fontsize=16,color="black",shape="box"];2760 -> 2774[label="",style="solid", color="black", weight=3]; 2761[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS (Succ ww2910) Zero)",fontsize=16,color="black",shape="box"];2761 -> 2775[label="",style="solid", color="black", weight=3]; 2762[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS Zero (Succ ww2920))",fontsize=16,color="black",shape="box"];2762 -> 2776[label="",style="solid", color="black", weight=3]; 2763[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2763 -> 2777[label="",style="solid", color="black", weight=3]; 2962[label="Zero",fontsize=16,color="green",shape="box"];2963[label="Zero",fontsize=16,color="green",shape="box"];2964[label="Succ ww2390",fontsize=16,color="green",shape="box"];2961[label="primDivNatS (primMinusNatS ww303 ww304) (Succ ww305)",fontsize=16,color="burlywood",shape="triangle"];3064[label="ww303/Succ ww3030",fontsize=10,color="white",style="solid",shape="box"];2961 -> 3064[label="",style="solid", color="burlywood", weight=9]; 3064 -> 2986[label="",style="solid", color="burlywood", weight=3]; 3065[label="ww303/Zero",fontsize=10,color="white",style="solid",shape="box"];2961 -> 3065[label="",style="solid", color="burlywood", weight=9]; 3065 -> 2987[label="",style="solid", color="burlywood", weight=3]; 2965[label="Zero",fontsize=16,color="green",shape="box"];2966[label="Zero",fontsize=16,color="green",shape="box"];2967[label="Zero",fontsize=16,color="green",shape="box"];2783[label="ww2450",fontsize=16,color="green",shape="box"];2784[label="ww2450",fontsize=16,color="green",shape="box"];2785[label="ww2460",fontsize=16,color="green",shape="box"];2786[label="ww2460",fontsize=16,color="green",shape="box"];2782[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS ww296 ww297)",fontsize=16,color="burlywood",shape="triangle"];3066[label="ww296/Succ ww2960",fontsize=10,color="white",style="solid",shape="box"];2782 -> 3066[label="",style="solid", color="burlywood", weight=9]; 3066 -> 2823[label="",style="solid", color="burlywood", weight=3]; 3067[label="ww296/Zero",fontsize=10,color="white",style="solid",shape="box"];2782 -> 3067[label="",style="solid", color="burlywood", weight=9]; 3067 -> 2824[label="",style="solid", color="burlywood", weight=3]; 2233 -> 2869[label="",style="dashed", color="red", weight=0]; 2233[label="primModNatS (primMinusNatS (Succ ww2450) Zero) (Succ Zero)",fontsize=16,color="magenta"];2233 -> 2870[label="",style="dashed", color="magenta", weight=3]; 2233 -> 2871[label="",style="dashed", color="magenta", weight=3]; 2233 -> 2872[label="",style="dashed", color="magenta", weight=3]; 2234[label="Succ Zero",fontsize=16,color="green",shape="box"];2235 -> 2869[label="",style="dashed", color="red", weight=0]; 2235[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2235 -> 2873[label="",style="dashed", color="magenta", weight=3]; 2235 -> 2874[label="",style="dashed", color="magenta", weight=3]; 2235 -> 2875[label="",style="dashed", color="magenta", weight=3]; 2774 -> 2707[label="",style="dashed", color="red", weight=0]; 2774[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS ww2910 ww2920)",fontsize=16,color="magenta"];2774 -> 2825[label="",style="dashed", color="magenta", weight=3]; 2774 -> 2826[label="",style="dashed", color="magenta", weight=3]; 2775[label="primDivNatS0 (Succ ww289) (Succ ww290) True",fontsize=16,color="black",shape="triangle"];2775 -> 2827[label="",style="solid", color="black", weight=3]; 2776[label="primDivNatS0 (Succ ww289) (Succ ww290) False",fontsize=16,color="black",shape="box"];2776 -> 2828[label="",style="solid", color="black", weight=3]; 2777 -> 2775[label="",style="dashed", color="red", weight=0]; 2777[label="primDivNatS0 (Succ ww289) (Succ ww290) True",fontsize=16,color="magenta"];2986[label="primDivNatS (primMinusNatS (Succ ww3030) ww304) (Succ ww305)",fontsize=16,color="burlywood",shape="box"];3068[label="ww304/Succ ww3040",fontsize=10,color="white",style="solid",shape="box"];2986 -> 3068[label="",style="solid", color="burlywood", weight=9]; 3068 -> 2988[label="",style="solid", color="burlywood", weight=3]; 3069[label="ww304/Zero",fontsize=10,color="white",style="solid",shape="box"];2986 -> 3069[label="",style="solid", color="burlywood", weight=9]; 3069 -> 2989[label="",style="solid", color="burlywood", weight=3]; 2987[label="primDivNatS (primMinusNatS Zero ww304) (Succ ww305)",fontsize=16,color="burlywood",shape="box"];3070[label="ww304/Succ ww3040",fontsize=10,color="white",style="solid",shape="box"];2987 -> 3070[label="",style="solid", color="burlywood", weight=9]; 3070 -> 2990[label="",style="solid", color="burlywood", weight=3]; 3071[label="ww304/Zero",fontsize=10,color="white",style="solid",shape="box"];2987 -> 3071[label="",style="solid", color="burlywood", weight=9]; 3071 -> 2991[label="",style="solid", color="burlywood", weight=3]; 2823[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS (Succ ww2960) ww297)",fontsize=16,color="burlywood",shape="box"];3072[label="ww297/Succ ww2970",fontsize=10,color="white",style="solid",shape="box"];2823 -> 3072[label="",style="solid", color="burlywood", weight=9]; 3072 -> 2833[label="",style="solid", color="burlywood", weight=3]; 3073[label="ww297/Zero",fontsize=10,color="white",style="solid",shape="box"];2823 -> 3073[label="",style="solid", color="burlywood", weight=9]; 3073 -> 2834[label="",style="solid", color="burlywood", weight=3]; 2824[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS Zero ww297)",fontsize=16,color="burlywood",shape="box"];3074[label="ww297/Succ ww2970",fontsize=10,color="white",style="solid",shape="box"];2824 -> 3074[label="",style="solid", color="burlywood", weight=9]; 3074 -> 2835[label="",style="solid", color="burlywood", weight=3]; 3075[label="ww297/Zero",fontsize=10,color="white",style="solid",shape="box"];2824 -> 3075[label="",style="solid", color="burlywood", weight=9]; 3075 -> 2836[label="",style="solid", color="burlywood", weight=3]; 2870[label="Succ ww2450",fontsize=16,color="green",shape="box"];2871[label="Zero",fontsize=16,color="green",shape="box"];2872[label="Zero",fontsize=16,color="green",shape="box"];2869[label="primModNatS (primMinusNatS ww299 ww300) (Succ ww301)",fontsize=16,color="burlywood",shape="triangle"];3076[label="ww299/Succ ww2990",fontsize=10,color="white",style="solid",shape="box"];2869 -> 3076[label="",style="solid", color="burlywood", weight=9]; 3076 -> 2900[label="",style="solid", color="burlywood", weight=3]; 3077[label="ww299/Zero",fontsize=10,color="white",style="solid",shape="box"];2869 -> 3077[label="",style="solid", color="burlywood", weight=9]; 3077 -> 2901[label="",style="solid", color="burlywood", weight=3]; 2873[label="Zero",fontsize=16,color="green",shape="box"];2874[label="Zero",fontsize=16,color="green",shape="box"];2875[label="Zero",fontsize=16,color="green",shape="box"];2825[label="ww2910",fontsize=16,color="green",shape="box"];2826[label="ww2920",fontsize=16,color="green",shape="box"];2827[label="Succ (primDivNatS (primMinusNatS (Succ ww289) (Succ ww290)) (Succ (Succ ww290)))",fontsize=16,color="green",shape="box"];2827 -> 2837[label="",style="dashed", color="green", weight=3]; 2828[label="Zero",fontsize=16,color="green",shape="box"];2988[label="primDivNatS (primMinusNatS (Succ ww3030) (Succ ww3040)) (Succ ww305)",fontsize=16,color="black",shape="box"];2988 -> 2992[label="",style="solid", color="black", weight=3]; 2989[label="primDivNatS (primMinusNatS (Succ ww3030) Zero) (Succ ww305)",fontsize=16,color="black",shape="box"];2989 -> 2993[label="",style="solid", color="black", weight=3]; 2990[label="primDivNatS (primMinusNatS Zero (Succ ww3040)) (Succ ww305)",fontsize=16,color="black",shape="box"];2990 -> 2994[label="",style="solid", color="black", weight=3]; 2991[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww305)",fontsize=16,color="black",shape="box"];2991 -> 2995[label="",style="solid", color="black", weight=3]; 2833[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS (Succ ww2960) (Succ ww2970))",fontsize=16,color="black",shape="box"];2833 -> 2844[label="",style="solid", color="black", weight=3]; 2834[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS (Succ ww2960) Zero)",fontsize=16,color="black",shape="box"];2834 -> 2845[label="",style="solid", color="black", weight=3]; 2835[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS Zero (Succ ww2970))",fontsize=16,color="black",shape="box"];2835 -> 2846[label="",style="solid", color="black", weight=3]; 2836[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2836 -> 2847[label="",style="solid", color="black", weight=3]; 2900[label="primModNatS (primMinusNatS (Succ ww2990) ww300) (Succ ww301)",fontsize=16,color="burlywood",shape="box"];3078[label="ww300/Succ ww3000",fontsize=10,color="white",style="solid",shape="box"];2900 -> 3078[label="",style="solid", color="burlywood", weight=9]; 3078 -> 2906[label="",style="solid", color="burlywood", weight=3]; 3079[label="ww300/Zero",fontsize=10,color="white",style="solid",shape="box"];2900 -> 3079[label="",style="solid", color="burlywood", weight=9]; 3079 -> 2907[label="",style="solid", color="burlywood", weight=3]; 2901[label="primModNatS (primMinusNatS Zero ww300) (Succ ww301)",fontsize=16,color="burlywood",shape="box"];3080[label="ww300/Succ ww3000",fontsize=10,color="white",style="solid",shape="box"];2901 -> 3080[label="",style="solid", color="burlywood", weight=9]; 3080 -> 2908[label="",style="solid", color="burlywood", weight=3]; 3081[label="ww300/Zero",fontsize=10,color="white",style="solid",shape="box"];2901 -> 3081[label="",style="solid", color="burlywood", weight=9]; 3081 -> 2909[label="",style="solid", color="burlywood", weight=3]; 2837 -> 2961[label="",style="dashed", color="red", weight=0]; 2837[label="primDivNatS (primMinusNatS (Succ ww289) (Succ ww290)) (Succ (Succ ww290))",fontsize=16,color="magenta"];2837 -> 2968[label="",style="dashed", color="magenta", weight=3]; 2837 -> 2969[label="",style="dashed", color="magenta", weight=3]; 2837 -> 2970[label="",style="dashed", color="magenta", weight=3]; 2992 -> 2961[label="",style="dashed", color="red", weight=0]; 2992[label="primDivNatS (primMinusNatS ww3030 ww3040) (Succ ww305)",fontsize=16,color="magenta"];2992 -> 2996[label="",style="dashed", color="magenta", weight=3]; 2992 -> 2997[label="",style="dashed", color="magenta", weight=3]; 2993 -> 2176[label="",style="dashed", color="red", weight=0]; 2993[label="primDivNatS (Succ ww3030) (Succ ww305)",fontsize=16,color="magenta"];2993 -> 2998[label="",style="dashed", color="magenta", weight=3]; 2993 -> 2999[label="",style="dashed", color="magenta", weight=3]; 2994[label="primDivNatS Zero (Succ ww305)",fontsize=16,color="black",shape="triangle"];2994 -> 3000[label="",style="solid", color="black", weight=3]; 2995 -> 2994[label="",style="dashed", color="red", weight=0]; 2995[label="primDivNatS Zero (Succ ww305)",fontsize=16,color="magenta"];2844 -> 2782[label="",style="dashed", color="red", weight=0]; 2844[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS ww2960 ww2970)",fontsize=16,color="magenta"];2844 -> 2853[label="",style="dashed", color="magenta", weight=3]; 2844 -> 2854[label="",style="dashed", color="magenta", weight=3]; 2845[label="primModNatS0 (Succ ww294) (Succ ww295) True",fontsize=16,color="black",shape="triangle"];2845 -> 2855[label="",style="solid", color="black", weight=3]; 2846[label="primModNatS0 (Succ ww294) (Succ ww295) False",fontsize=16,color="black",shape="box"];2846 -> 2856[label="",style="solid", color="black", weight=3]; 2847 -> 2845[label="",style="dashed", color="red", weight=0]; 2847[label="primModNatS0 (Succ ww294) (Succ ww295) True",fontsize=16,color="magenta"];2906[label="primModNatS (primMinusNatS (Succ ww2990) (Succ ww3000)) (Succ ww301)",fontsize=16,color="black",shape="box"];2906 -> 2916[label="",style="solid", color="black", weight=3]; 2907[label="primModNatS (primMinusNatS (Succ ww2990) Zero) (Succ ww301)",fontsize=16,color="black",shape="box"];2907 -> 2917[label="",style="solid", color="black", weight=3]; 2908[label="primModNatS (primMinusNatS Zero (Succ ww3000)) (Succ ww301)",fontsize=16,color="black",shape="box"];2908 -> 2918[label="",style="solid", color="black", weight=3]; 2909[label="primModNatS (primMinusNatS Zero Zero) (Succ ww301)",fontsize=16,color="black",shape="box"];2909 -> 2919[label="",style="solid", color="black", weight=3]; 2968[label="Succ ww290",fontsize=16,color="green",shape="box"];2969[label="Succ ww290",fontsize=16,color="green",shape="box"];2970[label="Succ ww289",fontsize=16,color="green",shape="box"];2996[label="ww3040",fontsize=16,color="green",shape="box"];2997[label="ww3030",fontsize=16,color="green",shape="box"];2998[label="ww3030",fontsize=16,color="green",shape="box"];2999[label="ww305",fontsize=16,color="green",shape="box"];3000[label="Zero",fontsize=16,color="green",shape="box"];2853[label="ww2960",fontsize=16,color="green",shape="box"];2854[label="ww2970",fontsize=16,color="green",shape="box"];2855 -> 2869[label="",style="dashed", color="red", weight=0]; 2855[label="primModNatS (primMinusNatS (Succ ww294) (Succ ww295)) (Succ (Succ ww295))",fontsize=16,color="magenta"];2855 -> 2882[label="",style="dashed", color="magenta", weight=3]; 2855 -> 2883[label="",style="dashed", color="magenta", weight=3]; 2855 -> 2884[label="",style="dashed", color="magenta", weight=3]; 2856[label="Succ (Succ ww294)",fontsize=16,color="green",shape="box"];2916 -> 2869[label="",style="dashed", color="red", weight=0]; 2916[label="primModNatS (primMinusNatS ww2990 ww3000) (Succ ww301)",fontsize=16,color="magenta"];2916 -> 2924[label="",style="dashed", color="magenta", weight=3]; 2916 -> 2925[label="",style="dashed", color="magenta", weight=3]; 2917 -> 2190[label="",style="dashed", color="red", weight=0]; 2917[label="primModNatS (Succ ww2990) (Succ ww301)",fontsize=16,color="magenta"];2917 -> 2926[label="",style="dashed", color="magenta", weight=3]; 2917 -> 2927[label="",style="dashed", color="magenta", weight=3]; 2918[label="primModNatS Zero (Succ ww301)",fontsize=16,color="black",shape="triangle"];2918 -> 2928[label="",style="solid", color="black", weight=3]; 2919 -> 2918[label="",style="dashed", color="red", weight=0]; 2919[label="primModNatS Zero (Succ ww301)",fontsize=16,color="magenta"];2882[label="Succ ww294",fontsize=16,color="green",shape="box"];2883[label="Succ ww295",fontsize=16,color="green",shape="box"];2884[label="Succ ww295",fontsize=16,color="green",shape="box"];2924[label="ww2990",fontsize=16,color="green",shape="box"];2925[label="ww3000",fontsize=16,color="green",shape="box"];2926[label="ww301",fontsize=16,color="green",shape="box"];2927[label="ww2990",fontsize=16,color="green",shape="box"];2928[label="Zero",fontsize=16,color="green",shape="box"];} ---------------------------------------- (10) Complex Obligation (AND) ---------------------------------------- (11) Obligation: Q DP problem: The TRS P consists of the following rules: new_show(ww191, h, ba) -> new_show(ww191, h, ba) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (12) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show(ww191, h, ba) evaluates to t =new_show(ww191, h, ba) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show(ww191, h, ba) to new_show(ww191, h, ba). ---------------------------------------- (13) NO ---------------------------------------- (14) Obligation: Q DP problem: The TRS P consists of the following rules: new_show3(ww191) -> new_show3(ww191) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (15) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show3(ww191) evaluates to t =new_show3(ww191) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show3(ww191) to new_show3(ww191). ---------------------------------------- (16) NO ---------------------------------------- (17) Obligation: Q DP problem: The TRS P consists of the following rules: new_show10(ww191, h, ba, bb) -> new_show10(ww191, h, ba, bb) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (18) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show10(ww191, h, ba, bb) evaluates to t =new_show10(ww191, h, ba, bb) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show10(ww191, h, ba, bb) to new_show10(ww191, h, ba, bb). ---------------------------------------- (19) NO ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: new_show2(ww191) -> new_show2(ww191) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (21) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show2(ww191) evaluates to t =new_show2(ww191) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show2(ww191) to new_show2(ww191). ---------------------------------------- (22) NO ---------------------------------------- (23) Obligation: Q DP problem: The TRS P consists of the following rules: new_show11(ww191) -> new_show11(ww191) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (24) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show11(ww191) evaluates