/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty H-Termination with start terms of the given HASKELL could not be shown: (0) HASKELL (1) IFR [EQUIVALENT, 0 ms] (2) HASKELL (3) BR [EQUIVALENT, 0 ms] (4)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) DependencyGraphProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPOrderProof [EQUIVALENT, 3 ms] (15) QDP (16) DependencyGraphProof [EQUIVALENT, 0 ms] (17) QDP (18) QDPSizeChangeProof [EQUIVALENT, 0 ms] (19) YES (20) QDP (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] (22) YES (23) QDP (24) TransformationProof [EQUIVALENT, 26 ms] (25) QDP (26) TransformationProof [EQUIVALENT, 0 ms] (27) QDP (28) TransformationProof [EQUIVALENT, 0 ms] (29) QDP (30) TransformationProof [EQUIVALENT, 0 ms] (31) QDP (32) TransformationProof [EQUIVALENT, 0 ms] (33) QDP (34) TransformationProof [EQUIVALENT, 0 ms] (35) QDP (36) DependencyGraphProof [EQUIVALENT, 0 ms] (37) QDP (38) TransformationProof [EQUIVALENT, 0 ms] (39) QDP (40) DependencyGraphProof [EQUIVALENT, 0 ms] (41) QDP (42) TransformationProof [EQUIVALENT, 0 ms] (43) QDP (44) DependencyGraphProof [EQUIVALENT, 0 ms] (45) QDP (46) TransformationProof [EQUIVALENT, 0 ms] (47) QDP (48) DependencyGraphProof [EQUIVALENT, 0 ms] (49) QDP (50) TransformationProof [EQUIVALENT, 0 ms] (51) QDP (52) DependencyGraphProof [EQUIVALENT, 0 ms] (53) QDP (54) TransformationProof [EQUIVALENT, 0 ms] (55) QDP (56) DependencyGraphProof [EQUIVALENT, 0 ms] (57) QDP (58) TransformationProof [EQUIVALENT, 0 ms] (59) QDP (60) DependencyGraphProof [EQUIVALENT, 0 ms] (61) QDP (62) TransformationProof [EQUIVALENT, 0 ms] (63) QDP (64) DependencyGraphProof [EQUIVALENT, 0 ms] (65) QDP (66) TransformationProof [EQUIVALENT, 0 ms] (67) QDP (68) DependencyGraphProof [EQUIVALENT, 0 ms] (69) QDP (70) TransformationProof [EQUIVALENT, 11 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, 0 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) DependencyGraphProof [EQUIVALENT, 0 ms] (99) QDP (100) TransformationProof [EQUIVALENT, 0 ms] (101) QDP (102) DependencyGraphProof [EQUIVALENT, 0 ms] (103) QDP (104) TransformationProof [EQUIVALENT, 0 ms] (105) QDP (106) QDPSizeChangeProof [EQUIVALENT, 0 ms] (107) YES (108) QDP (109) DependencyGraphProof [EQUIVALENT, 0 ms] (110) QDP (111) QDPOrderProof [EQUIVALENT, 0 ms] (112) QDP (113) DependencyGraphProof [EQUIVALENT, 0 ms] (114) QDP (115) QDPSizeChangeProof [EQUIVALENT, 0 ms] (116) YES (117) QDP (118) DependencyGraphProof [EQUIVALENT, 0 ms] (119) QDP (120) TransformationProof [EQUIVALENT, 0 ms] (121) QDP (122) UsableRulesProof [EQUIVALENT, 0 ms] (123) QDP (124) QReductionProof [EQUIVALENT, 0 ms] (125) QDP (126) MNOCProof [EQUIVALENT, 0 ms] (127) QDP (128) InductionCalculusProof [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) DependencyGraphProof [EQUIVALENT, 0 ms] (137) QDP (138) TransformationProof [EQUIVALENT, 0 ms] (139) QDP (140) DependencyGraphProof [EQUIVALENT, 0 ms] (141) QDP (142) TransformationProof [EQUIVALENT, 0 ms] (143) QDP (144) DependencyGraphProof [EQUIVALENT, 0 ms] (145) QDP (146) MNOCProof [EQUIVALENT, 0 ms] (147) QDP (148) InductionCalculusProof [EQUIVALENT, 0 ms] (149) QDP (150) Narrow [COMPLETE, 0 ms] (151) 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="shows",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="shows ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="shows ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="showsPrec (Pos Zero) ww3 ww4",fontsize=16,color="burlywood",shape="box"];1224[label="ww3/ww30 :% ww31",fontsize=10,color="white",style="solid",shape="box"];5 -> 1224[label="",style="solid", color="burlywood", weight=9]; 1224 -> 6[label="",style="solid", color="burlywood", weight=3]; 6[label="showsPrec (Pos Zero) (ww30 :% ww31) ww4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7 -> 24[label="",style="dashed", color="red", weight=0]; 7[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) ww4",fontsize=16,color="magenta"];7 -> 25[label="",style="dashed", color="magenta", weight=3]; 7 -> 26[label="",style="dashed", color="magenta", weight=3]; 7 -> 27[label="",style="dashed", color="magenta", weight=3]; 7 -> 28[label="",style="dashed", color="magenta", weight=3]; 7 -> 29[label="",style="dashed", color="magenta", weight=3]; 7 -> 30[label="",style="dashed", color="magenta", weight=3]; 25[label="ww30",fontsize=16,color="green",shape="box"];26[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"];27[label="ww4",fontsize=16,color="green",shape="box"];28[label="ww31",fontsize=16,color="green",shape="box"];29[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"];30[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"];24[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) ww22",fontsize=16,color="black",shape="triangle"];24 -> 37[label="",style="solid", color="black", weight=3]; 37[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww22",fontsize=16,color="black",shape="box"];37 -> 38[label="",style="solid", color="black", weight=3]; 38[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww22",fontsize=16,color="black",shape="box"];38 -> 39[label="",style="solid", color="black", weight=3]; 39[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww22",fontsize=16,color="black",shape="box"];39 -> 40[label="",style="solid", color="black", weight=3]; 40[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww22",fontsize=16,color="black",shape="box"];40 -> 41[label="",style="solid", color="black", weight=3]; 41[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (LT == GT) ww22",fontsize=16,color="black",shape="box"];41 -> 42[label="",style="solid", color="black", weight=3]; 42[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) False ww22",fontsize=16,color="black",shape="box"];42 -> 43[label="",style="solid", color="black", weight=3]; 43[label="(shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="black",shape="box"];43 -> 44[label="",style="solid", color="black", weight=3]; 44[label="shows ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];44 -> 45[label="",style="solid", color="black", weight=3]; 45[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="blue",shape="box"];1225[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1225[label="",style="solid", color="blue", weight=9]; 1225 -> 46[label="",style="solid", color="blue", weight=3]; 1226[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1226[label="",style="solid", color="blue", weight=9]; 1226 -> 47[label="",style="solid", color="blue", weight=3]; 1227[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1227[label="",style="solid", color="blue", weight=9]; 1227 -> 48[label="",style="solid", color="blue", weight=3]; 1228[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1228[label="",style="solid", color="blue", weight=9]; 1228 -> 49[label="",style="solid", color="blue", weight=3]; 1229[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1229[label="",style="solid", color="blue", weight=9]; 1229 -> 50[label="",style="solid", color="blue", weight=3]; 1230[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1230[label="",style="solid", color="blue", weight=9]; 1230 -> 51[label="",style="solid", color="blue", weight=3]; 1231[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1231[label="",style="solid", color="blue", weight=9]; 1231 -> 52[label="",style="solid", color="blue", weight=3]; 1232[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1232[label="",style="solid", color="blue", weight=9]; 1232 -> 53[label="",style="solid", color="blue", weight=3]; 1233[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1233[label="",style="solid", color="blue", weight=9]; 1233 -> 54[label="",style="solid", color="blue", weight=3]; 1234[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1234[label="",style="solid", color="blue", weight=9]; 1234 -> 55[label="",style="solid", color="blue", weight=3]; 1235[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1235[label="",style="solid", color="blue", weight=9]; 1235 -> 56[label="",style="solid", color="blue", weight=3]; 1236[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1236[label="",style="solid", color="blue", weight=9]; 1236 -> 57[label="",style="solid", color="blue", weight=3]; 1237[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1237[label="",style="solid", color="blue", weight=9]; 1237 -> 58[label="",style="solid", color="blue", weight=3]; 1238[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1238[label="",style="solid", color="blue", weight=9]; 1238 -> 59[label="",style="solid", color="blue", weight=3]; 1239[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1239[label="",style="solid", color="blue", weight=9]; 1239 -> 60[label="",style="solid", color="blue", weight=3]; 1240[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1240[label="",style="solid", color="blue", weight=9]; 1240 -> 61[label="",style="solid", color="blue", weight=3]; 1241[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1241[label="",style="solid", color="blue", weight=9]; 1241 -> 62[label="",style="solid", color="blue", weight=3]; 1242[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1242[label="",style="solid", color="blue", weight=9]; 1242 -> 63[label="",style="solid", color="blue", weight=3]; 46[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];46 -> 64[label="",style="solid", color="black", weight=3]; 47[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];47 -> 65[label="",style="solid", color="black", weight=3]; 48[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];48 -> 66[label="",style="solid", color="black", weight=3]; 49[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];49 -> 67[label="",style="solid", color="black", weight=3]; 50[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];50 -> 68[label="",style="solid", color="black", weight=3]; 51[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];51 -> 69[label="",style="solid", color="black", weight=3]; 52[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];52 -> 70[label="",style="solid", color="black", weight=3]; 53[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="burlywood",shape="box"];1243[label="ww17/ww170 :% ww171",fontsize=10,color="white",style="solid",shape="box"];53 -> 1243[label="",style="solid", color="burlywood", weight=9]; 1243 -> 71[label="",style="solid", color="burlywood", weight=3]; 54[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];54 -> 72[label="",style="solid", color="black", weight=3]; 55[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];55 -> 73[label="",style="solid", color="black", weight=3]; 56[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];56 -> 74[label="",style="solid", color="black", weight=3]; 57[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];57 -> 75[label="",style="solid", color="black", weight=3]; 58[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];58 -> 76[label="",style="solid", color="black", weight=3]; 59[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];59 -> 77[label="",style="solid", color="black", weight=3]; 60[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];60 -> 78[label="",style="solid", color="black", weight=3]; 61[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];61 -> 79[label="",style="solid", color="black", weight=3]; 62[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];62 -> 80[label="",style="solid", color="black", weight=3]; 63[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];63 -> 81[label="",style="solid", color="black", weight=3]; 64 -> 182[label="",style="dashed", color="red", weight=0]; 64[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];64 -> 183[label="",style="dashed", color="magenta", weight=3]; 64 -> 184[label="",style="dashed", color="magenta", weight=3]; 65 -> 182[label="",style="dashed", color="red", weight=0]; 65[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];65 -> 185[label="",style="dashed", color="magenta", weight=3]; 65 -> 186[label="",style="dashed", color="magenta", weight=3]; 66 -> 182[label="",style="dashed", color="red", weight=0]; 66[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];66 -> 187[label="",style="dashed", color="magenta", weight=3]; 66 -> 188[label="",style="dashed", color="magenta", weight=3]; 67 -> 182[label="",style="dashed", color="red", weight=0]; 67[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];67 -> 189[label="",style="dashed", color="magenta", weight=3]; 67 -> 190[label="",style="dashed", color="magenta", weight=3]; 68 -> 182[label="",style="dashed", color="red", weight=0]; 68[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];68 -> 191[label="",style="dashed", color="magenta", weight=3]; 68 -> 192[label="",style="dashed", color="magenta", weight=3]; 69 -> 182[label="",style="dashed", color="red", weight=0]; 69[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];69 -> 193[label="",style="dashed", color="magenta", weight=3]; 69 -> 194[label="",style="dashed", color="magenta", weight=3]; 70 -> 182[label="",style="dashed", color="red", weight=0]; 70[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];70 -> 195[label="",style="dashed", color="magenta", weight=3]; 70 -> 196[label="",style="dashed", color="magenta", weight=3]; 71[label="showsPrec (Pos Zero) (ww170 :% ww171) ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];71 -> 89[label="",style="solid", color="black", weight=3]; 72 -> 182[label="",style="dashed", color="red", weight=0]; 72[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];72 -> 197[label="",style="dashed", color="magenta", weight=3]; 72 -> 198[label="",style="dashed", color="magenta", weight=3]; 73 -> 182[label="",style="dashed", color="red", weight=0]; 73[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];73 -> 199[label="",style="dashed", color="magenta", weight=3]; 73 -> 200[label="",style="dashed", color="magenta", weight=3]; 74 -> 182[label="",style="dashed", color="red", weight=0]; 74[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];74 -> 201[label="",style="dashed", color="magenta", weight=3]; 74 -> 202[label="",style="dashed", color="magenta", weight=3]; 75 -> 182[label="",style="dashed", color="red", weight=0]; 75[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];75 -> 203[label="",style="dashed", color="magenta", weight=3]; 75 -> 204[label="",style="dashed", color="magenta", weight=3]; 76 -> 182[label="",style="dashed", color="red", weight=0]; 76[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];76 -> 205[label="",style="dashed", color="magenta", weight=3]; 76 -> 206[label="",style="dashed", color="magenta", weight=3]; 77 -> 182[label="",style="dashed", color="red", weight=0]; 77[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];77 -> 207[label="",style="dashed", color="magenta", weight=3]; 77 -> 208[label="",style="dashed", color="magenta", weight=3]; 78 -> 182[label="",style="dashed", color="red", weight=0]; 78[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];78 -> 209[label="",style="dashed", color="magenta", weight=3]; 78 -> 210[label="",style="dashed", color="magenta", weight=3]; 79 -> 182[label="",style="dashed", color="red", weight=0]; 79[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];79 -> 211[label="",style="dashed", color="magenta", weight=3]; 79 -> 212[label="",style="dashed", color="magenta", weight=3]; 80 -> 182[label="",style="dashed", color="red", weight=0]; 80[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];80 -> 213[label="",style="dashed", color="magenta", weight=3]; 80 -> 214[label="",style="dashed", color="magenta", weight=3]; 81 -> 