to t =new_show11(ww191) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show11(ww191) to new_show11(ww191). ---------------------------------------- (25) NO ---------------------------------------- (26) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(:(ww2370, ww2371), ww197) -> new_psPs(ww2371, ww197) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (27) 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(:(ww2370, ww2371), ww197) -> new_psPs(ww2371, ww197) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (28) YES ---------------------------------------- (29) Obligation: Q DP problem: The TRS P consists of the following rules: new_show4(ww191) -> new_show4(ww191) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (30) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show4(ww191) evaluates to t =new_show4(ww191) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show4(ww191) to new_show4(ww191). ---------------------------------------- (31) NO ---------------------------------------- (32) Obligation: Q DP problem: The TRS P consists of the following rules: new_show9(ww191) -> new_show9(ww191) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (33) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show9(ww191) evaluates to t =new_show9(ww191) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show9(ww191) to new_show9(ww191). ---------------------------------------- (34) NO ---------------------------------------- (35) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(ww289, ww290, Zero, Zero) -> new_primDivNatS00(ww289, ww290) new_primDivNatS00(ww289, ww290) -> new_primDivNatS(Succ(ww289), Succ(ww290), Succ(ww290)) new_primDivNatS(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS(ww3030, ww3040, ww305) new_primDivNatS1(Succ(ww2390), Zero) -> new_primDivNatS(Succ(ww2390), Zero, Zero) new_primDivNatS0(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS0(ww289, ww290, ww2910, ww2920) new_primDivNatS0(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS(Succ(ww289), Succ(ww290), Succ(ww290)) new_primDivNatS1(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS0(ww2390, ww2400, ww2390, ww2400) new_primDivNatS1(Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) new_primDivNatS(Succ(ww3030), Zero, ww305) -> new_primDivNatS1(ww3030, ww305) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (36) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (37) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS00(ww289, ww290) -> new_primDivNatS(Succ(ww289), Succ(ww290), Succ(ww290)) new_primDivNatS(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS(ww3030, ww3040, ww305) new_primDivNatS(Succ(ww3030), Zero, ww305) -> new_primDivNatS1(ww3030, ww305) new_primDivNatS1(Succ(ww2390), Zero) -> new_primDivNatS(Succ(ww2390), Zero, Zero) new_primDivNatS1(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS0(ww2390, ww2400, ww2390, ww2400) new_primDivNatS0(ww289, ww290, Zero, Zero) -> new_primDivNatS00(ww289, ww290) new_primDivNatS0(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS0(ww289, ww290, ww2910, ww2920) new_primDivNatS0(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS(Succ(ww289), Succ(ww290), Succ(ww290)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (38) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_primDivNatS(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS(ww3030, ww3040, ww305) new_primDivNatS1(Succ(ww2390), Zero) -> new_primDivNatS(Succ(ww2390), Zero, Zero) new_primDivNatS1(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS0(ww2390, ww2400, ww2390, ww2400) 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 ---------------------------------------- (39) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS00(ww289, ww290) -> new_primDivNatS(Succ(ww289), Succ(ww290), Succ(ww290)) new_primDivNatS(Succ(ww3030), Zero, ww305) -> new_primDivNatS1(ww3030, ww305) new_primDivNatS0(ww289, ww290, Zero, Zero) -> new_primDivNatS00(ww289, ww290) new_primDivNatS0(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS0(ww289, ww290, ww2910, ww2920) new_primDivNatS0(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS(Succ(ww289), Succ(ww290), Succ(ww290)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (40) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. ---------------------------------------- (41) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS0(ww289, ww290, ww2910, ww2920) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (42) 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(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS0(ww289, ww290, ww2910, ww2920) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (43) YES ---------------------------------------- (44) Obligation: Q DP problem: The TRS P consists of the following rules: new_show7(ww191) -> new_show7(ww191) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (45) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show7(ww191) evaluates to t =new_show7(ww191) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show7(ww191) to new_show7(ww191). ---------------------------------------- (46) NO ---------------------------------------- (47) Obligation: Q DP problem: The TRS P consists of the following rules: new_show8(ww191) -> new_show8(ww191) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (48) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show8(ww191) evaluates to t =new_show8(ww191) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show8(ww191) to new_show8(ww191). ---------------------------------------- (49) NO ---------------------------------------- (50) Obligation: Q DP problem: The TRS P consists of the following rules: new_show13(ww191, h) -> new_show13(ww191, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (51) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show13(ww191, h) evaluates to t =new_show13(ww191, h) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show13(ww191, h) to new_show13(ww191, h). ---------------------------------------- (52) NO ---------------------------------------- (53) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (54) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) at position [5] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, bh)), bh, bh),new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, bh)), bh, bh)) ---------------------------------------- (55) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, bh)), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (56) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, bh)), bh, bh) at position [5] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), new_psPs0(:(Char(Succ(ww193)), :(Char(Succ(ww194)), [])), new_showsPrec(ww195, ww196, bh))), bh, bh),new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), new_psPs0(:(Char(Succ(ww193)), :(Char(Succ(ww194)), [])), new_showsPrec(ww195, ww196, bh))), bh, bh)) ---------------------------------------- (57) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), new_psPs0(:(Char(Succ(ww193)), :(Char(Succ(ww194)), [])), new_showsPrec(ww195, ww196, bh))), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (58) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), new_psPs0(:(Char(Succ(ww193)), :(Char(Succ(ww194)), [])), new_showsPrec(ww195, ww196, bh))), bh, bh) at position [5,1] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), new_psPs0(:(Char(Succ(ww194)), []), new_showsPrec(ww195, ww196, bh)))), bh, bh),new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), new_psPs0(:(Char(Succ(ww194)), []), new_showsPrec(ww195, ww196, bh)))), bh, bh)) ---------------------------------------- (59) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), new_psPs0(:(Char(Succ(ww194)), []), new_showsPrec(ww195, ww196, bh)))), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (60) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), new_psPs0(:(Char(Succ(ww194)), []), new_showsPrec(ww195, ww196, bh)))), bh, bh) at position [5,1,1] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_psPs0([], new_showsPrec(ww195, ww196, bh))))), bh, bh),new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_psPs0([], new_showsPrec(ww195, ww196, bh))))), bh, bh)) ---------------------------------------- (61) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_psPs0([], new_showsPrec(ww195, ww196, bh))))), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (62) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_psPs0([], new_showsPrec(ww195, ww196, bh))))), bh, bh) at position [5,1,1,1] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, bh)))), bh, bh),new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, bh)))), bh, bh)) ---------------------------------------- (63) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, bh)))), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (64) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) we obtained the following new rules [LPAR04]: (new_showParen(z5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, 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))))))))))))))))))))))))))))))), z6, z7, app(ty_IO, x6)),new_showParen(z5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, 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))))))))))))))))))))))))))))))), z6, z7, 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))) ---------------------------------------- (65) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, bh)))), bh, bh) new_showParen(z5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, 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))))))))))))))))))))))))))))))), z6, z7, 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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (66) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (67) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, bh)))), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (68) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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)) ---------------------------------------- (69) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (70) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (71) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, bh)))), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (72) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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_Ordering, ty_Ordering) -> 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_Ordering),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_Ordering, ty_Ordering) -> 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_Ordering)) (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_Ordering, ty_Ordering) -> 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_Ordering),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_Ordering, ty_Ordering) -> 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_Ordering)) ---------------------------------------- (73) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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_Ordering, ty_Ordering) -> 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_Ordering) 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_Ordering, ty_Ordering) -> 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_Ordering) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (74) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (75) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, bh)))), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (76) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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)) ---------------------------------------- (77) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (78) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (79) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, bh)))), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (80) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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))) ---------------------------------------- (81) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (82) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (83) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, bh)))), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (84) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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)) ---------------------------------------- (85) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (86) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (87) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, bh)))), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (88) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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)) ---------------------------------------- (89) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (90) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (91) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, bh)))), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (92) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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)) ---------------------------------------- (93) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (94) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (95) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, bh)))), bh, bh) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (96) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, bh), app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8),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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8)) (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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8),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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8)) ---------------------------------------- (97) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (98) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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))) ---------------------------------------- (99) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, 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(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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (100) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (101) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (102) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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))) ---------------------------------------- (103) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, 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(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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (104) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (105) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (106) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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)) ---------------------------------------- (107) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, 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, 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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (108) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (109) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (110) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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)) ---------------------------------------- (111) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, 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, 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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (112) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (113) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (114) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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))) ---------------------------------------- (115) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, 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(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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (116) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (117) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (118) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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)) ---------------------------------------- (119) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, 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, 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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (120) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (121) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (122) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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)) ---------------------------------------- (123) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, 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, 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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (124) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (125) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (126) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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))) ---------------------------------------- (127) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, 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)) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (128) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (129) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (130) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_pt(ww192, ww193, ww194, ww195, ww196, ba) 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)) ---------------------------------------- (131) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww192, ww193, ww194, :%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, 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, 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_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (132) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. ---------------------------------------- (133) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (134) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, :(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), new_showsPrec(ww195, ww196, 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))))))))))))))))))))))))))))))), z3, z4, 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(z3, z4, 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))))))))))))))))))))))))))))))), z3, z4, 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(z3, z4, x7)))), x7, x7)) ---------------------------------------- (135) 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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8) 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))))))))))))))))))))))))))))))), z3, z4, 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(z3, z4, x7)))), x7, x7) The TRS R consists of the following rules: new_show18(ww191) -> new_psPs0(new_show18(ww191), []) new_primModNatS2(Zero, Succ(ww3000), ww301) -> new_primModNatS4(ww301) new_show17(ww191, bc) -> new_psPs0(new_show17(ww191, bc), []) new_showsPrec(ww195, ww196, ty_Double) -> new_psPs0(new_show22(ww195), ww196) new_show15(ww191) -> new_psPs0(new_show15(ww191), []) new_showsPrec(ww195, ww196, ty_Float) -> new_psPs0(new_show23(ww195), ww196) new_show28(ww191, ca, cb) -> new_psPs0(new_show28(ww191, ca, cb), []) new_showsPrec(ww195, ww196, ty_IOError) -> new_psPs0(new_show30(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Integer, ba) -> new_psPs0(new_show21(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show20(ww191) -> new_psPs0(new_show20(ww191), []) new_show29(ww191) -> new_primShowInt0(ww191) new_primShowInt0(Neg(ww1910)) -> :(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(ww1910))) new_showsPrec(ww195, ww196, app(app(ty_@2, dd), de)) -> new_psPs0(new_show28(ww195, dd, de), ww196) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_show27(ww191) -> new_psPs0(new_show27(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_@2, ca), cb), ba) -> new_psPs0(new_show28(ww191, ca, cb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_showsPrec(ww195, ww196, ty_Char) -> new_psPs0(new_show20(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Float, ba) -> new_psPs0(new_show23(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primModNatS3(Succ(ww2450), Zero) -> new_primModNatS2(Succ(ww2450), Zero, Zero) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOError, ba) -> new_psPs0(new_show30(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, app(app(ty_Either, df), dg)) -> new_psPs0(new_show31(ww195, df, dg), ww196) new_primModNatS2(Zero, Zero, ww301) -> new_primModNatS4(ww301) new_showsPrec(ww195, ww196, app(app(app(ty_@3, cg), da), db)) -> new_psPs0(new_show19(ww195, cg, da, db), ww196) new_primModNatS2(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS2(ww2990, ww3000, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Double, ba) -> new_psPs0(new_show22(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS4(ww301) -> Zero new_show23(ww191) -> new_psPs0(new_show23(ww191), []) new_psPs0(:(ww2370, ww2371), ww197) -> :(ww2370, new_psPs0(ww2371, ww197)) new_primModNatS3(Zero, Succ(ww2460)) -> Succ(Zero) new_showsPrec(ww195, ww196, app(ty_Maybe, ce)) -> new_psPs0(new_show16(ww195, ce), ww196) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primIntToChar(ww245, ww246) -> Char(new_primModNatS3(ww245, ww246)) new_showsPrec(ww195, ww196, ty_Ordering) -> new_psPs0(new_show25(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Int, ba) -> new_psPs0(new_show29(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primModNatS01(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS01(ww294, ww295, ww2960, ww2970) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_[], bc), ba) -> new_psPs0(new_show17(ww191, bc), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(app(ty_@3, bd), be), bf), ba) -> new_psPs0(new_show19(ww191, bd, be, bf), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Char, ba) -> new_psPs0(new_show20(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(:%(ww1910, ww1911), ww192, ww193, ww194, ww195, ww196, app(ty_Ratio, bh), ba) -> new_showParen0(ww1910, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1911, new_pt0(ww192, ww193, ww194, ww195, ww196, bh), bh, bh) new_show25(ww191) -> new_psPs0(new_show25(ww191), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_HugsException, ba) -> new_psPs0(new_show18(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showsPrec(ww195, ww196, ty_@0) -> new_psPs0(new_show27(ww195), ww196) new_psPs0([], ww197) -> ww197 new_primModNatS01(ww294, ww295, Zero, Succ(ww2970)) -> Succ(Succ(ww294)) new_showsPrec(ww195, ww196, ty_IOErrorKind) -> new_psPs0(new_show26(ww195), ww196) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_IO, bg), ba) -> new_psPs0(new_show24(ww191, bg), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_IOErrorKind, ba) -> new_psPs0(new_show26(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_@0, ba) -> new_psPs0(new_show27(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show30(ww191) -> new_psPs0(new_show30(ww191), []) new_pt0(ww192, ww193, ww194, ww195, ww196, ba) -> new_psPs0(:(Char(Succ(ww192)), :(Char(Succ(ww193)), :(Char(Succ(ww194)), []))), new_showsPrec(ww195, ww196, ba)) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Bool, ba) -> new_psPs0(new_show15(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS2(Succ(ww2990), Zero, ww301) -> new_primModNatS3(ww2990, ww301) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(app(ty_Either, cc), cd), ba) -> new_psPs0(new_show31(ww191, cc, cd), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_show22(ww191) -> new_psPs0(new_show22(ww191), []) new_show31(ww191, cc, cd) -> new_psPs0(new_show31(ww191, cc, cd), []) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, app(ty_Maybe, bb), ba) -> new_psPs0(new_show16(ww191, bb), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_show21(ww191) -> new_psPs0(new_show21(ww191), []) new_showsPrec(ww195, ww196, ty_Int) -> new_psPs0(new_show29(ww195), ww196) new_primModNatS02(ww294, ww295) -> new_primModNatS2(Succ(ww294), Succ(ww295), Succ(ww295)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primShowInt0(Pos(Succ(ww19100))) -> new_psPs0(new_primShowInt0(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19100, 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(ww294, ww295, Zero, Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_showParen0(ww191, ww192, ww193, ww194, ww195, ww196, ty_Ordering, ba) -> new_psPs0(new_show25(ww191), new_pt0(ww192, ww193, ww194, ww195, ww196, ba)) new_primModNatS01(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS02(ww294, ww295) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_show26(ww191) -> new_psPs0(new_show26(ww191), []) new_showsPrec(ww195, ww196, app(ty_IO, dc)) -> new_psPs0(new_show24(ww195, dc), ww196) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_showsPrec(:%(ww1950, ww1951), ww196, app(ty_Ratio, h)) -> new_showParen0(ww1950, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1951, ww196, h, h) new_showsPrec(ww195, ww196, ty_Integer) -> new_psPs0(new_show21(ww195), ww196) new_show16(ww191, bb) -> new_psPs0(new_show16(ww191, bb), []) new_show19(ww191, bd, be, bf) -> new_psPs0(new_show19(ww191, bd, be, bf), []) new_showsPrec(ww195, ww196, app(ty_[], cf)) -> new_psPs0(new_show17(ww195, cf), ww196) new_showsPrec(ww195, ww196, ty_Bool) -> new_psPs0(new_show15(ww195), ww196) new_primDivNatS4(ww305) -> Zero new_showsPrec(ww195, ww196, ty_HugsException) -> new_psPs0(new_show18(ww195), ww196) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_show24(ww191, bg) -> new_psPs0(new_show24(ww191, bg), []) new_primModNatS3(Succ(ww2450), Succ(ww2460)) -> new_primModNatS01(ww2450, ww2460, ww2450, ww2460) The set Q consists of the following terms: new_div(x0, x1) new_showsPrec(x0, x1, ty_IOError) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_showsPrec(x0, x1, ty_Bool) new_show22(x0) new_show19(x0, x1, x2, x3) new_show23(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_primModNatS3(Zero, Succ(x0)) new_primDivNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, app(ty_IO, x2)) new_show28(x0, x1, x2) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showsPrec(x0, x1, ty_IOErrorKind) new_primIntToChar(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_show29(x0) new_showsPrec(x0, x1, ty_Ordering) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_primDivNatS3(Succ(x0), Zero) new_show26(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_show21(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_psPs0([], x0) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primModNatS3(Zero, Zero) new_show16(x0, x1) new_primModNatS3(Succ(x0), Zero) new_show27(x0) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primModNatS01(x0, x1, Succ(x2), Zero) new_primModNatS2(Succ(x0), Succ(x1), x2) new_show17(x0, x1) new_primShowInt0(Pos(Zero)) new_primDivNatS4(x0) new_primModNatS02(x0, x1) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primDivNatS02(x0, x1) new_showsPrec(x0, x1, ty_Integer) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primModNatS4(x0) new_showsPrec(x0, x1, ty_Int) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_show30(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show31(x0, x1, x2) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_psPs0(:(x0, x1), x2) new_primDivNatS2(Zero, Zero, x0) new_showsPrec(x0, x1, app(ty_[], x2)) new_show18(x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Zero, Succ(x0), x1) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show24(x0, x1) new_primModNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_show20(x0) new_primModNatS2(Succ(x0), Zero, x1) new_show15(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_show25(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_primShowInt0(Neg(x0)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (136) 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_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))))))))))))))))))))))))))))))), :%(x5, x6), z7, app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, z7, x8, x8) The graph contains the following edges 5 > 1, 2 >= 2, 3 > 2, 4 >= 2, 3 >= 3, 2 >= 4, 3 > 4, 4 >= 4, 5 > 5, 6 >= 6, 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))))))))))))))))))))))))))))))), :%(x5, x6), :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Ratio, x8), app(ty_Ratio, x8)) -> new_showParen(x5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), x6, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), x8, x8) The graph contains the following edges 5 > 1, 2 >= 2, 3 > 2, 4 >= 2, 3 >= 3, 2 >= 4, 3 > 4, 4 >= 4, 5 > 5, 6 >= 6, 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))))))))))))))))))))))))))))))), 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))))))))))))))))))))))))))))))), z3, z4, 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(z3, z4, 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 ---------------------------------------- (137) YES ---------------------------------------- (138) Obligation: Q DP problem: The TRS P consists of the following rules: new_show1(ww191, h, ba) -> new_show1(ww191, h, ba) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (139) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show1(ww191, h, ba) evaluates to t =new_show1(ww191, h, ba) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show1(ww191, h, ba) to new_show1(ww191, h, ba). ---------------------------------------- (140) NO ---------------------------------------- (141) Obligation: Q DP problem: The TRS P consists of the following rules: new_show12(ww191, h) -> new_show12(ww191, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (142) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show12(ww191, h) evaluates to t =new_show12(ww191, h) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show12(ww191, h) to new_show12(ww191, h). ---------------------------------------- (143) NO ---------------------------------------- (144) Obligation: Q DP problem: The TRS P consists of the following rules: new_show0(ww191) -> new_show0(ww191) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (145) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show0(ww191) evaluates to t =new_show0(ww191) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show0(ww191) to new_show0(ww191). ---------------------------------------- (146) NO ---------------------------------------- (147) Obligation: Q DP problem: The TRS P consists of the following rules: new_show14(ww191) -> new_show14(ww191) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (148) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show14(ww191) evaluates to t =new_show14(ww191) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show14(ww191) to new_show14(ww191). ---------------------------------------- (149) NO ---------------------------------------- (150) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(ww2990), Zero, ww301) -> new_primModNatS1(ww2990, ww301) new_primModNatS1(Zero, Zero) -> new_primModNatS(Zero, Zero, Zero) new_primModNatS00(ww294, ww295) -> new_primModNatS(Succ(ww294), Succ(ww295), Succ(ww295)) new_primModNatS0(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS(Succ(ww294), Succ(ww295), Succ(ww295)) new_primModNatS(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS(ww2990, ww3000, ww301) new_primModNatS0(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS0(ww294, ww295, ww2960, ww2970) new_primModNatS1(Succ(ww2450), Succ(ww2460)) -> new_primModNatS0(ww2450, ww2460, ww2450, ww2460) new_primModNatS0(ww294, ww295, Zero, Zero) -> new_primModNatS00(ww294, ww295) new_primModNatS1(Succ(ww2450), Zero) -> new_primModNatS(Succ(ww2450), Zero, Zero) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (151) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (152) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS1(Succ(ww2450), Succ(ww2460)) -> new_primModNatS0(ww2450, ww2460, ww2450, ww2460) new_primModNatS0(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS(Succ(ww294), Succ(ww295), Succ(ww295)) new_primModNatS(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS(ww2990, ww3000, ww301) new_primModNatS(Succ(ww2990), Zero, ww301) -> new_primModNatS1(ww2990, ww301) new_primModNatS1(Succ(ww2450), Zero) -> new_primModNatS(Succ(ww2450), Zero, Zero) new_primModNatS0(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS0(ww294, ww295, ww2960, ww2970) new_primModNatS0(ww294, ww295, Zero, Zero) -> new_primModNatS00(ww294, ww295) new_primModNatS00(ww294, ww295) -> new_primModNatS(Succ(ww294), Succ(ww295), Succ(ww295)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (153) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_primModNatS1(Succ(ww2450), Succ(ww2460)) -> new_primModNatS0(ww2450, ww2460, ww2450, ww2460) new_primModNatS(Succ(ww2990), Succ(ww3000), ww301) -> new_primModNatS(ww2990, ww3000, ww301) new_primModNatS1(Succ(ww2450), Zero) -> new_primModNatS(Succ(ww2450), 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 ---------------------------------------- (154) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS0(ww294, ww295, Succ(ww2960), Zero) -> new_primModNatS(Succ(ww294), Succ(ww295), Succ(ww295)) new_primModNatS(Succ(ww2990), Zero, ww301) -> new_primModNatS1(ww2990, ww301) new_primModNatS0(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS0(ww294, ww295, ww2960, ww2970) new_primModNatS0(ww294, ww295, Zero, Zero) -> new_primModNatS00(ww294, ww295) new_primModNatS00(ww294, ww295) -> new_primModNatS(Succ(ww294), Succ(ww295), Succ(ww295)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (155) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. ---------------------------------------- (156) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS0(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS0(ww294, ww295, ww2960, ww2970) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (157) 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(ww294, ww295, Succ(ww2960), Succ(ww2970)) -> new_primModNatS0(ww294, ww295, ww2960, ww2970) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (158) YES ---------------------------------------- (159) Obligation: Q DP problem: The TRS P consists of the following rules: new_show5(ww191, h) -> new_show5(ww191, h) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (160) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show5(ww191, h) evaluates to t =new_show5(ww191, h) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show5(ww191, h) to new_show5(ww191, h). ---------------------------------------- (161) NO ---------------------------------------- (162) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Neg(ww1910)) -> new_primShowInt(Pos(ww1910)) new_primShowInt(Pos(Succ(ww19100))) -> new_primShowInt(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS4(ww305) -> Zero new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero The set Q consists of the following terms: new_div(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (163) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (164) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww19100))) -> new_primShowInt(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS4(ww305) -> Zero new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero The set Q consists of the following terms: new_div(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (165) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_primShowInt(Pos(Succ(ww19100))) -> new_primShowInt(new_div(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(ww19100))) -> new_primShowInt(Pos(new_primDivNatS3(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))),new_primShowInt(Pos(Succ(ww19100))) -> new_primShowInt(Pos(new_primDivNatS3(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ---------------------------------------- (166) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww19100))) -> new_primShowInt(Pos(new_primDivNatS3(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_div(ww239, ww240) -> Pos(new_primDivNatS3(ww239, ww240)) new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS4(ww305) -> Zero new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero The set Q consists of the following terms: new_div(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (167) 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. ---------------------------------------- (168) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww19100))) -> new_primShowInt(Pos(new_primDivNatS3(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_div(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (169) 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) ---------------------------------------- (170) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww19100))) -> new_primShowInt(Pos(new_primDivNatS3(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (171) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (172) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww19100))) -> new_primShowInt(Pos(new_primDivNatS3(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (173) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_primShowInt(Pos(Succ(ww19100))) -> new_primShowInt(Pos(new_primDivNatS3(ww19100, 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_primDivNatS3(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), new_primShowInt(Pos(Succ(x1))) -> new_primShowInt(Pos(new_primDivNatS3(x1, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) which results in the following constraint: (1) (new_primShowInt(Pos(new_primDivNatS3(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_primDivNatS3(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_primDivNatS3(x0, x2)=Succ(x1) ==> new_primShowInt(Pos(Succ(x0)))_>=_new_primShowInt(Pos(new_primDivNatS3(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_primDivNatS3(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_primDivNatS3(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) (4) (Succ(new_primDivNatS2(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_primDivNatS3(Succ(x6), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) (5) (Succ(new_primDivNatS2(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_primDivNatS3(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_primDivNatS3(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_primDivNatS3(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_primDivNatS3(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_primDivNatS3(Succ(x20), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ==> new_primShowInt(Pos(Succ(Succ(x20))))_>=_new_primShowInt(Pos(new_primDivNatS3(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_primDivNatS3(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(ww19100))) -> new_primShowInt(Pos(new_primDivNatS3(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) *(new_primShowInt(Pos(Succ(Succ(Succ(x18)))))_>=_new_primShowInt(Pos(new_primDivNatS3(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. ---------------------------------------- (174) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww19100))) -> new_primShowInt(Pos(new_primDivNatS3(ww19100, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (175) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(ww19100))) -> new_primShowInt(Pos(new_primDivNatS3(ww19100, 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))) ---------------------------------------- (176) 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_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (177) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (178) 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_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (179) 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))))))))))) ---------------------------------------- (180) 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_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (181) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (182) 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_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (183) 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)))))))))) ---------------------------------------- (184) 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_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (185) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (186) 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_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (187) 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))))))))) ---------------------------------------- (188) 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_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (189) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (190) 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_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (191) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (192) 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_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (193) 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. ---------------------------------------- (194) 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_primDivNatS3(Succ(ww2390), Succ(ww2400)) -> new_primDivNatS01(ww2390, ww2400, ww2390, ww2400) new_primDivNatS3(Zero, Succ(ww2400)) -> Zero new_primDivNatS01(ww289, ww290, Zero, Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Zero, Succ(ww2920)) -> Zero new_primDivNatS01(ww289, ww290, Succ(ww2910), Zero) -> new_primDivNatS02(ww289, ww290) new_primDivNatS01(ww289, ww290, Succ(ww2910), Succ(ww2920)) -> new_primDivNatS01(ww289, ww290, ww2910, ww2920) new_primDivNatS02(ww289, ww290) -> Succ(new_primDivNatS2(Succ(ww289), Succ(ww290), Succ(ww290))) new_primDivNatS2(Succ(ww3030), Succ(ww3040), ww305) -> new_primDivNatS2(ww3030, ww3040, ww305) new_primDivNatS2(Succ(ww3030), Zero, ww305) -> new_primDivNatS3(ww3030, ww305) new_primDivNatS2(Zero, Zero, ww305) -> new_primDivNatS4(ww305) new_primDivNatS2(Zero, Succ(ww3040), ww305) -> new_primDivNatS4(ww305) new_primDivNatS4(ww305) -> Zero new_primDivNatS3(Succ(ww2390), Zero) -> Succ(new_primDivNatS2(Succ(ww2390), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS4(x0) new_primDivNatS02(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (195) Obligation: Q DP problem: The TRS P consists of the following rules: new_show6(ww191) -> new_show6(ww191) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (196) NonTerminationLoopProof (COMPLETE) We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. Found a loop by semiunifying a rule from P directly. s = new_show6(ww191) evaluates to t =new_show6(ww191) Thus s starts an infinite chain as s semiunifies with t with the following substitutions: * Matcher: [ ] * Semiunifier: [ ] -------------------------------------------------------------------------------- Rewriting sequence The DP semiunifies directly so there is only one rewrite step from new_show6(ww191) to new_show6(ww191). ---------------------------------------- (197) NO ---------------------------------------- (198) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="show",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="show ww3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 4[label="showsPrec (Pos Zero) ww3 []",fontsize=16,color="burlywood",shape="box"];3001[label="ww3/ww30 :% ww31",fontsize=10,color="white",style="solid",shape="box"];4 -> 3001[label="",style="solid", color="burlywood", weight=9]; 3001 -> 5[label="",style="solid", color="burlywood", weight=3]; 5[label="showsPrec (Pos Zero) (ww30 :% ww31) []",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 6 -> 1529[label="",style="dashed", color="red", weight=0]; 6[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww30) . (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 ww31) []",fontsize=16,color="magenta"];6 -> 1530[label="",style="dashed", color="magenta", weight=3]; 6 -> 1531[label="",style="dashed", color="magenta", weight=3]; 6 -> 1532[label="",style="dashed", color="magenta", weight=3]; 6 -> 1533[label="",style="dashed", color="magenta", weight=3]; 6 -> 1534[label="",style="dashed", color="magenta", weight=3]; 6 -> 1535[label="",style="dashed", color="magenta", weight=3]; 1530[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"];1531[label="[]",fontsize=16,color="green",shape="box"];1532[label="ww31",fontsize=16,color="green",shape="box"];1533[label="ww30",fontsize=16,color="green",shape="box"];1534[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"];1535[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"];1529[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) ww196",fontsize=16,color="black",shape="triangle"];1529 -> 1542[label="",style="solid", color="black", weight=3]; 1542[label="showParen0 ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww196",fontsize=16,color="black",shape="box"];1542 -> 1543[label="",style="solid", color="black", weight=3]; 1543[label="showParen0 ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww196",fontsize=16,color="black",shape="box"];1543 -> 1544[label="",style="solid", color="black", weight=3]; 1544[label="showParen0 ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww196",fontsize=16,color="black",shape="box"];1544 -> 1545[label="",style="solid", color="black", weight=3]; 1545[label="showParen0 ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww196",fontsize=16,color="black",shape="box"];1545 -> 1546[label="",style="solid", color="black", weight=3]; 1546[label="showParen0 ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) (LT == GT) ww196",fontsize=16,color="black",shape="box"];1546 -> 1547[label="",style="solid", color="black", weight=3]; 1547[label="showParen0 ((shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195) False ww196",fontsize=16,color="black",shape="box"];1547 -> 1548[label="",style="solid", color="black", weight=3]; 1548[label="(shows ww191) . (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="black",shape="box"];1548 -> 1549[label="",style="solid", color="black", weight=3]; 1549[label="shows ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1549 -> 1550[label="",style="solid", color="black", weight=3]; 1550[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="blue",shape="box"];3002[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3002[label="",style="solid", color="blue", weight=9]; 3002 -> 1551[label="",style="solid", color="blue", weight=3]; 3003[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3003[label="",style="solid", color="blue", weight=9]; 3003 -> 1552[label="",style="solid", color="blue", weight=3]; 3004[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3004[label="",style="solid", color="blue", weight=9]; 3004 -> 1553[label="",style="solid", color="blue", weight=3]; 3005[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3005[label="",style="solid", color="blue", weight=9]; 3005 -> 1554[label="",style="solid", color="blue", weight=3]; 3006[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3006[label="",style="solid", color="blue", weight=9]; 3006 -> 1555[label="",style="solid", color="blue", weight=3]; 3007[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3007[label="",style="solid", color="blue", weight=9]; 3007 -> 1556[label="",style="solid", color="blue", weight=3]; 3008[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3008[label="",style="solid", color="blue", weight=9]; 3008 -> 1557[label="",style="solid", color="blue", weight=3]; 3009[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3009[label="",style="solid", color="blue", weight=9]; 3009 -> 1558[label="",style="solid", color="blue", weight=3]; 3010[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3010[label="",style="solid", color="blue", weight=9]; 3010 -> 1559[label="",style="solid", color="blue", weight=3]; 3011[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3011[label="",style="solid", color="blue", weight=9]; 3011 -> 1560[label="",style="solid", color="blue", weight=3]; 3012[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3012[label="",style="solid", color="blue", weight=9]; 3012 -> 1561[label="",style="solid", color="blue", weight=3]; 3013[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3013[label="",style="solid", color="blue", weight=9]; 3013 -> 1562[label="",style="solid", color="blue", weight=3]; 3014[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3014[label="",style="solid", color="blue", weight=9]; 3014 -> 1563[label="",style="solid", color="blue", weight=3]; 3015[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3015[label="",style="solid", color="blue", weight=9]; 3015 -> 1564[label="",style="solid", color="blue", weight=3]; 3016[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3016[label="",style="solid", color="blue", weight=9]; 3016 -> 1565[label="",style="solid", color="blue", weight=3]; 3017[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3017[label="",style="solid", color="blue", weight=9]; 3017 -> 1566[label="",style="solid", color="blue", weight=3]; 3018[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3018[label="",style="solid", color="blue", weight=9]; 3018 -> 1567[label="",style="solid", color="blue", weight=3]; 3019[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1550 -> 3019[label="",style="solid", color="blue", weight=9]; 3019 -> 1568[label="",style="solid", color="blue", weight=3]; 1551[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1551 -> 1569[label="",style="solid", color="black", weight=3]; 1552[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1552 -> 1570[label="",style="solid", color="black", weight=3]; 1553[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1553 -> 1571[label="",style="solid", color="black", weight=3]; 1554[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1554 -> 1572[label="",style="solid", color="black", weight=3]; 