182[label="",style="dashed", color="red", weight=0]; 81[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];81 -> 215[label="",style="dashed", color="magenta", weight=3]; 81 -> 216[label="",style="dashed", color="magenta", weight=3]; 183[label="show ww17",fontsize=16,color="black",shape="triangle"];183 -> 242[label="",style="solid", color="black", weight=3]; 184 -> 102[label="",style="dashed", color="red", weight=0]; 184[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];182[label="ww58 ++ ww56",fontsize=16,color="burlywood",shape="triangle"];1244[label="ww58/ww580 : ww581",fontsize=10,color="white",style="solid",shape="box"];182 -> 1244[label="",style="solid", color="burlywood", weight=9]; 1244 -> 243[label="",style="solid", color="burlywood", weight=3]; 1245[label="ww58/[]",fontsize=10,color="white",style="solid",shape="box"];182 -> 1245[label="",style="solid", color="burlywood", weight=9]; 1245 -> 244[label="",style="solid", color="burlywood", weight=3]; 185[label="show ww17",fontsize=16,color="black",shape="triangle"];185 -> 245[label="",style="solid", color="black", weight=3]; 186 -> 102[label="",style="dashed", color="red", weight=0]; 186[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];187[label="show ww17",fontsize=16,color="black",shape="triangle"];187 -> 246[label="",style="solid", color="black", weight=3]; 188 -> 102[label="",style="dashed", color="red", weight=0]; 188[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];189[label="show ww17",fontsize=16,color="black",shape="triangle"];189 -> 247[label="",style="solid", color="black", weight=3]; 190 -> 102[label="",style="dashed", color="red", weight=0]; 190[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];191[label="show ww17",fontsize=16,color="black",shape="triangle"];191 -> 248[label="",style="solid", color="black", weight=3]; 192 -> 102[label="",style="dashed", color="red", weight=0]; 192[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];193[label="show ww17",fontsize=16,color="black",shape="triangle"];193 -> 249[label="",style="solid", color="black", weight=3]; 194 -> 102[label="",style="dashed", color="red", weight=0]; 194[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];195[label="show ww17",fontsize=16,color="black",shape="triangle"];195 -> 250[label="",style="solid", color="black", weight=3]; 196 -> 102[label="",style="dashed", color="red", weight=0]; 196[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];89 -> 24[label="",style="dashed", color="red", weight=0]; 89[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww170) . (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 ww171) ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="magenta"];89 -> 100[label="",style="dashed", color="magenta", weight=3]; 89 -> 101[label="",style="dashed", color="magenta", weight=3]; 89 -> 102[label="",style="dashed", color="magenta", weight=3]; 89 -> 103[label="",style="dashed", color="magenta", weight=3]; 89 -> 104[label="",style="dashed", color="magenta", weight=3]; 89 -> 105[label="",style="dashed", color="magenta", weight=3]; 197[label="show ww17",fontsize=16,color="black",shape="triangle"];197 -> 251[label="",style="solid", color="black", weight=3]; 198 -> 102[label="",style="dashed", color="red", weight=0]; 198[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];199[label="show ww17",fontsize=16,color="black",shape="triangle"];199 -> 252[label="",style="solid", color="black", weight=3]; 200 -> 102[label="",style="dashed", color="red", weight=0]; 200[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];201[label="show ww17",fontsize=16,color="black",shape="triangle"];201 -> 253[label="",style="solid", color="black", weight=3]; 202 -> 102[label="",style="dashed", color="red", weight=0]; 202[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];203[label="show ww17",fontsize=16,color="black",shape="triangle"];203 -> 254[label="",style="solid", color="black", weight=3]; 204 -> 102[label="",style="dashed", color="red", weight=0]; 204[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];205[label="show ww17",fontsize=16,color="black",shape="triangle"];205 -> 255[label="",style="solid", color="black", weight=3]; 206 -> 102[label="",style="dashed", color="red", weight=0]; 206[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];207[label="show ww17",fontsize=16,color="black",shape="triangle"];207 -> 256[label="",style="solid", color="black", weight=3]; 208 -> 102[label="",style="dashed", color="red", weight=0]; 208[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];209[label="show ww17",fontsize=16,color="black",shape="triangle"];209 -> 257[label="",style="solid", color="black", weight=3]; 210 -> 102[label="",style="dashed", color="red", weight=0]; 210[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];211[label="show ww17",fontsize=16,color="black",shape="triangle"];211 -> 258[label="",style="solid", color="black", weight=3]; 212 -> 102[label="",style="dashed", color="red", weight=0]; 212[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];213[label="show ww17",fontsize=16,color="black",shape="triangle"];213 -> 259[label="",style="solid", color="black", weight=3]; 214 -> 102[label="",style="dashed", color="red", weight=0]; 214[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];215[label="show ww17",fontsize=16,color="black",shape="triangle"];215 -> 260[label="",style="solid", color="black", weight=3]; 216 -> 102[label="",style="dashed", color="red", weight=0]; 216[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];242[label="error []",fontsize=16,color="red",shape="box"];102[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="black",shape="triangle"];102 -> 108[label="",style="solid", color="black", weight=3]; 243[label="(ww580 : ww581) ++ ww56",fontsize=16,color="black",shape="box"];243 -> 262[label="",style="solid", color="black", weight=3]; 244[label="[] ++ ww56",fontsize=16,color="black",shape="box"];244 -> 263[label="",style="solid", color="black", weight=3]; 245[label="error []",fontsize=16,color="red",shape="box"];246[label="error []",fontsize=16,color="red",shape="box"];247[label="error []",fontsize=16,color="red",shape="box"];248[label="error []",fontsize=16,color="red",shape="box"];249[label="error []",fontsize=16,color="red",shape="box"];250[label="error []",fontsize=16,color="red",shape="box"];100[label="ww170",fontsize=16,color="green",shape="box"];101[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"];103[label="ww171",fontsize=16,color="green",shape="box"];104[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"];105[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"];251[label="error []",fontsize=16,color="red",shape="box"];252[label="error []",fontsize=16,color="red",shape="box"];253[label="error []",fontsize=16,color="red",shape="box"];254[label="primShowInt ww17",fontsize=16,color="burlywood",shape="triangle"];1246[label="ww17/Pos ww170",fontsize=10,color="white",style="solid",shape="box"];254 -> 1246[label="",style="solid", color="burlywood", weight=9]; 1246 -> 264[label="",style="solid", color="burlywood", weight=3]; 1247[label="ww17/Neg ww170",fontsize=10,color="white",style="solid",shape="box"];254 -> 1247[label="",style="solid", color="burlywood", weight=9]; 1247 -> 265[label="",style="solid", color="burlywood", weight=3]; 255[label="error []",fontsize=16,color="red",shape="box"];256[label="error []",fontsize=16,color="red",shape="box"];257[label="error []",fontsize=16,color="red",shape="box"];258[label="error []",fontsize=16,color="red",shape="box"];259[label="error []",fontsize=16,color="red",shape="box"];260[label="error []",fontsize=16,color="red",shape="box"];108[label="showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : []) (shows ww21 ww22)",fontsize=16,color="black",shape="box"];108 -> 112[label="",style="solid", color="black", weight=3]; 262[label="ww580 : ww581 ++ ww56",fontsize=16,color="green",shape="box"];262 -> 284[label="",style="dashed", color="green", weight=3]; 263[label="ww56",fontsize=16,color="green",shape="box"];264[label="primShowInt (Pos ww170)",fontsize=16,color="burlywood",shape="box"];1248[label="ww170/Succ ww1700",fontsize=10,color="white",style="solid",shape="box"];264 -> 1248[label="",style="solid", color="burlywood", weight=9]; 1248 -> 285[label="",style="solid", color="burlywood", weight=3]; 1249[label="ww170/Zero",fontsize=10,color="white",style="solid",shape="box"];264 -> 1249[label="",style="solid", color="burlywood", weight=9]; 1249 -> 286[label="",style="solid", color="burlywood", weight=3]; 265[label="primShowInt (Neg ww170)",fontsize=16,color="black",shape="box"];265 -> 287[label="",style="solid", color="black", weight=3]; 112 -> 182[label="",style="dashed", color="red", weight=0]; 112[label="(++) (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : []) shows ww21 ww22",fontsize=16,color="magenta"];112 -> 221[label="",style="dashed", color="magenta", weight=3]; 112 -> 222[label="",style="dashed", color="magenta", weight=3]; 284 -> 182[label="",style="dashed", color="red", weight=0]; 284[label="ww581 ++ ww56",fontsize=16,color="magenta"];284 -> 306[label="",style="dashed", color="magenta", weight=3]; 285[label="primShowInt (Pos (Succ ww1700))",fontsize=16,color="black",shape="box"];285 -> 307[label="",style="solid", color="black", weight=3]; 286[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];286 -> 308[label="",style="solid", color="black", weight=3]; 287[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 ww170)",fontsize=16,color="green",shape="box"];287 -> 309[label="",style="dashed", color="green", weight=3]; 221[label="Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : []",fontsize=16,color="green",shape="box"];222[label="shows ww21 ww22",fontsize=16,color="black",shape="box"];222 -> 261[label="",style="solid", color="black", weight=3]; 306[label="ww581",fontsize=16,color="green",shape="box"];307 -> 182[label="",style="dashed", color="red", weight=0]; 307[label="primShowInt (div Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];307 -> 345[label="",style="dashed", color="magenta", weight=3]; 307 -> 346[label="",style="dashed", color="magenta", weight=3]; 308[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"];309 -> 254[label="",style="dashed", color="red", weight=0]; 309[label="primShowInt (Pos ww170)",fontsize=16,color="magenta"];309 -> 347[label="",style="dashed", color="magenta", weight=3]; 261[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="blue",shape="box"];1250[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1250[label="",style="solid", color="blue", weight=9]; 1250 -> 266[label="",style="solid", color="blue", weight=3]; 1251[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1251[label="",style="solid", color="blue", weight=9]; 1251 -> 267[label="",style="solid", color="blue", weight=3]; 1252[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1252[label="",style="solid", color="blue", weight=9]; 1252 -> 268[label="",style="solid", color="blue", weight=3]; 1253[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1253[label="",style="solid", color="blue", weight=9]; 1253 -> 269[label="",style="solid", color="blue", weight=3]; 1254[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1254[label="",style="solid", color="blue", weight=9]; 1254 -> 270[label="",style="solid", color="blue", weight=3]; 1255[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1255[label="",style="solid", color="blue", weight=9]; 1255 -> 271[label="",style="solid", color="blue", weight=3]; 1256[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1256[label="",style="solid", color="blue", weight=9]; 1256 -> 272[label="",style="solid", color="blue", weight=3]; 1257[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1257[label="",style="solid", color="blue", weight=9]; 1257 -> 273[label="",style="solid", color="blue", weight=3]; 1258[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1258[label="",style="solid", color="blue", weight=9]; 1258 -> 274[label="",style="solid", color="blue", weight=3]; 1259[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1259[label="",style="solid", color="blue", weight=9]; 1259 -> 275[label="",style="solid", color="blue", weight=3]; 1260[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1260[label="",style="solid", color="blue", weight=9]; 1260 -> 276[label="",style="solid", color="blue", weight=3]; 1261[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1261[label="",style="solid", color="blue", weight=9]; 1261 -> 277[label="",style="solid", color="blue", weight=3]; 1262[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1262[label="",style="solid", color="blue", weight=9]; 1262 -> 278[label="",style="solid", color="blue", weight=3]; 1263[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1263[label="",style="solid", color="blue", weight=9]; 1263 -> 279[label="",style="solid", color="blue", weight=3]; 1264[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1264[label="",style="solid", color="blue", weight=9]; 1264 -> 280[label="",style="solid", color="blue", weight=3]; 1265[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1265[label="",style="solid", color="blue", weight=9]; 1265 -> 281[label="",style="solid", color="blue", weight=3]; 1266[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1266[label="",style="solid", color="blue", weight=9]; 1266 -> 282[label="",style="solid", color="blue", weight=3]; 1267[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1267[label="",style="solid", color="blue", weight=9]; 1267 -> 283[label="",style="solid", color="blue", weight=3]; 345 -> 254[label="",style="dashed", color="red", weight=0]; 345[label="primShowInt (div Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];345 -> 370[label="",style="dashed", color="magenta", weight=3]; 346[label="toEnum (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];346 -> 371[label="",style="dashed", color="green", weight=3]; 347[label="Pos ww170",fontsize=16,color="green",shape="box"];266[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];266 -> 288[label="",style="solid", color="black", weight=3]; 267[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];267 -> 289[label="",style="solid", color="black", weight=3]; 268[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];268 -> 290[label="",style="solid", color="black", weight=3]; 269[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];269 -> 291[label="",style="solid", color="black", weight=3]; 270[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];270 -> 292[label="",style="solid", color="black", weight=3]; 271[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];271 -> 293[label="",style="solid", color="black", weight=3]; 272[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];272 -> 294[label="",style="solid", color="black", weight=3]; 273[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="burlywood",shape="box"];1268[label="ww21/ww210 :% ww211",fontsize=10,color="white",style="solid",shape="box"];273 -> 1268[label="",style="solid", color="burlywood", weight=9]; 1268 -> 295[label="",style="solid", color="burlywood", weight=3]; 274[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];274 -> 296[label="",style="solid", color="black", weight=3]; 275[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];275 -> 297[label="",style="solid", color="black", weight=3]; 276[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];276 -> 298[label="",style="solid", color="black", weight=3]; 277[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];277 -> 299[label="",style="solid", color="black", weight=3]; 278[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];278 -> 300[label="",style="solid", color="black", weight=3]; 279[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];279 -> 301[label="",style="solid", color="black", weight=3]; 280[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];280 -> 302[label="",style="solid", color="black", weight=3]; 281[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];281 -> 303[label="",style="solid", color="black", weight=3]; 282[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];282 -> 304[label="",style="solid", color="black", weight=3]; 283[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];283 -> 305[label="",style="solid", color="black", weight=3]; 370 -> 372[label="",style="dashed", color="red", weight=0]; 370[label="div Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];370 -> 373[label="",style="dashed", color="magenta", weight=3]; 370 -> 374[label="",style="dashed", color="magenta", weight=3]; 371[label="toEnum (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];371 -> 389[label="",style="solid", color="black", weight=3]; 288 -> 182[label="",style="dashed", color="red", weight=0]; 288[label="show ww21 ++ ww22",fontsize=16,color="magenta"];288 -> 310[label="",style="dashed", color="magenta", weight=3]; 288 -> 311[label="",style="dashed", color="magenta", weight=3]; 289 -> 182[label="",style="dashed", color="red", weight=0]; 289[label="show ww21 ++ ww22",fontsize=16,color="magenta"];289 -> 312[label="",style="dashed", color="magenta", weight=3]; 289 -> 313[label="",style="dashed", color="magenta", weight=3]; 290 -> 182[label="",style="dashed", color="red", weight=0]; 290[label="show ww21 ++ ww22",fontsize=16,color="magenta"];290 -> 314[label="",style="dashed", color="magenta", weight=3]; 290 -> 315[label="",style="dashed", color="magenta", weight=3]; 291 -> 182[label="",style="dashed", color="red", weight=0]; 291[label="show ww21 ++ ww22",fontsize=16,color="magenta"];291 -> 316[label="",style="dashed", color="magenta", weight=3]; 291 -> 317[label="",style="dashed", color="magenta", weight=3]; 292 -> 182[label="",style="dashed", color="red", weight=0]; 292[label="show ww21 ++ ww22",fontsize=16,color="magenta"];292 -> 318[label="",style="dashed", color="magenta", weight=3]; 292 -> 319[label="",style="dashed", color="magenta", weight=3]; 293 -> 182[label="",style="dashed", color="red", weight=0]; 293[label="show ww21 ++ ww22",fontsize=16,color="magenta"];293 -> 320[label="",style="dashed", color="magenta", weight=3]; 293 -> 321[label="",style="dashed", color="magenta", weight=3]; 294 -> 182[label="",style="dashed", color="red", weight=0]; 294[label="show ww21 ++ ww22",fontsize=16,color="magenta"];294 -> 322[label="",style="dashed", color="magenta", weight=3]; 294 -> 323[label="",style="dashed", color="magenta", weight=3]; 295[label="showsPrec (Pos Zero) (ww210 :% ww211) ww22",fontsize=16,color="black",shape="box"];295 -> 324[label="",style="solid", color="black", weight=3]; 296 -> 182[label="",style="dashed", color="red", weight=0]; 296[label="show ww21 ++ ww22",fontsize=16,color="magenta"];296 -> 325[label="",style="dashed", color="magenta", weight=3]; 296 -> 326[label="",style="dashed", color="magenta", weight=3]; 297 -> 182[label="",style="dashed", color="red", weight=0]; 297[label="show ww21 ++ ww22",fontsize=16,color="magenta"];297 -> 327[label="",style="dashed", color="magenta", weight=3]; 297 -> 328[label="",style="dashed", color="magenta", weight=3]; 298 -> 182[label="",style="dashed", color="red", weight=0]; 298[label="show ww21 ++ ww22",fontsize=16,color="magenta"];298 -> 329[label="",style="dashed", color="magenta", weight=3]; 298 -> 330[label="",style="dashed", color="magenta", weight=3]; 299 -> 182[label="",style="dashed", color="red", weight=0]; 299[label="show ww21 ++ ww22",fontsize=16,color="magenta"];299 -> 331[label="",style="dashed", color="magenta", weight=3]; 299 -> 332[label="",style="dashed", color="magenta", weight=3]; 300 -> 182[label="",style="dashed", color="red", weight=0]; 300[label="show ww21 ++ ww22",fontsize=16,color="magenta"];300 -> 333[label="",style="dashed", color="magenta", weight=3]; 300 -> 334[label="",style="dashed", color="magenta", weight=3]; 301 -> 182[label="",style="dashed", color="red", weight=0]; 301[label="show ww21 ++ ww22",fontsize=16,color="magenta"];301 -> 335[label="",style="dashed", color="magenta", weight=3]; 301 -> 336[label="",style="dashed", color="magenta", weight=3]; 302 -> 182[label="",style="dashed", color="red", weight=0]; 302[label="show ww21 ++ ww22",fontsize=16,color="magenta"];302 -> 337[label="",style="dashed", color="magenta", weight=3]; 302 -> 338[label="",style="dashed", color="magenta", weight=3]; 303 -> 182[label="",style="dashed", color="red", weight=0]; 303[label="show ww21 ++ ww22",fontsize=16,color="magenta"];303 -> 339[label="",style="dashed", color="magenta", weight=3]; 303 -> 340[label="",style="dashed", color="magenta", weight=3]; 304 -> 182[label="",style="dashed", color="red", weight=0]; 304[label="show ww21 ++ ww22",fontsize=16,color="magenta"];304 -> 341[label="",style="dashed", color="magenta", weight=3]; 304 -> 342[label="",style="dashed", color="magenta", weight=3]; 305 -> 182[label="",style="dashed", color="red", weight=0]; 305[label="show ww21 ++ ww22",fontsize=16,color="magenta"];305 -> 343[label="",style="dashed", color="magenta", weight=3]; 305 -> 344[label="",style="dashed", color="magenta", weight=3]; 373[label="ww1700",fontsize=16,color="green",shape="box"];374[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];372[label="div Pos (Succ ww60) Pos (Succ ww61)",fontsize=16,color="black",shape="triangle"];372 -> 378[label="",style="solid", color="black", weight=3]; 389 -> 400[label="",style="dashed", color="red", weight=0]; 389[label="primIntToChar (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];389 -> 401[label="",style="dashed", color="magenta", weight=3]; 389 -> 402[label="",style="dashed", color="magenta", weight=3]; 310 -> 183[label="",style="dashed", color="red", weight=0]; 310[label="show ww21",fontsize=16,color="magenta"];310 -> 348[label="",style="dashed", color="magenta", weight=3]; 311[label="ww22",fontsize=16,color="green",shape="box"];312 -> 185[label="",style="dashed", color="red", weight=0]; 312[label="show ww21",fontsize=16,color="magenta"];312 -> 349[label="",style="dashed", color="magenta", weight=3]; 313[label="ww22",fontsize=16,color="green",shape="box"];314 -> 187[label="",style="dashed", color="red", weight=0]; 314[label="show ww21",fontsize=16,color="magenta"];314 -> 350[label="",style="dashed", color="magenta", weight=3]; 315[label="ww22",fontsize=16,color="green",shape="box"];316 -> 189[label="",style="dashed", color="red", weight=0]; 316[label="show ww21",fontsize=16,color="magenta"];316 -> 351[label="",style="dashed", color="magenta", weight=3]; 317[label="ww22",fontsize=16,color="green",shape="box"];318 -> 191[label="",style="dashed", color="red", weight=0]; 318[label="show ww21",fontsize=16,color="magenta"];318 -> 352[label="",style="dashed", color="magenta", weight=3]; 319[label="ww22",fontsize=16,color="green",shape="box"];320 -> 193[label="",style="dashed", color="red", weight=0]; 320[label="show ww21",fontsize=16,color="magenta"];320 -> 353[label="",style="dashed", color="magenta", weight=3]; 321[label="ww22",fontsize=16,color="green",shape="box"];322 -> 195[label="",style="dashed", color="red", weight=0]; 322[label="show ww21",fontsize=16,color="magenta"];322 -> 354[label="",style="dashed", color="magenta", weight=3]; 323[label="ww22",fontsize=16,color="green",shape="box"];324 -> 24[label="",style="dashed", color="red", weight=0]; 324[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww210) . (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 ww211) ww22",fontsize=16,color="magenta"];324 -> 355[label="",style="dashed", color="magenta", weight=3]; 324 -> 356[label="",style="dashed", color="magenta", weight=3]; 324 -> 357[label="",style="dashed", color="magenta", weight=3]; 324 -> 358[label="",style="dashed", color="magenta", weight=3]; 324 -> 359[label="",style="dashed", color="magenta", weight=3]; 325 -> 197[label="",style="dashed", color="red", weight=0]; 325[label="show ww21",fontsize=16,color="magenta"];325 -> 360[label="",style="dashed", color="magenta", weight=3]; 326[label="ww22",fontsize=16,color="green",shape="box"];327 -> 199[label="",style="dashed", color="red", weight=0]; 327[label="show ww21",fontsize=16,color="magenta"];327 -> 361[label="",style="dashed", color="magenta", weight=3]; 328[label="ww22",fontsize=16,color="green",shape="box"];329 -> 201[label="",style="dashed", color="red", weight=0]; 329[label="show ww21",fontsize=16,color="magenta"];329 -> 362[label="",style="dashed", color="magenta", weight=3]; 330[label="ww22",fontsize=16,color="green",shape="box"];331 -> 203[label="",style="dashed", color="red", weight=0]; 331[label="show ww21",fontsize=16,color="magenta"];331 -> 363[label="",style="dashed", color="magenta", weight=3]; 332[label="ww22",fontsize=16,color="green",shape="box"];333 -> 205[label="",style="dashed", color="red", weight=0]; 333[label="show ww21",fontsize=16,color="magenta"];333 -> 364[label="",style="dashed", color="magenta", weight=3]; 334[label="ww22",fontsize=16,color="green",shape="box"];335 -> 207[label="",style="dashed", color="red", weight=0]; 335[label="show ww21",fontsize=16,color="magenta"];335 -> 365[label="",style="dashed", color="magenta", weight=3]; 336[label="ww22",fontsize=16,color="green",shape="box"];337 -> 209[label="",style="dashed", color="red", weight=0]; 337[label="show ww21",fontsize=16,color="magenta"];337 -> 366[label="",style="dashed", color="magenta", weight=3]; 338[label="ww22",fontsize=16,color="green",shape="box"];339 -> 211[label="",style="dashed", color="red", weight=0]; 339[label="show ww21",fontsize=16,color="magenta"];339 -> 367[label="",style="dashed", color="magenta", weight=3]; 340[label="ww22",fontsize=16,color="green",shape="box"];341 -> 213[label="",style="dashed", color="red", weight=0]; 341[label="show ww21",fontsize=16,color="magenta"];341 -> 368[label="",style="dashed", color="magenta", weight=3]; 342[label="ww22",fontsize=16,color="green",shape="box"];343 -> 215[label="",style="dashed", color="red", weight=0]; 343[label="show ww21",fontsize=16,color="magenta"];343 -> 369[label="",style="dashed", color="magenta", weight=3]; 344[label="ww22",fontsize=16,color="green",shape="box"];378[label="primDivInt (Pos (Succ ww60)) (Pos (Succ ww61))",fontsize=16,color="black",shape="box"];378 -> 388[label="",style="solid", color="black", weight=3]; 401[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];402[label="ww1700",fontsize=16,color="green",shape="box"];400[label="primIntToChar (mod Pos (Succ ww66) Pos (Succ ww67))",fontsize=16,color="black",shape="triangle"];400 -> 403[label="",style="solid", color="black", weight=3]; 348[label="ww21",fontsize=16,color="green",shape="box"];349[label="ww21",fontsize=16,color="green",shape="box"];350[label="ww21",fontsize=16,color="green",shape="box"];351[label="ww21",fontsize=16,color="green",shape="box"];352[label="ww21",fontsize=16,color="green",shape="box"];353[label="ww21",fontsize=16,color="green",shape="box"];354[label="ww21",fontsize=16,color="green",shape="box"];355[label="ww210",fontsize=16,color="green",shape="box"];356[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"];357[label="ww211",fontsize=16,color="green",shape="box"];358[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"];359[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"];360[label="ww21",fontsize=16,color="green",shape="box"];361[label="ww21",fontsize=16,color="green",shape="box"];362[label="ww21",fontsize=16,color="green",shape="box"];363[label="ww21",fontsize=16,color="green",shape="box"];364[label="ww21",fontsize=16,color="green",shape="box"];365[label="ww21",fontsize=16,color="green",shape="box"];366[label="ww21",fontsize=16,color="green",shape="box"];367[label="ww21",fontsize=16,color="green",shape="box"];368[label="ww21",fontsize=16,color="green",shape="box"];369[label="ww21",fontsize=16,color="green",shape="box"];388[label="Pos (primDivNatS (Succ ww60) (Succ ww61))",fontsize=16,color="green",shape="box"];388 -> 399[label="",style="dashed", color="green", weight=3]; 403[label="primIntToChar (primModInt (Pos (Succ ww66)) (Pos (Succ ww67)))",fontsize=16,color="black",shape="box"];403 -> 405[label="",style="solid", color="black", weight=3]; 399[label="primDivNatS (Succ ww60) (Succ ww61)",fontsize=16,color="black",shape="triangle"];399 -> 404[label="",style="solid", color="black", weight=3]; 405[label="primIntToChar (Pos (primModNatS (Succ ww66) (Succ ww67)))",fontsize=16,color="black",shape="box"];405 -> 408[label="",style="solid", color="black", weight=3]; 404[label="primDivNatS0 ww60 ww61 (primGEqNatS ww60 ww61)",fontsize=16,color="burlywood",shape="box"];1269[label="ww60/Succ ww600",fontsize=10,color="white",style="solid",shape="box"];404 -> 1269[label="",style="solid", color="burlywood", weight=9]; 1269 -> 406[label="",style="solid", color="burlywood", weight=3]; 1270[label="ww60/Zero",fontsize=10,color="white",style="solid",shape="box"];404 -> 1270[label="",style="solid", color="burlywood", weight=9]; 1270 -> 407[label="",style="solid", color="burlywood", weight=3]; 408[label="Char (primModNatS (Succ ww66) (Succ ww67))",fontsize=16,color="green",shape="box"];408 -> 413[label="",style="dashed", color="green", weight=3]; 406[label="primDivNatS0 (Succ ww600) ww61 (primGEqNatS (Succ ww600) ww61)",fontsize=16,color="burlywood",shape="box"];1271[label="ww61/Succ ww610",fontsize=10,color="white",style="solid",shape="box"];406 -> 1271[label="",style="solid", color="burlywood", weight=9]; 1271 -> 409[label="",style="solid", color="burlywood", weight=3]; 1272[label="ww61/Zero",fontsize=10,color="white",style="solid",shape="box"];406 -> 1272[label="",style="solid", color="burlywood", weight=9]; 1272 -> 410[label="",style="solid", color="burlywood", weight=3]; 407[label="primDivNatS0 Zero ww61 (primGEqNatS Zero ww61)",fontsize=16,color="burlywood",shape="box"];1273[label="ww61/Succ ww610",fontsize=10,color="white",style="solid",shape="box"];407 -> 1273[label="",style="solid", color="burlywood", weight=9]; 1273 -> 411[label="",style="solid", color="burlywood", weight=3]; 1274[label="ww61/Zero",fontsize=10,color="white",style="solid",shape="box"];407 -> 1274[label="",style="solid", color="burlywood", weight=9]; 1274 -> 412[label="",style="solid", color="burlywood", weight=3]; 413[label="primModNatS (Succ ww66) (Succ ww67)",fontsize=16,color="black",shape="triangle"];413 -> 418[label="",style="solid", color="black", weight=3]; 409[label="primDivNatS0 (Succ ww600) (Succ ww610) (primGEqNatS (Succ ww600) (Succ ww610))",fontsize=16,color="black",shape="box"];409 -> 414[label="",style="solid", color="black", weight=3]; 410[label="primDivNatS0 (Succ ww600) Zero (primGEqNatS (Succ ww600) Zero)",fontsize=16,color="black",shape="box"];410 -> 415[label="",style="solid", color="black", weight=3]; 411[label="primDivNatS0 Zero (Succ ww610) (primGEqNatS Zero (Succ ww610))",fontsize=16,color="black",shape="box"];411 -> 416[label="",style="solid", color="black", weight=3]; 412[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];412 -> 417[label="",style="solid", color="black", weight=3]; 418[label="primModNatS0 ww66 ww67 (primGEqNatS ww66 ww67)",fontsize=16,color="burlywood",shape="box"];1275[label="ww66/Succ ww660",fontsize=10,color="white",style="solid",shape="box"];418 -> 1275[label="",style="solid", color="burlywood", weight=9]; 1275 -> 