1555[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1555 -> 1573[label="",style="solid", color="black", weight=3]; 1556[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1556 -> 1574[label="",style="solid", color="black", weight=3]; 1557[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1557 -> 1575[label="",style="solid", color="black", weight=3]; 1558[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1558 -> 1576[label="",style="solid", color="black", weight=3]; 1559[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1559 -> 1577[label="",style="solid", color="black", weight=3]; 1560[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1560 -> 1578[label="",style="solid", color="black", weight=3]; 1561[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="burlywood",shape="box"];3020[label="ww191/ww1910 :% ww1911",fontsize=10,color="white",style="solid",shape="box"];1561 -> 3020[label="",style="solid", color="burlywood", weight=9]; 3020 -> 1579[label="",style="solid", color="burlywood", weight=3]; 1562[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1562 -> 1580[label="",style="solid", color="black", weight=3]; 1563[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1563 -> 1581[label="",style="solid", color="black", weight=3]; 1564[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1564 -> 1582[label="",style="solid", color="black", weight=3]; 1565[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1565 -> 1583[label="",style="solid", color="black", weight=3]; 1566[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1566 -> 1584[label="",style="solid", color="black", weight=3]; 1567[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1567 -> 1585[label="",style="solid", color="black", weight=3]; 1568[label="showsPrec (Pos Zero) ww191 ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1568 -> 1586[label="",style="solid", color="black", weight=3]; 1569 -> 1741[label="",style="dashed", color="red", weight=0]; 1569[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1569 -> 1742[label="",style="dashed", color="magenta", weight=3]; 1569 -> 1743[label="",style="dashed", color="magenta", weight=3]; 1570 -> 1741[label="",style="dashed", color="red", weight=0]; 1570[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1570 -> 1744[label="",style="dashed", color="magenta", weight=3]; 1570 -> 1745[label="",style="dashed", color="magenta", weight=3]; 1571 -> 1741[label="",style="dashed", color="red", weight=0]; 1571[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1571 -> 1746[label="",style="dashed", color="magenta", weight=3]; 1571 -> 1747[label="",style="dashed", color="magenta", weight=3]; 1572 -> 1741[label="",style="dashed", color="red", weight=0]; 1572[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1572 -> 1748[label="",style="dashed", color="magenta", weight=3]; 1572 -> 1749[label="",style="dashed", color="magenta", weight=3]; 1573 -> 1741[label="",style="dashed", color="red", weight=0]; 1573[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1573 -> 1750[label="",style="dashed", color="magenta", weight=3]; 1573 -> 1751[label="",style="dashed", color="magenta", weight=3]; 1574 -> 1741[label="",style="dashed", color="red", weight=0]; 1574[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1574 -> 1752[label="",style="dashed", color="magenta", weight=3]; 1574 -> 1753[label="",style="dashed", color="magenta", weight=3]; 1575 -> 1741[label="",style="dashed", color="red", weight=0]; 1575[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1575 -> 1754[label="",style="dashed", color="magenta", weight=3]; 1575 -> 1755[label="",style="dashed", color="magenta", weight=3]; 1576 -> 1741[label="",style="dashed", color="red", weight=0]; 1576[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1576 -> 1756[label="",style="dashed", color="magenta", weight=3]; 1576 -> 1757[label="",style="dashed", color="magenta", weight=3]; 1577 -> 1741[label="",style="dashed", color="red", weight=0]; 1577[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1577 -> 1758[label="",style="dashed", color="magenta", weight=3]; 1577 -> 1759[label="",style="dashed", color="magenta", weight=3]; 1578 -> 1741[label="",style="dashed", color="red", weight=0]; 1578[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1578 -> 1760[label="",style="dashed", color="magenta", weight=3]; 1578 -> 1761[label="",style="dashed", color="magenta", weight=3]; 1579[label="showsPrec (Pos Zero) (ww1910 :% ww1911) ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="black",shape="box"];1579 -> 1597[label="",style="solid", color="black", weight=3]; 1580 -> 1741[label="",style="dashed", color="red", weight=0]; 1580[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1580 -> 1762[label="",style="dashed", color="magenta", weight=3]; 1580 -> 1763[label="",style="dashed", color="magenta", weight=3]; 1581 -> 1741[label="",style="dashed", color="red", weight=0]; 1581[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1581 -> 1764[label="",style="dashed", color="magenta", weight=3]; 1581 -> 1765[label="",style="dashed", color="magenta", weight=3]; 1582 -> 1741[label="",style="dashed", color="red", weight=0]; 1582[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1582 -> 1766[label="",style="dashed", color="magenta", weight=3]; 1582 -> 1767[label="",style="dashed", color="magenta", weight=3]; 1583 -> 1741[label="",style="dashed", color="red", weight=0]; 1583[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1583 -> 1768[label="",style="dashed", color="magenta", weight=3]; 1583 -> 1769[label="",style="dashed", color="magenta", weight=3]; 1584 -> 1741[label="",style="dashed", color="red", weight=0]; 1584[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1584 -> 1770[label="",style="dashed", color="magenta", weight=3]; 1584 -> 1771[label="",style="dashed", color="magenta", weight=3]; 1585 -> 1741[label="",style="dashed", color="red", weight=0]; 1585[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1585 -> 1772[label="",style="dashed", color="magenta", weight=3]; 1585 -> 1773[label="",style="dashed", color="magenta", weight=3]; 1586 -> 1741[label="",style="dashed", color="red", weight=0]; 1586[label="show ww191 ++ (showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1586 -> 1774[label="",style="dashed", color="magenta", weight=3]; 1586 -> 1775[label="",style="dashed", color="magenta", weight=3]; 1742[label="show ww191",fontsize=16,color="black",shape="triangle"];1742 -> 1971[label="",style="solid", color="black", weight=3]; 1743 -> 1616[label="",style="dashed", color="red", weight=0]; 1743[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1741[label="ww237 ++ ww197",fontsize=16,color="burlywood",shape="triangle"];3021[label="ww237/ww2370 : ww2371",fontsize=10,color="white",style="solid",shape="box"];1741 -> 3021[label="",style="solid", color="burlywood", weight=9]; 3021 -> 1972[label="",style="solid", color="burlywood", weight=3]; 3022[label="ww237/[]",fontsize=10,color="white",style="solid",shape="box"];1741 -> 3022[label="",style="solid", color="burlywood", weight=9]; 3022 -> 1973[label="",style="solid", color="burlywood", weight=3]; 1744[label="show ww191",fontsize=16,color="black",shape="triangle"];1744 -> 1974[label="",style="solid", color="black", weight=3]; 1745 -> 1616[label="",style="dashed", color="red", weight=0]; 1745[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1746[label="show ww191",fontsize=16,color="black",shape="triangle"];1746 -> 1975[label="",style="solid", color="black", weight=3]; 1747 -> 1616[label="",style="dashed", color="red", weight=0]; 1747[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1748[label="show ww191",fontsize=16,color="black",shape="triangle"];1748 -> 1976[label="",style="solid", color="black", weight=3]; 1749 -> 1616[label="",style="dashed", color="red", weight=0]; 1749[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1750[label="show ww191",fontsize=16,color="black",shape="triangle"];1750 -> 1977[label="",style="solid", color="black", weight=3]; 1751 -> 1616[label="",style="dashed", color="red", weight=0]; 1751[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1752[label="show ww191",fontsize=16,color="black",shape="triangle"];1752 -> 1978[label="",style="solid", color="black", weight=3]; 1753 -> 1616[label="",style="dashed", color="red", weight=0]; 1753[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1754[label="show ww191",fontsize=16,color="black",shape="triangle"];1754 -> 1979[label="",style="solid", color="black", weight=3]; 1755 -> 1616[label="",style="dashed", color="red", weight=0]; 1755[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1756[label="show ww191",fontsize=16,color="black",shape="triangle"];1756 -> 1980[label="",style="solid", color="black", weight=3]; 1757 -> 1616[label="",style="dashed", color="red", weight=0]; 1757[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1758[label="show ww191",fontsize=16,color="black",shape="triangle"];1758 -> 1981[label="",style="solid", color="black", weight=3]; 1759 -> 1616[label="",style="dashed", color="red", weight=0]; 1759[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1760[label="show ww191",fontsize=16,color="black",shape="triangle"];1760 -> 1982[label="",style="solid", color="black", weight=3]; 1761 -> 1616[label="",style="dashed", color="red", weight=0]; 1761[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1597 -> 1529[label="",style="dashed", color="red", weight=0]; 1597[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1910) . (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 ww1911) ((showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195)",fontsize=16,color="magenta"];1597 -> 1615[label="",style="dashed", color="magenta", weight=3]; 1597 -> 1616[label="",style="dashed", color="magenta", weight=3]; 1597 -> 1617[label="",style="dashed", color="magenta", weight=3]; 1597 -> 1618[label="",style="dashed", color="magenta", weight=3]; 1597 -> 1619[label="",style="dashed", color="magenta", weight=3]; 1597 -> 1620[label="",style="dashed", color="magenta", weight=3]; 1762[label="show ww191",fontsize=16,color="black",shape="triangle"];1762 -> 1983[label="",style="solid", color="black", weight=3]; 1763 -> 1616[label="",style="dashed", color="red", weight=0]; 1763[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1764[label="show ww191",fontsize=16,color="black",shape="triangle"];1764 -> 1984[label="",style="solid", color="black", weight=3]; 1765 -> 1616[label="",style="dashed", color="red", weight=0]; 1765[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1766[label="show ww191",fontsize=16,color="black",shape="triangle"];1766 -> 1985[label="",style="solid", color="black", weight=3]; 1767 -> 1616[label="",style="dashed", color="red", weight=0]; 1767[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1768[label="show ww191",fontsize=16,color="black",shape="triangle"];1768 -> 1986[label="",style="solid", color="black", weight=3]; 1769 -> 1616[label="",style="dashed", color="red", weight=0]; 1769[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1770[label="show ww191",fontsize=16,color="black",shape="triangle"];1770 -> 1987[label="",style="solid", color="black", weight=3]; 1771 -> 1616[label="",style="dashed", color="red", weight=0]; 1771[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1772[label="show ww191",fontsize=16,color="black",shape="triangle"];1772 -> 1988[label="",style="solid", color="black", weight=3]; 1773 -> 1616[label="",style="dashed", color="red", weight=0]; 1773[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1774[label="show ww191",fontsize=16,color="black",shape="triangle"];1774 -> 1989[label="",style="solid", color="black", weight=3]; 1775 -> 1616[label="",style="dashed", color="red", weight=0]; 1775[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="magenta"];1971[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1971 -> 1991[label="",style="solid", color="black", weight=3]; 1616[label="(showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : [])) . shows ww195",fontsize=16,color="black",shape="triangle"];1616 -> 1639[label="",style="solid", color="black", weight=3]; 1972[label="(ww2370 : ww2371) ++ ww197",fontsize=16,color="black",shape="box"];1972 -> 1992[label="",style="solid", color="black", weight=3]; 1973[label="[] ++ ww197",fontsize=16,color="black",shape="box"];1973 -> 1993[label="",style="solid", color="black", weight=3]; 1974[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1974 -> 1994[label="",style="solid", color="black", weight=3]; 1975[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1975 -> 1995[label="",style="solid", color="black", weight=3]; 1976[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1976 -> 1996[label="",style="solid", color="black", weight=3]; 1977[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1977 -> 1997[label="",style="solid", color="black", weight=3]; 1978[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1978 -> 1998[label="",style="solid", color="black", weight=3]; 1979[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1979 -> 1999[label="",style="solid", color="black", weight=3]; 1980[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1980 -> 2000[label="",style="solid", color="black", weight=3]; 1981[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1981 -> 2001[label="",style="solid", color="black", weight=3]; 1982[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1982 -> 2002[label="",style="solid", color="black", weight=3]; 1615[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"];1617[label="ww1911",fontsize=16,color="green",shape="box"];1618[label="ww1910",fontsize=16,color="green",shape="box"];1619[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"];1620[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"];1983[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1983 -> 2003[label="",style="solid", color="black", weight=3]; 1984[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1984 -> 2004[label="",style="solid", color="black", weight=3]; 1985[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1985 -> 2005[label="",style="solid", color="black", weight=3]; 1986[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1986 -> 2006[label="",style="solid", color="black", weight=3]; 1987[label="primShowInt ww191",fontsize=16,color="burlywood",shape="triangle"];3023[label="ww191/Pos ww1910",fontsize=10,color="white",style="solid",shape="box"];1987 -> 3023[label="",style="solid", color="burlywood", weight=9]; 3023 -> 2007[label="",style="solid", color="burlywood", weight=3]; 3024[label="ww191/Neg ww1910",fontsize=10,color="white",style="solid",shape="box"];1987 -> 3024[label="",style="solid", color="burlywood", weight=9]; 3024 -> 2008[label="",style="solid", color="burlywood", weight=3]; 1988[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1988 -> 2009[label="",style="solid", color="black", weight=3]; 1989[label="showsPrec (Pos Zero) ww191 []",fontsize=16,color="black",shape="box"];1989 -> 2010[label="",style="solid", color="black", weight=3]; 1991 -> 1741[label="",style="dashed", color="red", weight=0]; 1991[label="show ww191 ++ []",fontsize=16,color="magenta"];1991 -> 2029[label="",style="dashed", color="magenta", weight=3]; 1991 -> 2030[label="",style="dashed", color="magenta", weight=3]; 1639[label="showString (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : []) (shows ww195 ww196)",fontsize=16,color="black",shape="box"];1639 -> 1675[label="",style="solid", color="black", weight=3]; 1992[label="ww2370 : ww2371 ++ ww197",fontsize=16,color="green",shape="box"];1992 -> 2031[label="",style="dashed", color="green", weight=3]; 1993[label="ww197",fontsize=16,color="green",shape="box"];1994 -> 1741[label="",style="dashed", color="red", weight=0]; 1994[label="show ww191 ++ []",fontsize=16,color="magenta"];1994 -> 2032[label="",style="dashed", color="magenta", weight=3]; 1994 -> 2033[label="",style="dashed", color="magenta", weight=3]; 1995 -> 1741[label="",style="dashed", color="red", weight=0]; 1995[label="show ww191 ++ []",fontsize=16,color="magenta"];1995 -> 2034[label="",style="dashed", color="magenta", weight=3]; 1995 -> 2035[label="",style="dashed", color="magenta", weight=3]; 1996 -> 1741[label="",style="dashed", color="red", weight=0]; 1996[label="show ww191 ++ []",fontsize=16,color="magenta"];1996 -> 2036[label="",style="dashed", color="magenta", weight=3]; 1996 -> 2037[label="",style="dashed", color="magenta", weight=3]; 1997 -> 1741[label="",style="dashed", color="red", weight=0]; 1997[label="show ww191 ++ []",fontsize=16,color="magenta"];1997 -> 2038[label="",style="dashed", color="magenta", weight=3]; 1997 -> 2039[label="",style="dashed", color="magenta", weight=3]; 1998 -> 1741[label="",style="dashed", color="red", weight=0]; 1998[label="show ww191 ++ []",fontsize=16,color="magenta"];1998 -> 2040[label="",style="dashed", color="magenta", weight=3]; 