424[label="",style="solid", color="burlywood", weight=3]; 1276[label="ww66/Zero",fontsize=10,color="white",style="solid",shape="box"];418 -> 1276[label="",style="solid", color="burlywood", weight=9]; 1276 -> 425[label="",style="solid", color="burlywood", weight=3]; 414 -> 930[label="",style="dashed", color="red", weight=0]; 414[label="primDivNatS0 (Succ ww600) (Succ ww610) (primGEqNatS ww600 ww610)",fontsize=16,color="magenta"];414 -> 931[label="",style="dashed", color="magenta", weight=3]; 414 -> 932[label="",style="dashed", color="magenta", weight=3]; 414 -> 933[label="",style="dashed", color="magenta", weight=3]; 414 -> 934[label="",style="dashed", color="magenta", weight=3]; 415[label="primDivNatS0 (Succ ww600) Zero True",fontsize=16,color="black",shape="box"];415 -> 421[label="",style="solid", color="black", weight=3]; 416[label="primDivNatS0 Zero (Succ ww610) False",fontsize=16,color="black",shape="box"];416 -> 422[label="",style="solid", color="black", weight=3]; 417[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];417 -> 423[label="",style="solid", color="black", weight=3]; 424[label="primModNatS0 (Succ ww660) ww67 (primGEqNatS (Succ ww660) ww67)",fontsize=16,color="burlywood",shape="box"];1277[label="ww67/Succ ww670",fontsize=10,color="white",style="solid",shape="box"];424 -> 1277[label="",style="solid", color="burlywood", weight=9]; 1277 -> 432[label="",style="solid", color="burlywood", weight=3]; 1278[label="ww67/Zero",fontsize=10,color="white",style="solid",shape="box"];424 -> 1278[label="",style="solid", color="burlywood", weight=9]; 1278 -> 433[label="",style="solid", color="burlywood", weight=3]; 425[label="primModNatS0 Zero ww67 (primGEqNatS Zero ww67)",fontsize=16,color="burlywood",shape="box"];1279[label="ww67/Succ ww670",fontsize=10,color="white",style="solid",shape="box"];425 -> 1279[label="",style="solid", color="burlywood", weight=9]; 1279 -> 434[label="",style="solid", color="burlywood", weight=3]; 1280[label="ww67/Zero",fontsize=10,color="white",style="solid",shape="box"];425 -> 1280[label="",style="solid", color="burlywood", weight=9]; 1280 -> 435[label="",style="solid", color="burlywood", weight=3]; 931[label="ww610",fontsize=16,color="green",shape="box"];932[label="ww600",fontsize=16,color="green",shape="box"];933[label="ww600",fontsize=16,color="green",shape="box"];934[label="ww610",fontsize=16,color="green",shape="box"];930[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS ww112 ww113)",fontsize=16,color="burlywood",shape="triangle"];1281[label="ww112/Succ ww1120",fontsize=10,color="white",style="solid",shape="box"];930 -> 1281[label="",style="solid", color="burlywood", weight=9]; 1281 -> 971[label="",style="solid", color="burlywood", weight=3]; 1282[label="ww112/Zero",fontsize=10,color="white",style="solid",shape="box"];930 -> 1282[label="",style="solid", color="burlywood", weight=9]; 1282 -> 972[label="",style="solid", color="burlywood", weight=3]; 421[label="Succ (primDivNatS (primMinusNatS (Succ ww600) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];421 -> 430[label="",style="dashed", color="green", weight=3]; 422[label="Zero",fontsize=16,color="green",shape="box"];423[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];423 -> 431[label="",style="dashed", color="green", weight=3]; 432[label="primModNatS0 (Succ ww660) (Succ ww670) (primGEqNatS (Succ ww660) (Succ ww670))",fontsize=16,color="black",shape="box"];432 -> 442[label="",style="solid", color="black", weight=3]; 433[label="primModNatS0 (Succ ww660) Zero (primGEqNatS (Succ ww660) Zero)",fontsize=16,color="black",shape="box"];433 -> 443[label="",style="solid", color="black", weight=3]; 434[label="primModNatS0 Zero (Succ ww670) (primGEqNatS Zero (Succ ww670))",fontsize=16,color="black",shape="box"];434 -> 444[label="",style="solid", color="black", weight=3]; 435[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];435 -> 445[label="",style="solid", color="black", weight=3]; 971[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS (Succ ww1120) ww113)",fontsize=16,color="burlywood",shape="box"];1283[label="ww113/Succ ww1130",fontsize=10,color="white",style="solid",shape="box"];971 -> 1283[label="",style="solid", color="burlywood", weight=9]; 1283 -> 983[label="",style="solid", color="burlywood", weight=3]; 1284[label="ww113/Zero",fontsize=10,color="white",style="solid",shape="box"];971 -> 1284[label="",style="solid", color="burlywood", weight=9]; 1284 -> 984[label="",style="solid", color="burlywood", weight=3]; 972[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS Zero ww113)",fontsize=16,color="burlywood",shape="box"];1285[label="ww113/Succ ww1130",fontsize=10,color="white",style="solid",shape="box"];972 -> 1285[label="",style="solid", color="burlywood", weight=9]; 1285 -> 985[label="",style="solid", color="burlywood", weight=3]; 1286[label="ww113/Zero",fontsize=10,color="white",style="solid",shape="box"];972 -> 1286[label="",style="solid", color="burlywood", weight=9]; 1286 -> 986[label="",style="solid", color="burlywood", weight=3]; 430 -> 1184[label="",style="dashed", color="red", weight=0]; 430[label="primDivNatS (primMinusNatS (Succ ww600) Zero) (Succ Zero)",fontsize=16,color="magenta"];430 -> 1185[label="",style="dashed", color="magenta", weight=3]; 430 -> 1186[label="",style="dashed", color="magenta", weight=3]; 430 -> 1187[label="",style="dashed", color="magenta", weight=3]; 431 -> 1184[label="",style="dashed", color="red", weight=0]; 431[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];431 -> 1188[label="",style="dashed", color="magenta", weight=3]; 431 -> 1189[label="",style="dashed", color="magenta", weight=3]; 431 -> 1190[label="",style="dashed", color="magenta", weight=3]; 442 -> 1005[label="",style="dashed", color="red", weight=0]; 442[label="primModNatS0 (Succ ww660) (Succ ww670) (primGEqNatS ww660 ww670)",fontsize=16,color="magenta"];442 -> 1006[label="",style="dashed", color="magenta", weight=3]; 442 -> 1007[label="",style="dashed", color="magenta", weight=3]; 442 -> 1008[label="",style="dashed", color="magenta", weight=3]; 442 -> 1009[label="",style="dashed", color="magenta", weight=3]; 443[label="primModNatS0 (Succ ww660) Zero True",fontsize=16,color="black",shape="box"];443 -> 456[label="",style="solid", color="black", weight=3]; 444[label="primModNatS0 Zero (Succ ww670) False",fontsize=16,color="black",shape="box"];444 -> 457[label="",style="solid", color="black", weight=3]; 445[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];445 -> 458[label="",style="solid", color="black", weight=3]; 983[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS (Succ ww1120) (Succ ww1130))",fontsize=16,color="black",shape="box"];983 -> 997[label="",style="solid", color="black", weight=3]; 984[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS (Succ ww1120) Zero)",fontsize=16,color="black",shape="box"];984 -> 998[label="",style="solid", color="black", weight=3]; 985[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS Zero (Succ ww1130))",fontsize=16,color="black",shape="box"];985 -> 999[label="",style="solid", color="black", weight=3]; 986[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];986 -> 1000[label="",style="solid", color="black", weight=3]; 1185[label="Succ ww600",fontsize=16,color="green",shape="box"];1186[label="Zero",fontsize=16,color="green",shape="box"];1187[label="Zero",fontsize=16,color="green",shape="box"];1184[label="primDivNatS (primMinusNatS ww124 ww125) (Succ ww126)",fontsize=16,color="burlywood",shape="triangle"];1287[label="ww124/Succ ww1240",fontsize=10,color="white",style="solid",shape="box"];1184 -> 1287[label="",style="solid", color="burlywood", weight=9]; 1287 -> 1209[label="",style="solid", color="burlywood", weight=3]; 1288[label="ww124/Zero",fontsize=10,color="white",style="solid",shape="box"];1184 -> 1288[label="",style="solid", color="burlywood", weight=9]; 1288 -> 1210[label="",style="solid", color="burlywood", weight=3]; 1188[label="Zero",fontsize=16,color="green",shape="box"];1189[label="Zero",fontsize=16,color="green",shape="box"];1190[label="Zero",fontsize=16,color="green",shape="box"];1006[label="ww660",fontsize=16,color="green",shape="box"];1007[label="ww670",fontsize=16,color="green",shape="box"];1008[label="ww660",fontsize=16,color="green",shape="box"];1009[label="ww670",fontsize=16,color="green",shape="box"];1005[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS ww117 ww118)",fontsize=16,color="burlywood",shape="triangle"];1289[label="ww117/Succ ww1170",fontsize=10,color="white",style="solid",shape="box"];1005 -> 1289[label="",style="solid", color="burlywood", weight=9]; 1289 -> 1046[label="",style="solid", color="burlywood", weight=3]; 1290[label="ww117/Zero",fontsize=10,color="white",style="solid",shape="box"];1005 -> 1290[label="",style="solid", color="burlywood", weight=9]; 1290 -> 1047[label="",style="solid", color="burlywood", weight=3]; 456 -> 1092[label="",style="dashed", color="red", weight=0]; 456[label="primModNatS (primMinusNatS (Succ ww660) Zero) (Succ Zero)",fontsize=16,color="magenta"];456 -> 1093[label="",style="dashed", color="magenta", weight=3]; 456 -> 1094[label="",style="dashed", color="magenta", weight=3]; 456 -> 1095[label="",style="dashed", color="magenta", weight=3]; 457[label="Succ Zero",fontsize=16,color="green",shape="box"];458 -> 1092[label="",style="dashed", color="red", weight=0]; 458[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];458 -> 1096[label="",style="dashed", color="magenta", weight=3]; 458 -> 1097[label="",style="dashed", color="magenta", weight=3]; 458 -> 1098[label="",style="dashed", color="magenta", weight=3]; 997 -> 930[label="",style="dashed", color="red", weight=0]; 997[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS ww1120 ww1130)",fontsize=16,color="magenta"];997 -> 1048[label="",style="dashed", color="magenta", weight=3]; 997 -> 1049[label="",style="dashed", color="magenta", weight=3]; 998[label="primDivNatS0 (Succ ww110) (Succ ww111) True",fontsize=16,color="black",shape="triangle"];998 -> 1050[label="",style="solid", color="black", weight=3]; 999[label="primDivNatS0 (Succ ww110) (Succ ww111) False",fontsize=16,color="black",shape="box"];999 -> 1051[label="",style="solid", color="black", weight=3]; 1000 -> 998[label="",style="dashed", color="red", weight=0]; 1000[label="primDivNatS0 (Succ ww110) (Succ ww111) True",fontsize=16,color="magenta"];1209[label="primDivNatS (primMinusNatS (Succ ww1240) ww125) (Succ ww126)",fontsize=16,color="burlywood",shape="box"];1291[label="ww125/Succ ww1250",fontsize=10,color="white",style="solid",shape="box"];1209 -> 1291[label="",style="solid", color="burlywood", weight=9]; 1291 -> 1211[label="",style="solid", color="burlywood", weight=3]; 1292[label="ww125/Zero",fontsize=10,color="white",style="solid",shape="box"];1209 -> 1292[label="",style="solid", color="burlywood", weight=9]; 1292 -> 1212[label="",style="solid", color="burlywood", weight=3]; 1210[label="primDivNatS (primMinusNatS Zero ww125) (Succ ww126)",fontsize=16,color="burlywood",shape="box"];1293[label="ww125/Succ ww1250",fontsize=10,color="white",style="solid",shape="box"];1210 -> 1293[label="",style="solid", color="burlywood", weight=9]; 1293 -> 1213[label="",style="solid", color="burlywood", weight=3]; 1294[label="ww125/Zero",fontsize=10,color="white",style="solid",shape="box"];1210 -> 1294[label="",style="solid", color="burlywood", weight=9]; 1294 -> 1214[label="",style="solid", color="burlywood", weight=3]; 1046[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS (Succ ww1170) ww118)",fontsize=16,color="burlywood",shape="box"];1295[label="ww118/Succ ww1180",fontsize=10,color="white",style="solid",shape="box"];1046 -> 1295[label="",style="solid", color="burlywood", weight=9]; 1295 -> 1056[label="",style="solid", color="burlywood", weight=3]; 1296[label="ww118/Zero",fontsize=10,color="white",style="solid",shape="box"];1046 -> 1296[label="",style="solid", color="burlywood", weight=9]; 1296 -> 1057[label="",style="solid", color="burlywood", weight=3]; 1047[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS Zero ww118)",fontsize=16,color="burlywood",shape="box"];1297[label="ww118/Succ ww1180",fontsize=10,color="white",style="solid",shape="box"];1047 -> 1297[label="",style="solid", color="burlywood", weight=9]; 1297 -> 1058[label="",style="solid", color="burlywood", weight=3]; 1298[label="ww118/Zero",fontsize=10,color="white",style="solid",shape="box"];1047 -> 1298[label="",style="solid", color="burlywood", weight=9]; 1298 -> 1059[label="",style="solid", color="burlywood", weight=3]; 1093[label="Succ ww660",fontsize=16,color="green",shape="box"];1094[label="Zero",fontsize=16,color="green",shape="box"];1095[label="Zero",fontsize=16,color="green",shape="box"];1092[label="primModNatS (primMinusNatS ww120 ww121) (Succ ww122)",fontsize=16,color="burlywood",shape="triangle"];1299[label="ww120/Succ ww1200",fontsize=10,color="white",style="solid",shape="box"];1092 -> 1299[label="",style="solid", color="burlywood", weight=9]; 1299 -> 1123[label="",style="solid", color="burlywood", weight=3]; 1300[label="ww120/Zero",fontsize=10,color="white",style="solid",shape="box"];1092 -> 1300[label="",style="solid", color="burlywood", weight=9]; 1300 -> 1124[label="",style="solid", color="burlywood", weight=3]; 1096[label="Zero",fontsize=16,color="green",shape="box"];1097[label="Zero",fontsize=16,color="green",shape="box"];1098[label="Zero",fontsize=16,color="green",shape="box"];1048[label="ww1130",fontsize=16,color="green",shape="box"];1049[label="ww1120",fontsize=16,color="green",shape="box"];1050[label="Succ (primDivNatS (primMinusNatS (Succ ww110) (Succ ww111)) (Succ (Succ ww111)))",fontsize=16,color="green",shape="box"];1050 -> 1060[label="",style="dashed", color="green", weight=3]; 1051[label="Zero",fontsize=16,color="green",shape="box"];1211[label="primDivNatS (primMinusNatS (Succ ww1240) (Succ ww1250)) (Succ ww126)",fontsize=16,color="black",shape="box"];1211 -> 1215[label="",style="solid", color="black", weight=3]; 1212[label="primDivNatS (primMinusNatS (Succ ww1240) Zero) (Succ ww126)",fontsize=16,color="black",shape="box"];1212 -> 1216[label="",style="solid", color="black", weight=3]; 1213[label="primDivNatS (primMinusNatS Zero (Succ ww1250)) (Succ ww126)",fontsize=16,color="black",shape="box"];1213 -> 1217[label="",style="solid", color="black", weight=3]; 1214[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww126)",fontsize=16,color="black",shape="box"];1214 -> 1218[label="",style="solid", color="black", weight=3]; 1056[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS (Succ ww1170) (Succ ww1180))",fontsize=16,color="black",shape="box"];1056 -> 1067[label="",style="solid", color="black", weight=3]; 1057[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS (Succ ww1170) Zero)",fontsize=16,color="black",shape="box"];1057 -> 1068[label="",style="solid", color="black", weight=3]; 1058[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS Zero (Succ ww1180))",fontsize=16,color="black",shape="box"];1058 -> 1069[label="",style="solid", color="black", weight=3]; 1059[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1059 -> 1070[label="",style="solid", color="black", weight=3]; 1123[label="primModNatS (primMinusNatS (Succ ww1200) ww121) (Succ ww122)",fontsize=16,color="burlywood",shape="box"];1301[label="ww121/Succ ww1210",fontsize=10,color="white",style="solid",shape="box"];1123 -> 1301[label="",style="solid", color="burlywood", weight=9]; 1301 -> 1129[label="",style="solid", color="burlywood", weight=3]; 1302[label="ww121/Zero",fontsize=10,color="white",style="solid",shape="box"];1123 -> 1302[label="",style="solid", color="burlywood", weight=9]; 1302 -> 1130[label="",style="solid", color="burlywood", weight=3]; 1124[label="primModNatS (primMinusNatS Zero ww121) (Succ ww122)",fontsize=16,color="burlywood",shape="box"];1303[label="ww121/Succ ww1210",fontsize=10,color="white",style="solid",shape="box"];1124 -> 1303[label="",style="solid", color="burlywood", weight=9]; 1303 -> 1131[label="",style="solid", color="burlywood", weight=3]; 1304[label="ww121/Zero",fontsize=10,color="white",style="solid",shape="box"];1124 -> 1304[label="",style="solid", color="burlywood", weight=9]; 1304 -> 1132[label="",style="solid", color="burlywood", weight=3]; 1060 -> 1184[label="",style="dashed", color="red", weight=0]; 1060[label="primDivNatS (primMinusNatS (Succ ww110) (Succ ww111)) (Succ (Succ ww111))",fontsize=16,color="magenta"];1060 -> 1191[label="",style="dashed", color="magenta", weight=3]; 1060 -> 1192[label="",style="dashed", color="magenta", weight=3]; 1060 -> 1193[label="",style="dashed", color="magenta", weight=3]; 1215 -> 1184[label="",style="dashed", color="red", weight=0]; 1215[label="primDivNatS (primMinusNatS ww1240 ww1250) (Succ ww126)",fontsize=16,color="magenta"];1215 -> 1219[label="",style="dashed", color="magenta", weight=3]; 1215 -> 1220[label="",style="dashed", color="magenta", weight=3]; 1216 -> 399[label="",style="dashed", color="red", weight=0]; 1216[label="primDivNatS (Succ ww1240) (Succ ww126)",fontsize=16,color="magenta"];1216 -> 1221[label="",style="dashed", color="magenta", weight=3]; 1216 -> 1222[label="",style="dashed", color="magenta", weight=3]; 1217[label="primDivNatS Zero (Succ ww126)",fontsize=16,color="black",shape="triangle"];1217 -> 1223[label="",style="solid", color="black", weight=3]; 1218 -> 1217[label="",style="dashed", color="red", weight=0]; 1218[label="primDivNatS Zero (Succ ww126)",fontsize=16,color="magenta"];1067 -> 1005[label="",style="dashed", color="red", weight=0]; 1067[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS ww1170 ww1180)",fontsize=16,color="magenta"];1067 -> 1076[label="",style="dashed", color="magenta", weight=3]; 1067 -> 1077[label="",style="dashed", color="magenta", weight=3]; 1068[label="primModNatS0 (Succ ww115) (Succ ww116) True",fontsize=16,color="black",shape="triangle"];1068 -> 1078[label="",style="solid", color="black", weight=3]; 1069[label="primModNatS0 (Succ ww115) (Succ ww116) False",fontsize=16,color="black",shape="box"];1069 -> 1079[label="",style="solid", color="black", weight=3]; 1070 -> 1068[label="",style="dashed", color="red", weight=0]; 1070[label="primModNatS0 (Succ ww115) (Succ ww116) True",fontsize=16,color="magenta"];1129[label="primModNatS (primMinusNatS (Succ ww1200) (Succ ww1210)) (Succ ww122)",fontsize=16,color="black",shape="box"];1129 -> 1139[label="",style="solid", color="black", weight=3]; 1130[label="primModNatS (primMinusNatS (Succ ww1200) Zero) (Succ ww122)",fontsize=16,color="black",shape="box"];1130 -> 1140[label="",style="solid", color="black", weight=3]; 1131[label="primModNatS (primMinusNatS Zero (Succ ww1210)) (Succ ww122)",fontsize=16,color="black",shape="box"];1131 -> 1141[label="",style="solid", color="black", weight=3]; 1132[label="primModNatS (primMinusNatS Zero Zero) (Succ ww122)",fontsize=16,color="black",shape="box"];1132 -> 1142[label="",style="solid", color="black", weight=3]; 1191[label="Succ ww110",fontsize=16,color="green",shape="box"];1192[label="Succ ww111",fontsize=16,color="green",shape="box"];1193[label="Succ ww111",fontsize=16,color="green",shape="box"];1219[label="ww1240",fontsize=16,color="green",shape="box"];1220[label="ww1250",fontsize=16,color="green",shape="box"];1221[label="ww1240",fontsize=16,color="green",shape="box"];1222[label="ww126",fontsize=16,color="green",shape="box"];1223[label="Zero",fontsize=16,color="green",shape="box"];1076[label="ww1170",fontsize=16,color="green",shape="box"];1077[label="ww1180",fontsize=16,color="green",shape="box"];1078 -> 1092[label="",style="dashed", color="red", weight=0]; 1078[label="primModNatS (primMinusNatS (Succ ww115) (Succ ww116)) (Succ (Succ ww116))",fontsize=16,color="magenta"];1078 -> 1105[label="",style="dashed", color="magenta", weight=3]; 1078 -> 1106[label="",style="dashed", color="magenta", weight=3]; 1078 -> 1107[label="",style="dashed", color="magenta", weight=3]; 1079[label="Succ (Succ ww115)",fontsize=16,color="green",shape="box"];1139 -> 1092[label="",style="dashed", color="red", weight=0]; 1139[label="primModNatS (primMinusNatS ww1200 ww1210) (Succ ww122)",fontsize=16,color="magenta"];1139 -> 1147[label="",style="dashed", color="magenta", weight=3]; 1139 -> 1148[label="",style="dashed", color="magenta", weight=3]; 1140 -> 413[label="",style="dashed", color="red", weight=0]; 1140[label="primModNatS (Succ ww1200) (Succ ww122)",fontsize=16,color="magenta"];1140 -> 1149[label="",style="dashed", color="magenta", weight=3]; 1140 -> 1150[label="",style="dashed", color="magenta", weight=3]; 1141[label="primModNatS Zero (Succ ww122)",fontsize=16,color="black",shape="triangle"];1141 -> 1151[label="",style="solid", color="black", weight=3]; 1142 -> 1141[label="",style="dashed", color="red", weight=0]; 1142[label="primModNatS Zero (Succ ww122)",fontsize=16,color="magenta"];1105[label="Succ ww115",fontsize=16,color="green",shape="box"];1106[label="Succ ww116",fontsize=16,color="green",shape="box"];1107[label="Succ ww116",fontsize=16,color="green",shape="box"];1147[label="ww1200",fontsize=16,color="green",shape="box"];1148[label="ww1210",fontsize=16,color="green",shape="box"];1149[label="ww122",fontsize=16,color="green",shape="box"];1150[label="ww1200",fontsize=16,color="green",shape="box"];1151[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_primDivNatS0(ww110, ww111, Zero, Zero) -> new_primDivNatS00(ww110, ww111) new_primDivNatS00(ww110, ww111) -> new_primDivNatS(Succ(ww110), Succ(ww111), Succ(ww111)) new_primDivNatS(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS(ww1240, ww1250, ww126) new_primDivNatS1(Succ(ww600), Zero) -> new_primDivNatS(Succ(ww600), Zero, Zero) new_primDivNatS0(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS0(ww110, ww111, ww1120, ww1130) new_primDivNatS0(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS(Succ(ww110), Succ(ww111), Succ(ww111)) new_primDivNatS1(Succ(ww600), Succ(ww610)) -> new_primDivNatS0(ww600, ww610, ww600, ww610) new_primDivNatS1(Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) new_primDivNatS(Succ(ww1240), Zero, ww126) -> new_primDivNatS1(ww1240, ww126) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (12) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (13) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS00(ww110, ww111) -> new_primDivNatS(Succ(ww110), Succ(ww111), Succ(ww111)) new_primDivNatS(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS(ww1240, ww1250, ww126) new_primDivNatS(Succ(ww1240), Zero, ww126) -> new_primDivNatS1(ww1240, ww126) new_primDivNatS1(Succ(ww600), Zero) -> new_primDivNatS(Succ(ww600), Zero, Zero) new_primDivNatS1(Succ(ww600), Succ(ww610)) -> new_primDivNatS0(ww600, ww610, ww600, ww610) new_primDivNatS0(ww110, ww111, Zero, Zero) -> new_primDivNatS00(ww110, ww111) new_primDivNatS0(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS0(ww110, ww111, ww1120, ww1130) new_primDivNatS0(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS(Succ(ww110), Succ(ww111), Succ(ww111)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (14) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_primDivNatS(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS(ww1240, ww1250, ww126) new_primDivNatS1(Succ(ww600), Zero) -> new_primDivNatS(Succ(ww600), Zero, Zero) new_primDivNatS1(Succ(ww600), Succ(ww610)) -> new_primDivNatS0(ww600, ww610, ww600, ww610) 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 ---------------------------------------- (15) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS00(ww110, ww111) -> new_primDivNatS(Succ(ww110), Succ(ww111), Succ(ww111)) new_primDivNatS(Succ(ww1240), Zero, ww126) -> new_primDivNatS1(ww1240, ww126) new_primDivNatS0(ww110, ww111, Zero, Zero) -> new_primDivNatS00(ww110, ww111) new_primDivNatS0(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS0(ww110, ww111, ww1120, ww1130) new_primDivNatS0(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS(Succ(ww110), Succ(ww111), Succ(ww111)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (16) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. ---------------------------------------- (17) Obligation: Q DP problem: The TRS P consists of the following rules: new_primDivNatS0(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS0(ww110, ww111, ww1120, ww1130) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (18) 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(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS0(ww110, ww111, ww1120, ww1130) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (19) YES ---------------------------------------- (20) Obligation: Q DP problem: The TRS P consists of the following rules: new_psPs(:(ww580, ww581), ww56) -> new_psPs(ww581, ww56) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (21) 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(:(ww580, ww581), ww56) -> new_psPs(ww581, ww56) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (22) YES ---------------------------------------- (23) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (24) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) at position [5] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bf)), bf, bf),new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bf)), bf, bf)) ---------------------------------------- (25) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bf)), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (26) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bf)), bf, bf) at position [5] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), new_psPs0(:(Char(Succ(ww19)), :(Char(Succ(ww20)), [])), new_showsPrec(ww21, ww22, bf))), bf, bf),new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), new_psPs0(:(Char(Succ(ww19)), :(Char(Succ(ww20)), [])), new_showsPrec(ww21, ww22, bf))), bf, bf)) ---------------------------------------- (27) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), new_psPs0(:(Char(Succ(ww19)), :(Char(Succ(ww20)), [])), new_showsPrec(ww21, ww22, bf))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (28) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), new_psPs0(:(Char(Succ(ww19)), :(Char(Succ(ww20)), [])), new_showsPrec(ww21, ww22, bf))), bf, bf) at position [5,1] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), new_psPs0(:(Char(Succ(ww20)), []), new_showsPrec(ww21, ww22, bf)))), bf, bf),new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), new_psPs0(:(Char(Succ(ww20)), []), new_showsPrec(ww21, ww22, bf)))), bf, bf)) ---------------------------------------- (29) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), new_psPs0(:(Char(Succ(ww20)), []), new_showsPrec(ww21, ww22, bf)))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (30) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), new_psPs0(:(Char(Succ(ww20)), []), new_showsPrec(ww21, ww22, bf)))), bf, bf) at position [5,1,1] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_psPs0([], new_showsPrec(ww21, ww22, bf))))), bf, bf),new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_psPs0([], new_showsPrec(ww21, ww22, bf))))), bf, bf)) ---------------------------------------- (31) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_psPs0([], new_showsPrec(ww21, ww22, bf))))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (32) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_psPs0([], new_showsPrec(ww21, ww22, bf))))), bf, bf) at position [5,1,1,1] we obtained the following new rules [LPAR04]: (new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf),new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)) ---------------------------------------- (33) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (34) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) 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, 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))))))))))))))))))))))))))))))), z6, z7, ty_IOError),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, 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))))))))))))))))))))))))))))))), z6, z7, 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)) ---------------------------------------- (35) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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, 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))))))))))))))))))))))))))))))), z6, z7, 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) 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 2 less nodes. ---------------------------------------- (37) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (38) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6))) ---------------------------------------- (39) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6)) new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_IO, x6)) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (40) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (41) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (42) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_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)) ---------------------------------------- (43) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (44) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (45) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (46) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Int)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int, ty_Int) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Int)) ---------------------------------------- (47) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (48) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (49) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (50) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_Maybe, x6))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6), app(ty_Maybe, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_Maybe, x6))) ---------------------------------------- (51) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (52) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (53) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (54) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Bool)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool, ty_Bool) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Bool)) ---------------------------------------- (55) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (56) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (57) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (58) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Double)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double, ty_Double) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Double)) ---------------------------------------- (59) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (60) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (61) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (62) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Char)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char, ty_Char) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Char)) ---------------------------------------- (63) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (64) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (65) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (66) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_@2, x6), x7))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7), app(app(ty_@2, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_@2, x6), x7))) ---------------------------------------- (67) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (68) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (69) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) The