1998 -> 2041[label="",style="dashed", color="magenta", weight=3]; 1999 -> 1741[label="",style="dashed", color="red", weight=0]; 1999[label="show ww191 ++ []",fontsize=16,color="magenta"];1999 -> 2042[label="",style="dashed", color="magenta", weight=3]; 1999 -> 2043[label="",style="dashed", color="magenta", weight=3]; 2000 -> 1741[label="",style="dashed", color="red", weight=0]; 2000[label="show ww191 ++ []",fontsize=16,color="magenta"];2000 -> 2044[label="",style="dashed", color="magenta", weight=3]; 2000 -> 2045[label="",style="dashed", color="magenta", weight=3]; 2001 -> 1741[label="",style="dashed", color="red", weight=0]; 2001[label="show ww191 ++ []",fontsize=16,color="magenta"];2001 -> 2046[label="",style="dashed", color="magenta", weight=3]; 2001 -> 2047[label="",style="dashed", color="magenta", weight=3]; 2002 -> 1741[label="",style="dashed", color="red", weight=0]; 2002[label="show ww191 ++ []",fontsize=16,color="magenta"];2002 -> 2048[label="",style="dashed", color="magenta", weight=3]; 2002 -> 2049[label="",style="dashed", color="magenta", weight=3]; 2003 -> 1741[label="",style="dashed", color="red", weight=0]; 2003[label="show ww191 ++ []",fontsize=16,color="magenta"];2003 -> 2050[label="",style="dashed", color="magenta", weight=3]; 2003 -> 2051[label="",style="dashed", color="magenta", weight=3]; 2004 -> 1741[label="",style="dashed", color="red", weight=0]; 2004[label="show ww191 ++ []",fontsize=16,color="magenta"];2004 -> 2052[label="",style="dashed", color="magenta", weight=3]; 2004 -> 2053[label="",style="dashed", color="magenta", weight=3]; 2005 -> 1741[label="",style="dashed", color="red", weight=0]; 2005[label="show ww191 ++ []",fontsize=16,color="magenta"];2005 -> 2054[label="",style="dashed", color="magenta", weight=3]; 2005 -> 2055[label="",style="dashed", color="magenta", weight=3]; 2006 -> 1741[label="",style="dashed", color="red", weight=0]; 2006[label="show ww191 ++ []",fontsize=16,color="magenta"];2006 -> 2056[label="",style="dashed", color="magenta", weight=3]; 2006 -> 2057[label="",style="dashed", color="magenta", weight=3]; 2007[label="primShowInt (Pos ww1910)",fontsize=16,color="burlywood",shape="box"];3025[label="ww1910/Succ ww19100",fontsize=10,color="white",style="solid",shape="box"];2007 -> 3025[label="",style="solid", color="burlywood", weight=9]; 3025 -> 2058[label="",style="solid", color="burlywood", weight=3]; 3026[label="ww1910/Zero",fontsize=10,color="white",style="solid",shape="box"];2007 -> 3026[label="",style="solid", color="burlywood", weight=9]; 3026 -> 2059[label="",style="solid", color="burlywood", weight=3]; 2008[label="primShowInt (Neg ww1910)",fontsize=16,color="black",shape="box"];2008 -> 2060[label="",style="solid", color="black", weight=3]; 2009 -> 1741[label="",style="dashed", color="red", weight=0]; 2009[label="show ww191 ++ []",fontsize=16,color="magenta"];2009 -> 2061[label="",style="dashed", color="magenta", weight=3]; 2009 -> 2062[label="",style="dashed", color="magenta", weight=3]; 2010 -> 1741[label="",style="dashed", color="red", weight=0]; 2010[label="show ww191 ++ []",fontsize=16,color="magenta"];2010 -> 2063[label="",style="dashed", color="magenta", weight=3]; 2010 -> 2064[label="",style="dashed", color="magenta", weight=3]; 2029 -> 1742[label="",style="dashed", color="red", weight=0]; 2029[label="show ww191",fontsize=16,color="magenta"];2030[label="[]",fontsize=16,color="green",shape="box"];1675 -> 1741[label="",style="dashed", color="red", weight=0]; 1675[label="(++) (Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : []) shows ww195 ww196",fontsize=16,color="magenta"];1675 -> 1895[label="",style="dashed", color="magenta", weight=3]; 1675 -> 1896[label="",style="dashed", color="magenta", weight=3]; 2031 -> 1741[label="",style="dashed", color="red", weight=0]; 2031[label="ww2371 ++ ww197",fontsize=16,color="magenta"];2031 -> 2083[label="",style="dashed", color="magenta", weight=3]; 2032 -> 1744[label="",style="dashed", color="red", weight=0]; 2032[label="show ww191",fontsize=16,color="magenta"];2033[label="[]",fontsize=16,color="green",shape="box"];2034 -> 1746[label="",style="dashed", color="red", weight=0]; 2034[label="show ww191",fontsize=16,color="magenta"];2035[label="[]",fontsize=16,color="green",shape="box"];2036 -> 1748[label="",style="dashed", color="red", weight=0]; 2036[label="show ww191",fontsize=16,color="magenta"];2037[label="[]",fontsize=16,color="green",shape="box"];2038 -> 1750[label="",style="dashed", color="red", weight=0]; 2038[label="show ww191",fontsize=16,color="magenta"];2039[label="[]",fontsize=16,color="green",shape="box"];2040 -> 1752[label="",style="dashed", color="red", weight=0]; 2040[label="show ww191",fontsize=16,color="magenta"];2041[label="[]",fontsize=16,color="green",shape="box"];2042 -> 1754[label="",style="dashed", color="red", weight=0]; 2042[label="show ww191",fontsize=16,color="magenta"];2043[label="[]",fontsize=16,color="green",shape="box"];2044 -> 1756[label="",style="dashed", color="red", weight=0]; 2044[label="show ww191",fontsize=16,color="magenta"];2045[label="[]",fontsize=16,color="green",shape="box"];2046 -> 1758[label="",style="dashed", color="red", weight=0]; 2046[label="show ww191",fontsize=16,color="magenta"];2047[label="[]",fontsize=16,color="green",shape="box"];2048 -> 1760[label="",style="dashed", color="red", weight=0]; 2048[label="show ww191",fontsize=16,color="magenta"];2049[label="[]",fontsize=16,color="green",shape="box"];2050 -> 1762[label="",style="dashed", color="red", weight=0]; 2050[label="show ww191",fontsize=16,color="magenta"];2051[label="[]",fontsize=16,color="green",shape="box"];2052 -> 1764[label="",style="dashed", color="red", weight=0]; 2052[label="show ww191",fontsize=16,color="magenta"];2053[label="[]",fontsize=16,color="green",shape="box"];2054 -> 1766[label="",style="dashed", color="red", weight=0]; 2054[label="show ww191",fontsize=16,color="magenta"];2055[label="[]",fontsize=16,color="green",shape="box"];2056 -> 1768[label="",style="dashed", color="red", weight=0]; 2056[label="show ww191",fontsize=16,color="magenta"];2057[label="[]",fontsize=16,color="green",shape="box"];2058[label="primShowInt (Pos (Succ ww19100))",fontsize=16,color="black",shape="box"];2058 -> 2084[label="",style="solid", color="black", weight=3]; 2059[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];2059 -> 2085[label="",style="solid", color="black", weight=3]; 2060[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 ww1910)",fontsize=16,color="green",shape="box"];2060 -> 2086[label="",style="dashed", color="green", weight=3]; 2061 -> 1772[label="",style="dashed", color="red", weight=0]; 2061[label="show ww191",fontsize=16,color="magenta"];2062[label="[]",fontsize=16,color="green",shape="box"];2063 -> 1774[label="",style="dashed", color="red", weight=0]; 2063[label="show ww191",fontsize=16,color="magenta"];2064[label="[]",fontsize=16,color="green",shape="box"];1895[label="Char (Succ ww192) : Char (Succ ww193) : Char (Succ ww194) : []",fontsize=16,color="green",shape="box"];1896[label="shows ww195 ww196",fontsize=16,color="black",shape="box"];1896 -> 1990[label="",style="solid", color="black", weight=3]; 2083[label="ww2371",fontsize=16,color="green",shape="box"];2084 -> 1741[label="",style="dashed", color="red", weight=0]; 2084[label="primShowInt (div Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];2084 -> 2122[label="",style="dashed", color="magenta", weight=3]; 2084 -> 2123[label="",style="dashed", color="magenta", weight=3]; 2085[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"];2086 -> 1987[label="",style="dashed", color="red", weight=0]; 2086[label="primShowInt (Pos ww1910)",fontsize=16,color="magenta"];2086 -> 2124[label="",style="dashed", color="magenta", weight=3]; 1990[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="blue",shape="box"];3027[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3027[label="",style="solid", color="blue", weight=9]; 3027 -> 2011[label="",style="solid", color="blue", weight=3]; 3028[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3028[label="",style="solid", color="blue", weight=9]; 3028 -> 2012[label="",style="solid", color="blue", weight=3]; 3029[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3029[label="",style="solid", color="blue", weight=9]; 3029 -> 2013[label="",style="solid", color="blue", weight=3]; 3030[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3030[label="",style="solid", color="blue", weight=9]; 3030 -> 2014[label="",style="solid", color="blue", weight=3]; 3031[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3031[label="",style="solid", color="blue", weight=9]; 3031 -> 2015[label="",style="solid", color="blue", weight=3]; 3032[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3032[label="",style="solid", color="blue", weight=9]; 3032 -> 2016[label="",style="solid", color="blue", weight=3]; 3033[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3033[label="",style="solid", color="blue", weight=9]; 3033 -> 2017[label="",style="solid", color="blue", weight=3]; 3034[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3034[label="",style="solid", color="blue", weight=9]; 3034 -> 2018[label="",style="solid", color="blue", weight=3]; 3035[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3035[label="",style="solid", color="blue", weight=9]; 3035 -> 2019[label="",style="solid", color="blue", weight=3]; 3036[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3036[label="",style="solid", color="blue", weight=9]; 3036 -> 2020[label="",style="solid", color="blue", weight=3]; 3037[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3037[label="",style="solid", color="blue", weight=9]; 3037 -> 2021[label="",style="solid", color="blue", weight=3]; 3038[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3038[label="",style="solid", color="blue", weight=9]; 3038 -> 2022[label="",style="solid", color="blue", weight=3]; 3039[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3039[label="",style="solid", color="blue", weight=9]; 3039 -> 2023[label="",style="solid", color="blue", weight=3]; 3040[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3040[label="",style="solid", color="blue", weight=9]; 3040 -> 2024[label="",style="solid", color="blue", weight=3]; 3041[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3041[label="",style="solid", color="blue", weight=9]; 3041 -> 2025[label="",style="solid", color="blue", weight=3]; 3042[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3042[label="",style="solid", color="blue", weight=9]; 3042 -> 2026[label="",style="solid", color="blue", weight=3]; 3043[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3043[label="",style="solid", color="blue", weight=9]; 3043 -> 2027[label="",style="solid", color="blue", weight=3]; 3044[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1990 -> 3044[label="",style="solid", color="blue", weight=9]; 3044 -> 2028[label="",style="solid", color="blue", weight=3]; 2122 -> 1987[label="",style="dashed", color="red", weight=0]; 2122[label="primShowInt (div Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];2122 -> 2147[label="",style="dashed", color="magenta", weight=3]; 2123[label="toEnum (mod Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];2123 -> 2148[label="",style="dashed", color="green", weight=3]; 2124[label="Pos ww1910",fontsize=16,color="green",shape="box"];2011[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2011 -> 2065[label="",style="solid", color="black", weight=3]; 2012[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2012 -> 2066[label="",style="solid", color="black", weight=3]; 2013[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2013 -> 2067[label="",style="solid", color="black", weight=3]; 2014[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2014 -> 2068[label="",style="solid", color="black", weight=3]; 2015[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2015 -> 2069[label="",style="solid", color="black", weight=3]; 2016[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2016 -> 2070[label="",style="solid", color="black", weight=3]; 2017[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2017 -> 2071[label="",style="solid", color="black", weight=3]; 2018[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2018 -> 2072[label="",style="solid", color="black", weight=3]; 2019[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2019 -> 2073[label="",style="solid", color="black", weight=3]; 2020[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2020 -> 2074[label="",style="solid", color="black", weight=3]; 2021[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="burlywood",shape="box"];3045[label="ww195/ww1950 :% ww1951",fontsize=10,color="white",style="solid",shape="box"];2021 -> 3045[label="",style="solid", color="burlywood", weight=9]; 3045 -> 2075[label="",style="solid", color="burlywood", weight=3]; 2022[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2022 -> 2076[label="",style="solid", color="black", weight=3]; 2023[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2023 -> 2077[label="",style="solid", color="black", weight=3]; 2024[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2024 -> 2078[label="",style="solid", color="black", weight=3]; 2025[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2025 -> 2079[label="",style="solid", color="black", weight=3]; 2026[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2026 -> 2080[label="",style="solid", color="black", weight=3]; 2027[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2027 -> 2081[label="",style="solid", color="black", weight=3]; 2028[label="showsPrec (Pos Zero) ww195 ww196",fontsize=16,color="black",shape="box"];2028 -> 2082[label="",style="solid", color="black", weight=3]; 2147 -> 2149[label="",style="dashed", color="red", weight=0]; 2147[label="div Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];2147 -> 2150[label="",style="dashed", color="magenta", weight=3]; 2147 -> 2151[label="",style="dashed", color="magenta", weight=3]; 2148[label="toEnum (mod Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];2148 -> 2166[label="",style="solid", color="black", weight=3]; 2065 -> 1741[label="",style="dashed", color="red", weight=0]; 2065[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2065 -> 2087[label="",style="dashed", color="magenta", weight=3]; 2065 -> 2088[label="",style="dashed", color="magenta", weight=3]; 2066 -> 1741[label="",style="dashed", color="red", weight=0]; 2066[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2066 -> 2089[label="",style="dashed", color="magenta", weight=3]; 2066 -> 2090[label="",style="dashed", color="magenta", weight=3]; 2067 -> 1741[label="",style="dashed", color="red", weight=0]; 2067[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2067 -> 2091[label="",style="dashed", color="magenta", weight=3]; 2067 -> 2092[label="",style="dashed", color="magenta", weight=3]; 2068 -> 1741[label="",style="dashed", color="red", weight=0]; 2068[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2068 -> 2093[label="",style="dashed", color="magenta", weight=3]; 2068 -> 2094[label="",style="dashed", color="magenta", weight=3]; 2069 -> 1741[label="",style="dashed", color="red", weight=0]; 2069[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2069 -> 2095[label="",style="dashed", color="magenta", weight=3]; 2069 -> 2096[label="",style="dashed", color="magenta", weight=3]; 2070 -> 1741[label="",style="dashed", color="red", weight=0]; 2070[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2070 -> 2097[label="",style="dashed", color="magenta", weight=3]; 2070 -> 2098[label="",style="dashed", color="magenta", weight=3]; 2071 -> 1741[label="",style="dashed", color="red", weight=0]; 2071[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2071 -> 2099[label="",style="dashed", color="magenta", weight=3]; 2071 -> 2100[label="",style="dashed", color="magenta", weight=3]; 2072 -> 1741[label="",style="dashed", color="red", weight=0]; 2072[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2072 -> 2101[label="",style="dashed", color="magenta", weight=3]; 2072 -> 2102[label="",style="dashed", color="magenta", weight=3]; 2073 -> 1741[label="",style="dashed", color="red", weight=0]; 2073[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2073 -> 2103[label="",style="dashed", color="magenta", weight=3]; 2073 -> 2104[label="",style="dashed", color="magenta", weight=3]; 2074 -> 1741[label="",style="dashed", color="red", weight=0]; 2074[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2074 -> 2105[label="",style="dashed", color="magenta", weight=3]; 2074 -> 2106[label="",style="dashed", color="magenta", weight=3]; 2075[label="showsPrec (Pos Zero) (ww1950 :% ww1951) ww196",fontsize=16,color="black",shape="box"];2075 -> 2107[label="",style="solid", color="black", weight=3]; 2076 -> 