TRS R consists of the following rules: new_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (70) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, 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)) ---------------------------------------- (71) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (72) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_[], x6))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6), app(ty_[], x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(ty_[], x6))) ---------------------------------------- (73) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) 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(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (76) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Float)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float, ty_Float) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Float)) ---------------------------------------- (77) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (78) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (79) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (80) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(ty_Either, x6), x7))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7), app(app(ty_Either, x6), x7)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(ty_Either, x6), x7))) ---------------------------------------- (81) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) 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(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (84) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_HugsException)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException, ty_HugsException) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_HugsException)) ---------------------------------------- (85) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) 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(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (88) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_Integer)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer, ty_Integer) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_Integer)) ---------------------------------------- (89) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) 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(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (92) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_@0)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0, ty_@0) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_@0)) ---------------------------------------- (93) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) 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(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (96) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOErrorKind)) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind, ty_IOErrorKind) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), ty_IOErrorKind)) ---------------------------------------- (97) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (98) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (99) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (100) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]: (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(app(app(ty_@3, x6), x7), x8))) (new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8)),new_showParen(z0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8), app(app(app(ty_@3, x6), x7), x8)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z1, :(Char(Succ(z2)), :(Char(Succ(z3)), :(Char(Succ(z4)), y_0))), app(app(app(ty_@3, x6), x7), x8))) ---------------------------------------- (101) Obligation: Q DP problem: The TRS P consists of the following rules: new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (102) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. ---------------------------------------- (103) Obligation: Q DP problem: The TRS P consists of the following rules: new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (104) TransformationProof (EQUIVALENT) By instantiating [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) 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)) ---------------------------------------- (105) 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_show2(ww17) -> error([]) new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show6(ww17, be) -> error([]) new_show(ww17, bg, bh) -> error([]) new_show7(ww17) -> error([]) new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww170))) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show1(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero) new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22) new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122) new_show3(ww17, ba) -> error([]) new_show8(ww17) -> error([]) new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122) new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22) new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22) new_primModNatS4(ww122) -> Zero new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56)) new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22) new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22) new_show0(ww17) -> error([]) new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67)) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22) new_show9(ww17) -> error([]) new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show13(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_show14(ww17, cb, cc, cd) -> error([]) new_psPs0([], ww56) -> ww56 new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22) new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115)) new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22) new_show5(ww17) -> error([]) new_show12(ww17, ca) -> error([]) new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122) new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22) new_show10(ww17) -> new_primShowInt0(ww17) new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22) new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22) new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, 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_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116) new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero) new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) new_show11(ww17) -> error([]) new_show4(ww17, bc, bd) -> error([]) new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22) new_show15(ww17) -> error([]) new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb)) new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22) new_primDivNatS4(ww126) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670) The set Q consists of the following terms: new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) new_primShowInt0(Neg(x0)) new_showsPrec(x0, x1, ty_IOError) new_primModNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) new_primDivNatS3(Succ(x0), Zero) new_primModNatS3(Succ(x0), Zero) new_show0(x0) new_primDivNatS2(Succ(x0), Zero, x1) new_showsPrec(x0, x1, ty_Double) new_showsPrec(x0, x1, ty_Float) new_primModNatS01(x0, x1, Zero, Zero) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_@0) new_showsPrec(x0, x1, ty_Ordering) new_show9(x0) new_primModNatS02(x0, x1) new_show15(x0) new_show3(x0, x1) new_show8(x0) new_show11(x0) new_primModNatS2(Succ(x0), Succ(x1), x2) new_showsPrec(x0, x1, ty_IOErrorKind) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) new_primModNatS2(Zero, Succ(x0), x1) new_primDivNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) new_show(x0, x1, x2) new_show10(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) new_showsPrec(x0, x1, ty_Integer) new_psPs0(:(x0, x1), x2) new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) new_primModNatS4(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) new_primDivNatS2(Zero, Succ(x0), x1) new_show1(x0) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) new_primDivNatS3(Succ(x0), Succ(x1)) new_show6(x0, x1) new_showsPrec(x0, x1, ty_Bool) new_show13(x0) new_showsPrec(x0, x1, app(ty_Maybe, x2)) new_primModNatS3(Zero, Zero) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) new_primShowInt0(Pos(Succ(x0))) new_div(x0, x1) new_primIntToChar(x0, x1) new_show14(x0, x1, x2, x3) new_primDivNatS3(Zero, Succ(x0)) new_primModNatS3(Zero, Succ(x0)) new_showsPrec(x0, x1, ty_Int) new_primModNatS01(x0, x1, Succ(x2), Zero) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) new_show5(x0) new_primShowInt0(Pos(Zero)) new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) new_primDivNatS02(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_show12(x0, x1) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_showsPrec(x0, x1, ty_HugsException) new_primModNatS2(Succ(x0), Zero, x1) new_primModNatS2(Zero, Zero, x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) new_psPs0([], x0) new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) new_show2(x0) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) new_show7(x0) new_pt0(x0, x1, x2, x3, x4, x5) new_show4(x0, x1, x2) new_showsPrec(x0, x1, app(ty_[], x2)) new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) new_showsPrec(x0, x1, ty_Char) new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) new_primDivNatS01(x0, x1, Zero, Zero) new_showsPrec(x0, x1, app(ty_IO, x2)) new_primModNatS3(Succ(x0), Succ(x1)) new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (106) 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 ---------------------------------------- (107) YES ---------------------------------------- (108) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS(Succ(ww1200), Zero, ww122) -> new_primModNatS1(ww1200, ww122) new_primModNatS1(Zero, Zero) -> new_primModNatS(Zero, Zero, Zero) new_primModNatS00(ww115, ww116) -> new_primModNatS(Succ(ww115), Succ(ww116), Succ(ww116)) new_primModNatS0(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS(Succ(ww115), Succ(ww116), Succ(ww116)) new_primModNatS(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS(ww1200, ww1210, ww122) new_primModNatS0(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS0(ww115, ww116, ww1170, ww1180) new_primModNatS1(Succ(ww660), Succ(ww670)) -> new_primModNatS0(ww660, ww670, ww660, ww670) new_primModNatS0(ww115, ww116, Zero, Zero) -> new_primModNatS00(ww115, ww116) new_primModNatS1(Succ(ww660), Zero) -> new_primModNatS(Succ(ww660), Zero, Zero) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (109) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (110) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS1(Succ(ww660), Succ(ww670)) -> new_primModNatS0(ww660, ww670, ww660, ww670) new_primModNatS0(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS(Succ(ww115), Succ(ww116), Succ(ww116)) new_primModNatS(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS(ww1200, ww1210, ww122) new_primModNatS(Succ(ww1200), Zero, ww122) -> new_primModNatS1(ww1200, ww122) new_primModNatS1(Succ(ww660), Zero) -> new_primModNatS(Succ(ww660), Zero, Zero) new_primModNatS0(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS0(ww115, ww116, ww1170, ww1180) new_primModNatS0(ww115, ww116, Zero, Zero) -> new_primModNatS00(ww115, ww116) new_primModNatS00(ww115, ww116) -> new_primModNatS(Succ(ww115), Succ(ww116), Succ(ww116)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (111) QDPOrderProof (EQUIVALENT) We use the reduction pair processor [LPAR04,JAR06]. The following pairs can be oriented strictly and are deleted. new_primModNatS1(Succ(ww660), Succ(ww670)) -> new_primModNatS0(ww660, ww670, ww660, ww670) new_primModNatS(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS(ww1200, ww1210, ww122) new_primModNatS1(Succ(ww660), Zero) -> new_primModNatS(Succ(ww660), 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 ---------------------------------------- (112) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS0(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS(Succ(ww115), Succ(ww116), Succ(ww116)) new_primModNatS(Succ(ww1200), Zero, ww122) -> new_primModNatS1(ww1200, ww122) new_primModNatS0(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS0(ww115, ww116, ww1170, ww1180) new_primModNatS0(ww115, ww116, Zero, Zero) -> new_primModNatS00(ww115, ww116) new_primModNatS00(ww115, ww116) -> new_primModNatS(Succ(ww115), Succ(ww116), Succ(ww116)) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (113) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. ---------------------------------------- (114) Obligation: Q DP problem: The TRS P consists of the following rules: new_primModNatS0(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS0(ww115, ww116, ww1170, ww1180) R is empty. Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (115) 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(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS0(ww115, ww116, ww1170, ww1180) The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 ---------------------------------------- (116) YES ---------------------------------------- (117) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Neg(ww170)) -> new_primShowInt(Pos(ww170)) new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS4(ww126) -> Zero new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS3(Zero, Succ(ww610)) -> Zero The set Q consists of the following terms: new_div(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (118) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (119) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS4(ww126) -> Zero new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS3(Zero, Succ(ww610)) -> Zero The set Q consists of the following terms: new_div(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (120) TransformationProof (EQUIVALENT) By rewriting [LPAR04] the rule new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0] we obtained the following new rules [LPAR04]: (new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))),new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ---------------------------------------- (121) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61)) new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS4(ww126) -> Zero new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS3(Zero, Succ(ww610)) -> Zero The set Q consists of the following terms: new_div(x0, x1) new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (122) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (123) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), 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_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (124) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. new_div(x0, x1) ---------------------------------------- (125) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (126) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (127) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (128) InductionCalculusProof (EQUIVALENT) Note that final constraints are written in bold face. For Pair new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, 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(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, 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. ---------------------------------------- (129) Obligation: Q DP problem: The TRS P consists of the following rules: new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) The TRS R consists of the following rules: new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (130) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, 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))) ---------------------------------------- (131) 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(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) 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 1 less node. ---------------------------------------- (133) 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(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (134) 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))))))))))) ---------------------------------------- (135) 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(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (136) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (137) 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(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (138) 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)))))))))) ---------------------------------------- (139) 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(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (140) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (141) 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(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (142) 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))))))))) ---------------------------------------- (143) 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(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (144) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (145) 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(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (146) MNOCProof (EQUIVALENT) We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. ---------------------------------------- (147) 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(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) Q is empty. We have to consider all (P,Q,R)-chains. ---------------------------------------- (148) 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. ---------------------------------------- (149) 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(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610) new_primDivNatS3(Zero, Succ(ww610)) -> Zero new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111) new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130) new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111))) new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126) new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126) new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126) new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126) new_primDivNatS4(ww126) -> Zero new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero)) new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) The set Q consists of the following terms: new_primDivNatS3(Zero, Succ(x0)) new_primDivNatS2(Zero, Zero, x0) new_primDivNatS3(Succ(x0), Zero) new_primDivNatS2(Succ(x0), Zero, x1) new_primDivNatS02(x0, x1) new_primDivNatS2(Succ(x0), Succ(x1), x2) new_primDivNatS01(x0, x1, Succ(x2), Succ(x3)) new_primDivNatS2(Zero, Succ(x0), x1) new_primDivNatS01(x0, x1, Zero, Zero) new_primDivNatS01(x0, x1, Zero, Succ(x2)) new_primDivNatS3(Succ(x0), Succ(x1)) new_primDivNatS01(x0, x1, Succ(x2), Zero) new_primDivNatS4(x0) new_primDivNatS3(Zero, Zero) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (150) Narrow (COMPLETE) Haskell To QDPs digraph dp_graph { node [outthreshold=100, inthreshold=100];1[label="shows",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 3[label="shows ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3]; 4[label="shows ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3]; 5[label="showsPrec (Pos Zero) ww3 ww4",fontsize=16,color="burlywood",shape="box"];1224[label="ww3/ww30 :% ww31",fontsize=10,color="white",style="solid",shape="box"];5 -> 1224[label="",style="solid", color="burlywood", weight=9]; 1224 -> 6[label="",style="solid", color="burlywood", weight=3]; 6[label="showsPrec (Pos Zero) (ww30 :% ww31) ww4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3]; 7 -> 24[label="",style="dashed", color="red", weight=0]; 7[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) ww4",fontsize=16,color="magenta"];7 -> 25[label="",style="dashed", color="magenta", weight=3]; 7 -> 26[label="",style="dashed", color="magenta", weight=3]; 7 -> 27[label="",style="dashed", color="magenta", weight=3]; 7 -> 28[label="",style="dashed", color="magenta", weight=3]; 7 -> 29[label="",style="dashed", color="magenta", weight=3]; 7 -> 30[label="",style="dashed", color="magenta", weight=3]; 25[label="ww30",fontsize=16,color="green",shape="box"];26[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"];27[label="ww4",fontsize=16,color="green",shape="box"];28[label="ww31",fontsize=16,color="green",shape="box"];29[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"];30[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"];24[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) ww22",fontsize=16,color="black",shape="triangle"];24 -> 37[label="",style="solid", color="black", weight=3]; 37[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww22",fontsize=16,color="black",shape="box"];37 -> 38[label="",style="solid", color="black", weight=3]; 38[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww22",fontsize=16,color="black",shape="box"];38 -> 39[label="",style="solid", color="black", weight=3]; 39[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww22",fontsize=16,color="black",shape="box"];39 -> 40[label="",style="solid", color="black", weight=3]; 40[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww22",fontsize=16,color="black",shape="box"];40 -> 41[label="",style="solid", color="black", weight=3]; 41[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (LT == GT) ww22",fontsize=16,color="black",shape="box"];41 -> 42[label="",style="solid", color="black", weight=3]; 42[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) False ww22",fontsize=16,color="black",shape="box"];42 -> 43[label="",style="solid", color="black", weight=3]; 43[label="(shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="black",shape="box"];43 -> 44[label="",style="solid", color="black", weight=3]; 44[label="shows ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];44 -> 45[label="",style="solid", color="black", weight=3]; 45[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="blue",shape="box"];1225[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1225[label="",style="solid", color="blue", weight=9]; 1225 -> 46[label="",style="solid", color="blue", weight=3]; 1226[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1226[label="",style="solid", color="blue", weight=9]; 1226 -> 47[label="",style="solid", color="blue", weight=3]; 1227[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1227[label="",style="solid", color="blue", weight=9]; 1227 -> 48[label="",style="solid", color="blue", weight=3]; 1228[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1228[label="",style="solid", color="blue", weight=9]; 1228 -> 49[label="",style="solid", color="blue", weight=3]; 1229[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1229[label="",style="solid", color="blue", weight=9]; 1229 -> 50[label="",style="solid", color="blue", weight=3]; 1230[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1230[label="",style="solid", color="blue", weight=9]; 1230 -> 51[label="",style="solid", color="blue", weight=3]; 1231[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1231[label="",style="solid", color="blue", weight=9]; 1231 -> 52[label="",style="solid", color="blue", weight=3]; 1232[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1232[label="",style="solid", color="blue", weight=9]; 1232 -> 53[label="",style="solid", color="blue", weight=3]; 1233[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1233[label="",style="solid", color="blue", weight=9]; 1233 -> 54[label="",style="solid", color="blue", weight=3]; 1234[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1234[label="",style="solid", color="blue", weight=9]; 1234 -> 55[label="",style="solid", color="blue", weight=3]; 1235[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1235[label="",style="solid", color="blue", weight=9]; 1235 -> 56[label="",style="solid", color="blue", weight=3]; 1236[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1236[label="",style="solid", color="blue", weight=9]; 1236 -> 57[label="",style="solid", color="blue", weight=3]; 1237[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1237[label="",style="solid", color="blue", weight=9]; 1237 -> 58[label="",style="solid", color="blue", weight=3]; 1238[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1238[label="",style="solid", color="blue", weight=9]; 1238 -> 59[label="",style="solid", color="blue", weight=3]; 1239[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1239[label="",style="solid", color="blue", weight=9]; 1239 -> 60[label="",style="solid", color="blue", weight=3]; 1240[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1240[label="",style="solid", color="blue", weight=9]; 1240 -> 61[label="",style="solid", color="blue", weight=3]; 1241[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1241[label="",style="solid", color="blue", weight=9]; 1241 -> 62[label="",style="solid", color="blue", weight=3]; 1242[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1242[label="",style="solid", color="blue", weight=9]; 1242 -> 63[label="",style="solid", color="blue", weight=3]; 46[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];46 -> 64[label="",style="solid", color="black", weight=3]; 47[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];47 -> 65[label="",style="solid", color="black", weight=3]; 48[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];48 -> 66[label="",style="solid", color="black", weight=3]; 49[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];49 -> 67[label="",style="solid", color="black", weight=3]; 50[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];50 -> 68[label="",style="solid", color="black", weight=3]; 51[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];51 -> 69[label="",style="solid", color="black", weight=3]; 52[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];52 -> 70[label="",style="solid", color="black", weight=3]; 53[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="burlywood",shape="box"];1243[label="ww17/ww170 :% ww171",fontsize=10,color="white",style="solid",shape="box"];53 -> 1243[label="",style="solid", color="burlywood", weight=9]; 1243 -> 71[label="",style="solid", color="burlywood", weight=3]; 54[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];54 -> 72[label="",style="solid", color="black", weight=3]; 55[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];55 -> 73[label="",style="solid", color="black", weight=3]; 56[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];56 -> 74[label="",style="solid", color="black", weight=3]; 57[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];57 -> 75[label="",style="solid", color="black", weight=3]; 58[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];58 -> 76[label="",style="solid", color="black", weight=3]; 59[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];59 -> 77[label="",style="solid", color="black", weight=3]; 60[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];60 -> 78[label="",style="solid", color="black", weight=3]; 61[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];61 -> 79[label="",style="solid", color="black", weight=3]; 62[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];62 -> 80[label="",style="solid", color="black", weight=3]; 63[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];63 -> 81[label="",style="solid", color="black", weight=3]; 64 -> 182[label="",style="dashed", color="red", weight=0]; 64[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];64 -> 183[label="",style="dashed", color="magenta", weight=3]; 64 -> 184[label="",style="dashed", color="magenta", weight=3]; 65 -> 182[label="",style="dashed", color="red", weight=0]; 65[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];65 -> 185[label="",style="dashed", color="magenta", weight=3]; 65 -> 186[label="",style="dashed", color="magenta", weight=3]; 66 -> 182[label="",style="dashed", color="red", weight=0]; 66[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];66 -> 187[label="",style="dashed", color="magenta", weight=3]; 66 -> 188[label="",style="dashed", color="magenta", weight=3]; 67 -> 182[label="",style="dashed", color="red", weight=0]; 67[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];67 -> 189[label="",style="dashed", color="magenta", weight=3]; 67 -> 190[label="",style="dashed", color="magenta", weight=3]; 68 -> 182[label="",style="dashed", color="red", weight=0]; 68[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];68 -> 191[label="",style="dashed", color="magenta", weight=3]; 68 -> 192[label="",style="dashed", color="magenta", weight=3]; 69 -> 182[label="",style="dashed", color="red", weight=0]; 69[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];69 -> 193[label="",style="dashed", color="magenta", weight=3]; 69 -> 194[label="",style="dashed", color="magenta", weight=3]; 70 -> 182[label="",style="dashed", color="red", weight=0]; 70[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];70 -> 195[label="",style="dashed", color="magenta", weight=3]; 70 -> 196[label="",style="dashed", color="magenta", weight=3]; 71[label="showsPrec (Pos Zero) (ww170 :% ww171) ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];71 -> 89[label="",style="solid", color="black", weight=3]; 72 -> 182[label="",style="dashed", color="red", weight=0]; 72[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];72 -> 197[label="",style="dashed", color="magenta", weight=3]; 72 -> 198[label="",style="dashed", color="magenta", weight=3]; 73 -> 182[label="",style="dashed", color="red", weight=0]; 73[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];73 -> 199[label="",style="dashed", color="magenta", weight=3]; 73 -> 200[label="",style="dashed", color="magenta", weight=3]; 74 -> 182[label="",style="dashed", color="red", weight=0]; 74[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];74 -> 201[label="",style="dashed", color="magenta", weight=3]; 74 -> 202[label="",style="dashed", color="magenta", weight=3]; 75 -> 182[label="",style="dashed", color="red", weight=0]; 75[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];75 -> 203[label="",style="dashed", color="magenta", weight=3]; 75 -> 204[label="",style="dashed", color="magenta", weight=3]; 76 -> 182[label="",style="dashed", color="red", weight=0]; 76[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];76 -> 205[label="",style="dashed", color="magenta", weight=3]; 76 -> 206[label="",style="dashed", color="magenta", weight=3]; 77 -> 182[label="",style="dashed", color="red", weight=0]; 77[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];77 -> 207[label="",style="dashed", color="magenta", weight=3]; 