1741[label="",style="dashed", color="red", weight=0]; 2076[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2076 -> 2108[label="",style="dashed", color="magenta", weight=3]; 2076 -> 2109[label="",style="dashed", color="magenta", weight=3]; 2077 -> 1741[label="",style="dashed", color="red", weight=0]; 2077[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2077 -> 2110[label="",style="dashed", color="magenta", weight=3]; 2077 -> 2111[label="",style="dashed", color="magenta", weight=3]; 2078 -> 1741[label="",style="dashed", color="red", weight=0]; 2078[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2078 -> 2112[label="",style="dashed", color="magenta", weight=3]; 2078 -> 2113[label="",style="dashed", color="magenta", weight=3]; 2079 -> 1741[label="",style="dashed", color="red", weight=0]; 2079[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2079 -> 2114[label="",style="dashed", color="magenta", weight=3]; 2079 -> 2115[label="",style="dashed", color="magenta", weight=3]; 2080 -> 1741[label="",style="dashed", color="red", weight=0]; 2080[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2080 -> 2116[label="",style="dashed", color="magenta", weight=3]; 2080 -> 2117[label="",style="dashed", color="magenta", weight=3]; 2081 -> 1741[label="",style="dashed", color="red", weight=0]; 2081[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2081 -> 2118[label="",style="dashed", color="magenta", weight=3]; 2081 -> 2119[label="",style="dashed", color="magenta", weight=3]; 2082 -> 1741[label="",style="dashed", color="red", weight=0]; 2082[label="show ww195 ++ ww196",fontsize=16,color="magenta"];2082 -> 2120[label="",style="dashed", color="magenta", weight=3]; 2082 -> 2121[label="",style="dashed", color="magenta", weight=3]; 2150[label="ww19100",fontsize=16,color="green",shape="box"];2151[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];2149[label="div Pos (Succ ww239) Pos (Succ ww240)",fontsize=16,color="black",shape="triangle"];2149 -> 2155[label="",style="solid", color="black", weight=3]; 2166 -> 2177[label="",style="dashed", color="red", weight=0]; 2166[label="primIntToChar (mod Pos (Succ ww19100) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];2166 -> 2178[label="",style="dashed", color="magenta", weight=3]; 2166 -> 2179[label="",style="dashed", color="magenta", weight=3]; 2087 -> 1742[label="",style="dashed", color="red", weight=0]; 2087[label="show ww195",fontsize=16,color="magenta"];2087 -> 2125[label="",style="dashed", color="magenta", weight=3]; 2088[label="ww196",fontsize=16,color="green",shape="box"];2089 -> 1744[label="",style="dashed", color="red", weight=0]; 2089[label="show ww195",fontsize=16,color="magenta"];2089 -> 2126[label="",style="dashed", color="magenta", weight=3]; 2090[label="ww196",fontsize=16,color="green",shape="box"];2091 -> 1746[label="",style="dashed", color="red", weight=0]; 2091[label="show ww195",fontsize=16,color="magenta"];2091 -> 2127[label="",style="dashed", color="magenta", weight=3]; 2092[label="ww196",fontsize=16,color="green",shape="box"];2093 -> 1748[label="",style="dashed", color="red", weight=0]; 2093[label="show ww195",fontsize=16,color="magenta"];2093 -> 2128[label="",style="dashed", color="magenta", weight=3]; 2094[label="ww196",fontsize=16,color="green",shape="box"];2095 -> 1750[label="",style="dashed", color="red", weight=0]; 2095[label="show ww195",fontsize=16,color="magenta"];2095 -> 2129[label="",style="dashed", color="magenta", weight=3]; 2096[label="ww196",fontsize=16,color="green",shape="box"];2097 -> 1752[label="",style="dashed", color="red", weight=0]; 2097[label="show ww195",fontsize=16,color="magenta"];2097 -> 2130[label="",style="dashed", color="magenta", weight=3]; 2098[label="ww196",fontsize=16,color="green",shape="box"];2099 -> 1754[label="",style="dashed", color="red", weight=0]; 2099[label="show ww195",fontsize=16,color="magenta"];2099 -> 2131[label="",style="dashed", color="magenta", weight=3]; 2100[label="ww196",fontsize=16,color="green",shape="box"];2101 -> 1756[label="",style="dashed", color="red", weight=0]; 2101[label="show ww195",fontsize=16,color="magenta"];2101 -> 2132[label="",style="dashed", color="magenta", weight=3]; 2102[label="ww196",fontsize=16,color="green",shape="box"];2103 -> 1758[label="",style="dashed", color="red", weight=0]; 2103[label="show ww195",fontsize=16,color="magenta"];2103 -> 2133[label="",style="dashed", color="magenta", weight=3]; 2104[label="ww196",fontsize=16,color="green",shape="box"];2105 -> 1760[label="",style="dashed", color="red", weight=0]; 2105[label="show ww195",fontsize=16,color="magenta"];2105 -> 2134[label="",style="dashed", color="magenta", weight=3]; 2106[label="ww196",fontsize=16,color="green",shape="box"];2107 -> 1529[label="",style="dashed", color="red", weight=0]; 2107[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1950) . (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 ww1951) ww196",fontsize=16,color="magenta"];2107 -> 2135[label="",style="dashed", color="magenta", weight=3]; 2107 -> 2136[label="",style="dashed", color="magenta", weight=3]; 2107 -> 2137[label="",style="dashed", color="magenta", weight=3]; 2107 -> 2138[label="",style="dashed", color="magenta", weight=3]; 2107 -> 2139[label="",style="dashed", color="magenta", weight=3]; 2108 -> 1762[label="",style="dashed", color="red", weight=0]; 2108[label="show ww195",fontsize=16,color="magenta"];2108 -> 2140[label="",style="dashed", color="magenta", weight=3]; 2109[label="ww196",fontsize=16,color="green",shape="box"];2110 -> 1764[label="",style="dashed", color="red", weight=0]; 2110[label="show ww195",fontsize=16,color="magenta"];2110 -> 2141[label="",style="dashed", color="magenta", weight=3]; 2111[label="ww196",fontsize=16,color="green",shape="box"];2112 -> 1766[label="",style="dashed", color="red", weight=0]; 2112[label="show ww195",fontsize=16,color="magenta"];2112 -> 2142[label="",style="dashed", color="magenta", weight=3]; 2113[label="ww196",fontsize=16,color="green",shape="box"];2114 -> 1768[label="",style="dashed", color="red", weight=0]; 2114[label="show ww195",fontsize=16,color="magenta"];2114 -> 2143[label="",style="dashed", color="magenta", weight=3]; 2115[label="ww196",fontsize=16,color="green",shape="box"];2116 -> 1770[label="",style="dashed", color="red", weight=0]; 2116[label="show ww195",fontsize=16,color="magenta"];2116 -> 2144[label="",style="dashed", color="magenta", weight=3]; 2117[label="ww196",fontsize=16,color="green",shape="box"];2118 -> 1772[label="",style="dashed", color="red", weight=0]; 2118[label="show ww195",fontsize=16,color="magenta"];2118 -> 2145[label="",style="dashed", color="magenta", weight=3]; 2119[label="ww196",fontsize=16,color="green",shape="box"];2120 -> 1774[label="",style="dashed", color="red", weight=0]; 2120[label="show ww195",fontsize=16,color="magenta"];2120 -> 2146[label="",style="dashed", color="magenta", weight=3]; 2121[label="ww196",fontsize=16,color="green",shape="box"];2155[label="primDivInt (Pos (Succ ww239)) (Pos (Succ ww240))",fontsize=16,color="black",shape="box"];2155 -> 2165[label="",style="solid", color="black", weight=3]; 2178[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];2179[label="ww19100",fontsize=16,color="green",shape="box"];2177[label="primIntToChar (mod Pos (Succ ww245) Pos (Succ ww246))",fontsize=16,color="black",shape="triangle"];2177 -> 2180[label="",style="solid", color="black", weight=3]; 2125[label="ww195",fontsize=16,color="green",shape="box"];2126[label="ww195",fontsize=16,color="green",shape="box"];2127[label="ww195",fontsize=16,color="green",shape="box"];2128[label="ww195",fontsize=16,color="green",shape="box"];2129[label="ww195",fontsize=16,color="green",shape="box"];2130[label="ww195",fontsize=16,color="green",shape="box"];2131[label="ww195",fontsize=16,color="green",shape="box"];2132[label="ww195",fontsize=16,color="green",shape="box"];2133[label="ww195",fontsize=16,color="green",shape="box"];2134[label="ww195",fontsize=16,color="green",shape="box"];2135[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"];2136[label="ww1951",fontsize=16,color="green",shape="box"];2137[label="ww1950",fontsize=16,color="green",shape="box"];2138[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"];2139[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"];2140[label="ww195",fontsize=16,color="green",shape="box"];2141[label="ww195",fontsize=16,color="green",shape="box"];2142[label="ww195",fontsize=16,color="green",shape="box"];2143[label="ww195",fontsize=16,color="green",shape="box"];2144[label="ww195",fontsize=16,color="green",shape="box"];2145[label="ww195",fontsize=16,color="green",shape="box"];2146[label="ww195",fontsize=16,color="green",shape="box"];2165[label="Pos (primDivNatS (Succ ww239) (Succ ww240))",fontsize=16,color="green",shape="box"];2165 -> 2176[label="",style="dashed", color="green", weight=3]; 2180[label="primIntToChar (primModInt (Pos (Succ ww245)) (Pos (Succ ww246)))",fontsize=16,color="black",shape="box"];2180 -> 2182[label="",style="solid", color="black", weight=3]; 2176[label="primDivNatS (Succ ww239) (Succ ww240)",fontsize=16,color="black",shape="triangle"];2176 -> 2181[label="",style="solid", color="black", weight=3]; 2182[label="primIntToChar (Pos (primModNatS (Succ ww245) (Succ ww246)))",fontsize=16,color="black",shape="box"];2182 -> 2185[label="",style="solid", color="black", weight=3]; 2181[label="primDivNatS0 ww239 ww240 (primGEqNatS ww239 ww240)",fontsize=16,color="burlywood",shape="box"];3046[label="ww239/Succ ww2390",fontsize=10,color="white",style="solid",shape="box"];2181 -> 3046[label="",style="solid", color="burlywood", weight=9]; 3046 -> 2183[label="",style="solid", color="burlywood", weight=3]; 3047[label="ww239/Zero",fontsize=10,color="white",style="solid",shape="box"];2181 -> 3047[label="",style="solid", color="burlywood", weight=9]; 3047 -> 2184[label="",style="solid", color="burlywood", weight=3]; 2185[label="Char (primModNatS (Succ ww245) (Succ ww246))",fontsize=16,color="green",shape="box"];2185 -> 2190[label="",style="dashed", color="green", weight=3]; 2183[label="primDivNatS0 (Succ ww2390) ww240 (primGEqNatS (Succ ww2390) ww240)",fontsize=16,color="burlywood",shape="box"];3048[label="ww240/Succ ww2400",fontsize=10,color="white",style="solid",shape="box"];2183 -> 3048[label="",style="solid", color="burlywood", weight=9]; 3048 -> 2186[label="",style="solid", color="burlywood", weight=3]; 3049[label="ww240/Zero",fontsize=10,color="white",style="solid",shape="box"];2183 -> 3049[label="",style="solid", color="burlywood", weight=9]; 3049 -> 2187[label="",style="solid", color="burlywood", weight=3]; 2184[label="primDivNatS0 Zero ww240 (primGEqNatS Zero ww240)",fontsize=16,color="burlywood",shape="box"];3050[label="ww240/Succ ww2400",fontsize=10,color="white",style="solid",shape="box"];2184 -> 3050[label="",style="solid", color="burlywood", weight=9]; 3050 -> 2188[label="",style="solid", color="burlywood", weight=3]; 3051[label="ww240/Zero",fontsize=10,color="white",style="solid",shape="box"];2184 -> 3051[label="",style="solid", color="burlywood", weight=9]; 3051 -> 2189[label="",style="solid", color="burlywood", weight=3]; 2190[label="primModNatS (Succ ww245) (Succ ww246)",fontsize=16,color="black",shape="triangle"];2190 -> 2195[label="",style="solid", color="black", weight=3]; 2186[label="primDivNatS0 (Succ ww2390) (Succ ww2400) (primGEqNatS (Succ ww2390) (Succ ww2400))",fontsize=16,color="black",shape="box"];2186 -> 2191[label="",style="solid", color="black", weight=3]; 2187[label="primDivNatS0 (Succ ww2390) Zero (primGEqNatS (Succ ww2390) Zero)",fontsize=16,color="black",shape="box"];2187 -> 2192[label="",style="solid", color="black", weight=3]; 2188[label="primDivNatS0 Zero (Succ ww2400) (primGEqNatS Zero (Succ ww2400))",fontsize=16,color="black",shape="box"];2188 -> 2193[label="",style="solid", color="black", weight=3]; 2189[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2189 -> 2194[label="",style="solid", color="black", weight=3]; 2195[label="primModNatS0 ww245 ww246 (primGEqNatS ww245 ww246)",fontsize=16,color="burlywood",shape="box"];3052[label="ww245/Succ ww2450",fontsize=10,color="white",style="solid",shape="box"];2195 -> 3052[label="",style="solid", color="burlywood", weight=9]; 3052 -> 2201[label="",style="solid", color="burlywood", weight=3]; 3053[label="ww245/Zero",fontsize=10,color="white",style="solid",shape="box"];2195 -> 3053[label="",style="solid", color="burlywood", weight=9]; 3053 -> 2202[label="",style="solid", color="burlywood", weight=3]; 2191 -> 2707[label="",style="dashed", color="red", weight=0]; 2191[label="primDivNatS0 (Succ ww2390) (Succ ww2400) (primGEqNatS ww2390 ww2400)",fontsize=16,color="magenta"];2191 -> 2708[label="",style="dashed", color="magenta", weight=3]; 2191 -> 2709[label="",style="dashed", color="magenta", weight=3]; 2191 -> 2710[label="",style="dashed", color="magenta", weight=3]; 2191 -> 2711[label="",style="dashed", color="magenta", weight=3]; 2192[label="primDivNatS0 (Succ ww2390) Zero True",fontsize=16,color="black",shape="box"];2192 -> 2198[label="",style="solid", color="black", weight=3]; 2193[label="primDivNatS0 Zero (Succ ww2400) False",fontsize=16,color="black",shape="box"];2193 -> 2199[label="",style="solid", color="black", weight=3]; 2194[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2194 -> 2200[label="",style="solid", color="black", weight=3]; 2201[label="primModNatS0 (Succ ww2450) ww246 (primGEqNatS (Succ ww2450) ww246)",fontsize=16,color="burlywood",shape="box"];3054[label="ww246/Succ ww2460",fontsize=10,color="white",style="solid",shape="box"];2201 -> 3054[label="",style="solid", color="burlywood", weight=9]; 3054 -> 2209[label="",style="solid", color="burlywood", weight=3]; 3055[label="ww246/Zero",fontsize=10,color="white",style="solid",shape="box"];2201 -> 3055[label="",style="solid", color="burlywood", weight=9]; 3055 -> 2210[label="",style="solid", color="burlywood", weight=3]; 2202[label="primModNatS0 Zero ww246 (primGEqNatS Zero ww246)",fontsize=16,color="burlywood",shape="box"];3056[label="ww246/Succ ww2460",fontsize=10,color="white",style="solid",shape="box"];2202 -> 3056[label="",style="solid", color="burlywood", weight=9]; 3056 -> 2211[label="",style="solid", color="burlywood", weight=3]; 3057[label="ww246/Zero",fontsize=10,color="white",style="solid",shape="box"];2202 -> 3057[label="",style="solid", color="burlywood", weight=9]; 3057 -> 2212[label="",style="solid", color="burlywood", weight=3]; 2708[label="ww2390",fontsize=16,color="green",shape="box"];2709[label="ww2400",fontsize=16,color="green",shape="box"];2710[label="ww2390",fontsize=16,color="green",shape="box"];2711[label="ww2400",fontsize=16,color="green",shape="box"];2707[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS ww291 ww292)",fontsize=16,color="burlywood",shape="triangle"];3058[label="ww291/Succ ww2910",fontsize=10,color="white",style="solid",shape="box"];2707 -> 3058[label="",style="solid", color="burlywood", weight=9]; 3058 -> 2748[label="",style="solid", color="burlywood", weight=3]; 3059[label="ww291/Zero",fontsize=10,color="white",style="solid",shape="box"];2707 -> 3059[label="",style="solid", color="burlywood", weight=9]; 3059 -> 2749[label="",style="solid", color="burlywood", weight=3]; 2198[label="Succ (primDivNatS (primMinusNatS (Succ ww2390) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2198 -> 2207[label="",style="dashed", color="green", weight=3]; 2199[label="Zero",fontsize=16,color="green",shape="box"];2200[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2200 -> 2208[label="",style="dashed", color="green", weight=3]; 2209[label="primModNatS0 (Succ ww2450) (Succ ww2460) (primGEqNatS (Succ ww2450) (Succ ww2460))",fontsize=16,color="black",shape="box"];2209 -> 2219[label="",style="solid", color="black", weight=3]; 2210[label="primModNatS0 (Succ ww2450) Zero (primGEqNatS (Succ ww2450) Zero)",fontsize=16,color="black",shape="box"];2210 -> 2220[label="",style="solid", color="black", weight=3]; 2211[label="primModNatS0 Zero (Succ ww2460) (primGEqNatS Zero (Succ ww2460))",fontsize=16,color="black",shape="box"];2211 -> 2221[label="",style="solid", color="black", weight=3]; 2212[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2212 -> 2222[label="",style="solid", color="black", weight=3]; 2748[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS (Succ ww2910) ww292)",fontsize=16,color="burlywood",shape="box"];3060[label="ww292/Succ ww2920",fontsize=10,color="white",style="solid",shape="box"];2748 -> 3060[label="",style="solid", color="burlywood", weight=9]; 3060 -> 2760[label="",style="solid", color="burlywood", weight=3]; 3061[label="ww292/Zero",fontsize=10,color="white",style="solid",shape="box"];2748 -> 3061[label="",style="solid", color="burlywood", weight=9]; 3061 -> 2761[label="",style="solid", color="burlywood", weight=3]; 2749[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS Zero ww292)",fontsize=16,color="burlywood",shape="box"];3062[label="ww292/Succ ww2920",fontsize=10,color="white",style="solid",shape="box"];2749 -> 3062[label="",style="solid", color="burlywood", weight=9]; 3062 -> 2762[label="",style="solid", color="burlywood", weight=3]; 3063[label="ww292/Zero",fontsize=10,color="white",style="solid",shape="box"];2749 -> 3063[label="",style="solid", color="burlywood", weight=9]; 3063 -> 2763[label="",style="solid", color="burlywood", weight=3]; 2207 -> 2961[label="",style="dashed", color="red", weight=0]; 2207[label="primDivNatS (primMinusNatS (Succ ww2390) Zero) (Succ Zero)",fontsize=16,color="magenta"];2207 -> 2962[label="",style="dashed", color="magenta", weight=3]; 2207 -> 2963[label="",style="dashed", color="magenta", weight=3]; 2207 -> 2964[label="",style="dashed", color="magenta", weight=3]; 2208 -> 2961[label="",style="dashed", color="red", weight=0]; 2208[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2208 -> 2965[label="",style="dashed", color="magenta", weight=3]; 2208 -> 2966[label="",style="dashed", color="magenta", weight=3]; 2208 -> 2967[label="",style="dashed", color="magenta", weight=3]; 2219 -> 2782[label="",style="dashed", color="red", weight=0]; 2219[label="primModNatS0 (Succ ww2450) (Succ ww2460) (primGEqNatS ww2450 ww2460)",fontsize=16,color="magenta"];2219 -> 2783[label="",style="dashed", color="magenta", weight=3]; 2219 -> 2784[label="",style="dashed", color="magenta", weight=3]; 2219 -> 2785[label="",style="dashed", color="magenta", weight=3]; 2219 -> 2786[label="",style="dashed", color="magenta", weight=3]; 2220[label="primModNatS0 (Succ ww2450) Zero True",fontsize=16,color="black",shape="box"];2220 -> 2233[label="",style="solid", color="black", weight=3]; 2221[label="primModNatS0 Zero (Succ ww2460) False",fontsize=16,color="black",shape="box"];2221 -> 2234[label="",style="solid", color="black", weight=3]; 2222[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2222 -> 2235[label="",style="solid", color="black", weight=3]; 2760[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS (Succ ww2910) (Succ ww2920))",fontsize=16,color="black",shape="box"];2760 -> 2774[label="",style="solid", color="black", weight=3]; 2761[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS (Succ ww2910) Zero)",fontsize=16,color="black",shape="box"];2761 -> 2775[label="",style="solid", color="black", weight=3]; 2762[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS Zero (Succ ww2920))",fontsize=16,color="black",shape="box"];2762 -> 2776[label="",style="solid", color="black", weight=3]; 2763[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2763 -> 2777[label="",style="solid", color="black", weight=3]; 2962[label="Zero",fontsize=16,color="green",shape="box"];2963[label="Zero",fontsize=16,color="green",shape="box"];2964[label="Succ ww2390",fontsize=16,color="green",shape="box"];2961[label="primDivNatS (primMinusNatS ww303 ww304) (Succ ww305)",fontsize=16,color="burlywood",shape="triangle"];3064[label="ww303/Succ ww3030",fontsize=10,color="white",style="solid",shape="box"];2961 -> 3064[label="",style="solid", color="burlywood", weight=9]; 3064 -> 2986[label="",style="solid", color="burlywood", weight=3]; 3065[label="ww303/Zero",fontsize=10,color="white",style="solid",shape="box"];2961 -> 3065[label="",style="solid", color="burlywood", weight=9]; 3065 -> 2987[label="",style="solid", color="burlywood", weight=3]; 2965[label="Zero",fontsize=16,color="green",shape="box"];2966[label="Zero",fontsize=16,color="green",shape="box"];2967[label="Zero",fontsize=16,color="green",shape="box"];2783[label="ww2450",fontsize=16,color="green",shape="box"];2784[label="ww2450",fontsize=16,color="green",shape="box"];2785[label="ww2460",fontsize=16,color="green",shape="box"];2786[label="ww2460",fontsize=16,color="green",shape="box"];2782[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS ww296 ww297)",fontsize=16,color="burlywood",shape="triangle"];3066[label="ww296/Succ ww2960",fontsize=10,color="white",style="solid",shape="box"];2782 -> 3066[label="",style="solid", color="burlywood", weight=9]; 3066 -> 2823[label="",style="solid", color="burlywood", weight=3]; 3067[label="ww296/Zero",fontsize=10,color="white",style="solid",shape="box"];2782 -> 3067[label="",style="solid", color="burlywood", weight=9]; 3067 -> 2824[label="",style="solid", color="burlywood", weight=3]; 2233 -> 2869[label="",style="dashed", color="red", weight=0]; 2233[label="primModNatS (primMinusNatS (Succ ww2450) Zero) (Succ Zero)",fontsize=16,color="magenta"];2233 -> 2870[label="",style="dashed", color="magenta", weight=3]; 2233 -> 2871[label="",style="dashed", color="magenta", weight=3]; 2233 -> 2872[label="",style="dashed", color="magenta", weight=3]; 2234[label="Succ Zero",fontsize=16,color="green",shape="box"];2235 -> 2869[label="",style="dashed", color="red", weight=0]; 2235[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2235 -> 2873[label="",style="dashed", color="magenta", weight=3]; 2235 -> 2874[label="",style="dashed", color="magenta", weight=3]; 2235 -> 2875[label="",style="dashed", color="magenta", weight=3]; 2774 -> 2707[label="",style="dashed", color="red", weight=0]; 2774[label="primDivNatS0 (Succ ww289) (Succ ww290) (primGEqNatS ww2910 ww2920)",fontsize=16,color="magenta"];2774 -> 2825[label="",style="dashed", color="magenta", weight=3]; 2774 -> 2826[label="",style="dashed", color="magenta", weight=3]; 2775[label="primDivNatS0 (Succ ww289) (Succ ww290) True",fontsize=16,color="black",shape="triangle"];2775 -> 2827[label="",style="solid", color="black", weight=3]; 2776[label="primDivNatS0 (Succ ww289) (Succ ww290) False",fontsize=16,color="black",shape="box"];2776 -> 2828[label="",style="solid", color="black", weight=3]; 2777 -> 2775[label="",style="dashed", color="red", weight=0]; 2777[label="primDivNatS0 (Succ ww289) (Succ ww290) True",fontsize=16,color="magenta"];2986[label="primDivNatS (primMinusNatS (Succ ww3030) ww304) (Succ ww305)",fontsize=16,color="burlywood",shape="box"];3068[label="ww304/Succ ww3040",fontsize=10,color="white",style="solid",shape="box"];2986 -> 3068[label="",style="solid", color="burlywood", weight=9]; 3068 -> 2988[label="",style="solid", color="burlywood", weight=3]; 3069[label="ww304/Zero",fontsize=10,color="white",style="solid",shape="box"];2986 -> 3069[label="",style="solid", color="burlywood", weight=9]; 3069 -> 2989[label="",style="solid", color="burlywood", weight=3]; 2987[label="primDivNatS (primMinusNatS Zero ww304) (Succ ww305)",fontsize=16,color="burlywood",shape="box"];3070[label="ww304/Succ ww3040",fontsize=10,color="white",style="solid",shape="box"];2987 -> 3070[label="",style="solid", color="burlywood", weight=9]; 3070 -> 2990[label="",style="solid", color="burlywood", weight=3]; 3071[label="ww304/Zero",fontsize=10,color="white",style="solid",shape="box"];2987 -> 3071[label="",style="solid", color="burlywood", weight=9]; 3071 -> 2991[label="",style="solid", color="burlywood", weight=3]; 2823[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS (Succ ww2960) ww297)",fontsize=16,color="burlywood",shape="box"];3072[label="ww297/Succ ww2970",fontsize=10,color="white",style="solid",shape="box"];2823 -> 3072[label="",style="solid", color="burlywood", weight=9]; 3072 -> 2833[label="",style="solid", color="burlywood", weight=3]; 3073[label="ww297/Zero",fontsize=10,color="white",style="solid",shape="box"];2823 -> 3073[label="",style="solid", color="burlywood", weight=9]; 3073 -> 2834[label="",style="solid", color="burlywood", weight=3]; 2824[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS Zero ww297)",fontsize=16,color="burlywood",shape="box"];3074[label="ww297/Succ ww2970",fontsize=10,color="white",style="solid",shape="box"];2824 -> 3074[label="",style="solid", color="burlywood", weight=9]; 3074 -> 2835[label="",style="solid", color="burlywood", weight=3]; 3075[label="ww297/Zero",fontsize=10,color="white",style="solid",shape="box"];2824 -> 3075[label="",style="solid", color="burlywood", weight=9]; 3075 -> 2836[label="",style="solid", color="burlywood", weight=3]; 2870[label="Succ ww2450",fontsize=16,color="green",shape="box"];2871[label="Zero",fontsize=16,color="green",shape="box"];2872[label="Zero",fontsize=16,color="green",shape="box"];2869[label="primModNatS (primMinusNatS ww299 ww300) (Succ ww301)",fontsize=16,color="burlywood",shape="triangle"];3076[label="ww299/Succ ww2990",fontsize=10,color="white",style="solid",shape="box"];2869 -> 3076[label="",style="solid", color="burlywood", weight=9]; 3076 -> 2900[label="",style="solid", color="burlywood", weight=3]; 3077[label="ww299/Zero",fontsize=10,color="white",style="solid",shape="box"];2869 -> 3077[label="",style="solid", color="burlywood", weight=9]; 3077 -> 2901[label="",style="solid", color="burlywood", weight=3]; 2873[label="Zero",fontsize=16,color="green",shape="box"];2874[label="Zero",fontsize=16,color="green",shape="box"];2875[label="Zero",fontsize=16,color="green",shape="box"];2825[label="ww2910",fontsize=16,color="green",shape="box"];2826[label="ww2920",fontsize=16,color="green",shape="box"];2827[label="Succ (primDivNatS (primMinusNatS (Succ ww289) (Succ ww290)) (Succ (Succ ww290)))",fontsize=16,color="green",shape="box"];2827 -> 2837[label="",style="dashed", color="green", weight=3]; 2828[label="Zero",fontsize=16,color="green",shape="box"];2988[label="primDivNatS (primMinusNatS (Succ ww3030) (Succ ww3040)) (Succ ww305)",fontsize=16,color="black",shape="box"];2988 -> 2992[label="",style="solid", color="black", weight=3]; 2989[label="primDivNatS (primMinusNatS (Succ ww3030) Zero) (Succ ww305)",fontsize=16,color="black",shape="box"];2989 -> 2993[label="",style="solid", color="black", weight=3]; 2990[label="primDivNatS (primMinusNatS Zero (Succ ww3040)) (Succ ww305)",fontsize=16,color="black",shape="box"];2990 -> 2994[label="",style="solid", color="black", weight=3]; 2991[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww305)",fontsize=16,color="black",shape="box"];2991 -> 2995[label="",style="solid", color="black", weight=3]; 2833[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS (Succ ww2960) (Succ ww2970))",fontsize=16,color="black",shape="box"];2833 -> 2844[label="",style="solid", color="black", weight=3]; 2834[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS (Succ ww2960) Zero)",fontsize=16,color="black",shape="box"];2834 -> 2845[label="",style="solid", color="black", weight=3]; 2835[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS Zero (Succ ww2970))",fontsize=16,color="black",shape="box"];2835 -> 2846[label="",style="solid", color="black", weight=3]; 2836[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2836 -> 2847[label="",style="solid", color="black", weight=3]; 2900[label="primModNatS (primMinusNatS (Succ ww2990) ww300) (Succ ww301)",fontsize=16,color="burlywood",shape="box"];3078[label="ww300/Succ ww3000",fontsize=10,color="white",style="solid",shape="box"];2900 -> 3078[label="",style="solid", color="burlywood", weight=9]; 3078 -> 2906[label="",style="solid", color="burlywood", weight=3]; 3079[label="ww300/Zero",fontsize=10,color="white",style="solid",shape="box"];2900 -> 3079[label="",style="solid", color="burlywood", weight=9]; 3079 -> 2907[label="",style="solid", color="burlywood", weight=3]; 2901[label="primModNatS (primMinusNatS Zero ww300) (Succ ww301)",fontsize=16,color="burlywood",shape="box"];3080[label="ww300/Succ ww3000",fontsize=10,color="white",style="solid",shape="box"];2901 -> 3080[label="",style="solid", color="burlywood", weight=9]; 3080 -> 2908[label="",style="solid", color="burlywood", weight=3]; 3081[label="ww300/Zero",fontsize=10,color="white",style="solid",shape="box"];2901 -> 3081[label="",style="solid", color="burlywood", weight=9]; 3081 -> 2909[label="",style="solid", color="burlywood", weight=3]; 2837 -> 2961[label="",style="dashed", color="red", weight=0]; 2837[label="primDivNatS (primMinusNatS (Succ ww289) (Succ ww290)) (Succ (Succ ww290))",fontsize=16,color="magenta"];2837 -> 2968[label="",style="dashed", color="magenta", weight=3]; 2837 -> 2969[label="",style="dashed", color="magenta", weight=3]; 2837 -> 2970[label="",style="dashed", color="magenta", weight=3]; 2992 -> 2961[label="",style="dashed", color="red", weight=0]; 2992[label="primDivNatS (primMinusNatS ww3030 ww3040) (Succ ww305)",fontsize=16,color="magenta"];2992 -> 2996[label="",style="dashed", color="magenta", weight=3]; 2992 -> 2997[label="",style="dashed", color="magenta", weight=3]; 2993 -> 2176[label="",style="dashed", color="red", weight=0]; 2993[label="primDivNatS (Succ ww3030) (Succ ww305)",fontsize=16,color="magenta"];2993 -> 2998[label="",style="dashed", color="magenta", weight=3]; 2993 -> 2999[label="",style="dashed", color="magenta", weight=3]; 2994[label="primDivNatS Zero (Succ ww305)",fontsize=16,color="black",shape="triangle"];2994 -> 3000[label="",style="solid", color="black", weight=3]; 2995 -> 2994[label="",style="dashed", color="red", weight=0]; 2995[label="primDivNatS Zero (Succ ww305)",fontsize=16,color="magenta"];2844 -> 2782[label="",style="dashed", color="red", weight=0]; 2844[label="primModNatS0 (Succ ww294) (Succ ww295) (primGEqNatS ww2960 ww2970)",fontsize=16,color="magenta"];2844 -> 2853[label="",style="dashed", color="magenta", weight=3]; 2844 -> 2854[label="",style="dashed", color="magenta", weight=3]; 2845[label="primModNatS0 (Succ ww294) (Succ ww295) True",fontsize=16,color="black",shape="triangle"];2845 -> 2855[label="",style="solid", color="black", weight=3]; 2846[label="primModNatS0 (Succ ww294) (Succ ww295) False",fontsize=16,color="black",shape="box"];2846 -> 2856[label="",style="solid", color="black", weight=3]; 2847 -> 2845[label="",style="dashed", color="red", weight=0]; 2847[label="primModNatS0 (Succ ww294) (Succ ww295) True",fontsize=16,color="magenta"];2906[label="primModNatS (primMinusNatS (Succ ww2990) (Succ ww3000)) (Succ ww301)",fontsize=16,color="black",shape="box"];2906 -> 2916[label="",style="solid", color="black", weight=3]; 2907[label="primModNatS (primMinusNatS (Succ ww2990) Zero) (Succ ww301)",fontsize=16,color="black",shape="box"];2907 -> 2917[label="",style="solid", color="black", weight=3]; 2908[label="primModNatS (primMinusNatS Zero (Succ ww3000)) (Succ ww301)",fontsize=16,color="black",shape="box"];2908 -> 2918[label="",style="solid", color="black", weight=3]; 2909[label="primModNatS (primMinusNatS Zero Zero) (Succ ww301)",fontsize=16,color="black",shape="box"];2909 -> 2919[label="",style="solid", color="black", weight=3]; 2968[label="Succ ww290",fontsize=16,color="green",shape="box"];2969[label="Succ ww290",fontsize=16,color="green",shape="box"];2970[label="Succ ww289",fontsize=16,color="green",shape="box"];2996[label="ww3040",fontsize=16,color="green",shape="box"];2997[label="ww3030",fontsize=16,color="green",shape="box"];2998[label="ww3030",fontsize=16,color="green",shape="box"];2999[label="ww305",fontsize=16,color="green",shape="box"];3000[label="Zero",fontsize=16,color="green",shape="box"];2853[label="ww2960",fontsize=16,color="green",shape="box"];2854[label="ww2970",fontsize=16,color="green",shape="box"];2855 -> 2869[label="",style="dashed", color="red", weight=0]; 2855[label="primModNatS (primMinusNatS (Succ ww294) (Succ ww295)) (Succ (Succ ww295))",fontsize=16,color="magenta"];2855 -> 2882[label="",style="dashed", color="magenta", weight=3]; 2855 -> 2883[label="",style="dashed", color="magenta", weight=3]; 2855 -> 2884[label="",style="dashed", color="magenta", weight=3]; 2856[label="Succ (Succ ww294)",fontsize=16,color="green",shape="box"];2916 -> 2869[label="",style="dashed", color="red", weight=0]; 2916[label="primModNatS (primMinusNatS ww2990 ww3000) (Succ ww301)",fontsize=16,color="magenta"];2916 -> 2924[label="",style="dashed", color="magenta", weight=3]; 2916 -> 2925[label="",style="dashed", color="magenta", weight=3]; 2917 -> 2190[label="",style="dashed", color="red", weight=0]; 2917[label="primModNatS (Succ ww2990) (Succ ww301)",fontsize=16,color="magenta"];2917 -> 2926[label="",style="dashed", color="magenta", weight=3]; 2917 -> 2927[label="",style="dashed", color="magenta", weight=3]; 2918[label="primModNatS Zero (Succ ww301)",fontsize=16,color="black",shape="triangle"];2918 -> 2928[label="",style="solid", color="black", weight=3]; 2919 -> 2918[label="",style="dashed", color="red", weight=0]; 2919[label="primModNatS Zero (Succ ww301)",fontsize=16,color="magenta"];2882[label="Succ ww294",fontsize=16,color="green",shape="box"];2883[label="Succ ww295",fontsize=16,color="green",shape="box"];2884[label="Succ ww295",fontsize=16,color="green",shape="box"];2924[label="ww2990",fontsize=16,color="green",shape="box"];2925[label="ww3000",fontsize=16,color="green",shape="box"];2926[label="ww301",fontsize=16,color="green",shape="box"];2927[label="ww2990",fontsize=16,color="green",shape="box"];2928[label="Zero",fontsize=16,color="green",shape="box"];} ---------------------------------------- (199) TRUE