77 -> 208[label="",style="dashed", color="magenta", weight=3]; 78 -> 182[label="",style="dashed", color="red", weight=0]; 78[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];78 -> 209[label="",style="dashed", color="magenta", weight=3]; 78 -> 210[label="",style="dashed", color="magenta", weight=3]; 79 -> 182[label="",style="dashed", color="red", weight=0]; 79[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];79 -> 211[label="",style="dashed", color="magenta", weight=3]; 79 -> 212[label="",style="dashed", color="magenta", weight=3]; 80 -> 182[label="",style="dashed", color="red", weight=0]; 80[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];80 -> 213[label="",style="dashed", color="magenta", weight=3]; 80 -> 214[label="",style="dashed", color="magenta", weight=3]; 81 -> 182[label="",style="dashed", color="red", weight=0]; 81[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];81 -> 215[label="",style="dashed", color="magenta", weight=3]; 81 -> 216[label="",style="dashed", color="magenta", weight=3]; 183[label="show ww17",fontsize=16,color="black",shape="triangle"];183 -> 242[label="",style="solid", color="black", weight=3]; 184 -> 102[label="",style="dashed", color="red", weight=0]; 184[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];182[label="ww58 ++ ww56",fontsize=16,color="burlywood",shape="triangle"];1244[label="ww58/ww580 : ww581",fontsize=10,color="white",style="solid",shape="box"];182 -> 1244[label="",style="solid", color="burlywood", weight=9]; 1244 -> 243[label="",style="solid", color="burlywood", weight=3]; 1245[label="ww58/[]",fontsize=10,color="white",style="solid",shape="box"];182 -> 1245[label="",style="solid", color="burlywood", weight=9]; 1245 -> 244[label="",style="solid", color="burlywood", weight=3]; 185[label="show ww17",fontsize=16,color="black",shape="triangle"];185 -> 245[label="",style="solid", color="black", weight=3]; 186 -> 102[label="",style="dashed", color="red", weight=0]; 186[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];187[label="show ww17",fontsize=16,color="black",shape="triangle"];187 -> 246[label="",style="solid", color="black", weight=3]; 188 -> 102[label="",style="dashed", color="red", weight=0]; 188[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];189[label="show ww17",fontsize=16,color="black",shape="triangle"];189 -> 247[label="",style="solid", color="black", weight=3]; 190 -> 102[label="",style="dashed", color="red", weight=0]; 190[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];191[label="show ww17",fontsize=16,color="black",shape="triangle"];191 -> 248[label="",style="solid", color="black", weight=3]; 192 -> 102[label="",style="dashed", color="red", weight=0]; 192[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];193[label="show ww17",fontsize=16,color="black",shape="triangle"];193 -> 249[label="",style="solid", color="black", weight=3]; 194 -> 102[label="",style="dashed", color="red", weight=0]; 194[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];195[label="show ww17",fontsize=16,color="black",shape="triangle"];195 -> 250[label="",style="solid", color="black", weight=3]; 196 -> 102[label="",style="dashed", color="red", weight=0]; 196[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];89 -> 24[label="",style="dashed", color="red", weight=0]; 89[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww170) . (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 ww171) ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="magenta"];89 -> 100[label="",style="dashed", color="magenta", weight=3]; 89 -> 101[label="",style="dashed", color="magenta", weight=3]; 89 -> 102[label="",style="dashed", color="magenta", weight=3]; 89 -> 103[label="",style="dashed", color="magenta", weight=3]; 89 -> 104[label="",style="dashed", color="magenta", weight=3]; 89 -> 105[label="",style="dashed", color="magenta", weight=3]; 197[label="show ww17",fontsize=16,color="black",shape="triangle"];197 -> 251[label="",style="solid", color="black", weight=3]; 198 -> 102[label="",style="dashed", color="red", weight=0]; 198[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];199[label="show ww17",fontsize=16,color="black",shape="triangle"];199 -> 252[label="",style="solid", color="black", weight=3]; 200 -> 102[label="",style="dashed", color="red", weight=0]; 200[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];201[label="show ww17",fontsize=16,color="black",shape="triangle"];201 -> 253[label="",style="solid", color="black", weight=3]; 202 -> 102[label="",style="dashed", color="red", weight=0]; 202[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];203[label="show ww17",fontsize=16,color="black",shape="triangle"];203 -> 254[label="",style="solid", color="black", weight=3]; 204 -> 102[label="",style="dashed", color="red", weight=0]; 204[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];205[label="show ww17",fontsize=16,color="black",shape="triangle"];205 -> 255[label="",style="solid", color="black", weight=3]; 206 -> 102[label="",style="dashed", color="red", weight=0]; 206[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];207[label="show ww17",fontsize=16,color="black",shape="triangle"];207 -> 256[label="",style="solid", color="black", weight=3]; 208 -> 102[label="",style="dashed", color="red", weight=0]; 208[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];209[label="show ww17",fontsize=16,color="black",shape="triangle"];209 -> 257[label="",style="solid", color="black", weight=3]; 210 -> 102[label="",style="dashed", color="red", weight=0]; 210[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];211[label="show ww17",fontsize=16,color="black",shape="triangle"];211 -> 258[label="",style="solid", color="black", weight=3]; 212 -> 102[label="",style="dashed", color="red", weight=0]; 212[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];213[label="show ww17",fontsize=16,color="black",shape="triangle"];213 -> 259[label="",style="solid", color="black", weight=3]; 214 -> 102[label="",style="dashed", color="red", weight=0]; 214[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];215[label="show ww17",fontsize=16,color="black",shape="triangle"];215 -> 260[label="",style="solid", color="black", weight=3]; 216 -> 102[label="",style="dashed", color="red", weight=0]; 216[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];242[label="error []",fontsize=16,color="red",shape="box"];102[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="black",shape="triangle"];102 -> 108[label="",style="solid", color="black", weight=3]; 243[label="(ww580 : ww581) ++ ww56",fontsize=16,color="black",shape="box"];243 -> 262[label="",style="solid", color="black", weight=3]; 244[label="[] ++ ww56",fontsize=16,color="black",shape="box"];244 -> 263[label="",style="solid", color="black", weight=3]; 245[label="error []",fontsize=16,color="red",shape="box"];246[label="error []",fontsize=16,color="red",shape="box"];247[label="error []",fontsize=16,color="red",shape="box"];248[label="error []",fontsize=16,color="red",shape="box"];249[label="error []",fontsize=16,color="red",shape="box"];250[label="error []",fontsize=16,color="red",shape="box"];100[label="ww170",fontsize=16,color="green",shape="box"];101[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"];103[label="ww171",fontsize=16,color="green",shape="box"];104[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"];105[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"];251[label="error []",fontsize=16,color="red",shape="box"];252[label="error []",fontsize=16,color="red",shape="box"];253[label="error []",fontsize=16,color="red",shape="box"];254[label="primShowInt ww17",fontsize=16,color="burlywood",shape="triangle"];1246[label="ww17/Pos ww170",fontsize=10,color="white",style="solid",shape="box"];254 -> 1246[label="",style="solid", color="burlywood", weight=9]; 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286[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];286 -> 308[label="",style="solid", color="black", weight=3]; 287[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 ww170)",fontsize=16,color="green",shape="box"];287 -> 309[label="",style="dashed", color="green", weight=3]; 221[label="Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : []",fontsize=16,color="green",shape="box"];222[label="shows ww21 ww22",fontsize=16,color="black",shape="box"];222 -> 261[label="",style="solid", color="black", weight=3]; 306[label="ww581",fontsize=16,color="green",shape="box"];307 -> 182[label="",style="dashed", color="red", weight=0]; 307[label="primShowInt (div Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];307 -> 345[label="",style="dashed", color="magenta", weight=3]; 307 -> 346[label="",style="dashed", color="magenta", weight=3]; 308[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"];309 -> 254[label="",style="dashed", color="red", weight=0]; 309[label="primShowInt (Pos ww170)",fontsize=16,color="magenta"];309 -> 347[label="",style="dashed", color="magenta", weight=3]; 261[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="blue",shape="box"];1250[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1250[label="",style="solid", color="blue", weight=9]; 1250 -> 266[label="",style="solid", color="blue", weight=3]; 1251[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1251[label="",style="solid", color="blue", weight=9]; 1251 -> 267[label="",style="solid", color="blue", weight=3]; 1252[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1252[label="",style="solid", color="blue", weight=9]; 1252 -> 268[label="",style="solid", color="blue", weight=3]; 1253[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1253[label="",style="solid", color="blue", weight=9]; 1253 -> 269[label="",style="solid", color="blue", weight=3]; 1254[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1254[label="",style="solid", color="blue", weight=9]; 1254 -> 270[label="",style="solid", color="blue", weight=3]; 1255[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1255[label="",style="solid", color="blue", weight=9]; 1255 -> 271[label="",style="solid", color="blue", weight=3]; 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1260 -> 276[label="",style="solid", color="blue", weight=3]; 1261[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1261[label="",style="solid", color="blue", weight=9]; 1261 -> 277[label="",style="solid", color="blue", weight=3]; 1262[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1262[label="",style="solid", color="blue", weight=9]; 1262 -> 278[label="",style="solid", color="blue", weight=3]; 1263[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1263[label="",style="solid", color="blue", weight=9]; 1263 -> 279[label="",style="solid", color="blue", weight=3]; 1264[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1264[label="",style="solid", color="blue", weight=9]; 1264 -> 280[label="",style="solid", color="blue", weight=3]; 1265[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1265[label="",style="solid", color="blue", weight=9]; 1265 -> 281[label="",style="solid", color="blue", weight=3]; 1266[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1266[label="",style="solid", color="blue", weight=9]; 1266 -> 282[label="",style="solid", color="blue", weight=3]; 1267[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1267[label="",style="solid", color="blue", weight=9]; 1267 -> 283[label="",style="solid", color="blue", weight=3]; 345 -> 254[label="",style="dashed", color="red", weight=0]; 345[label="primShowInt (div Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];345 -> 370[label="",style="dashed", color="magenta", weight=3]; 346[label="toEnum (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];346 -> 371[label="",style="dashed", color="green", weight=3]; 347[label="Pos ww170",fontsize=16,color="green",shape="box"];266[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];266 -> 288[label="",style="solid", color="black", weight=3]; 267[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];267 -> 289[label="",style="solid", color="black", weight=3]; 268[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];268 -> 290[label="",style="solid", color="black", weight=3]; 269[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];269 -> 291[label="",style="solid", color="black", weight=3]; 270[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];270 -> 292[label="",style="solid", color="black", weight=3]; 271[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];271 -> 293[label="",style="solid", color="black", weight=3]; 272[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];272 -> 294[label="",style="solid", color="black", weight=3]; 273[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="burlywood",shape="box"];1268[label="ww21/ww210 :% ww211",fontsize=10,color="white",style="solid",shape="box"];273 -> 1268[label="",style="solid", color="burlywood", weight=9]; 1268 -> 295[label="",style="solid", color="burlywood", weight=3]; 274[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];274 -> 296[label="",style="solid", color="black", weight=3]; 275[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];275 -> 297[label="",style="solid", color="black", weight=3]; 276[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];276 -> 298[label="",style="solid", color="black", weight=3]; 277[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];277 -> 299[label="",style="solid", color="black", weight=3]; 278[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];278 -> 300[label="",style="solid", color="black", weight=3]; 279[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];279 -> 301[label="",style="solid", color="black", weight=3]; 280[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];280 -> 302[label="",style="solid", color="black", weight=3]; 281[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];281 -> 303[label="",style="solid", color="black", weight=3]; 282[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];282 -> 304[label="",style="solid", color="black", weight=3]; 283[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];283 -> 305[label="",style="solid", color="black", weight=3]; 370 -> 372[label="",style="dashed", color="red", weight=0]; 370[label="div Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];370 -> 373[label="",style="dashed", color="magenta", weight=3]; 370 -> 374[label="",style="dashed", color="magenta", weight=3]; 371[label="toEnum (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];371 -> 389[label="",style="solid", color="black", weight=3]; 288 -> 182[label="",style="dashed", color="red", weight=0]; 288[label="show ww21 ++ ww22",fontsize=16,color="magenta"];288 -> 310[label="",style="dashed", color="magenta", weight=3]; 288 -> 311[label="",style="dashed", color="magenta", weight=3]; 289 -> 182[label="",style="dashed", color="red", weight=0]; 289[label="show ww21 ++ ww22",fontsize=16,color="magenta"];289 -> 312[label="",style="dashed", color="magenta", weight=3]; 289 -> 313[label="",style="dashed", color="magenta", weight=3]; 290 -> 182[label="",style="dashed", color="red", weight=0]; 290[label="show ww21 ++ ww22",fontsize=16,color="magenta"];290 -> 314[label="",style="dashed", color="magenta", weight=3]; 290 -> 315[label="",style="dashed", color="magenta", weight=3]; 291 -> 182[label="",style="dashed", color="red", weight=0]; 291[label="show ww21 ++ ww22",fontsize=16,color="magenta"];291 -> 316[label="",style="dashed", color="magenta", weight=3]; 291 -> 317[label="",style="dashed", color="magenta", weight=3]; 292 -> 182[label="",style="dashed", color="red", weight=0]; 292[label="show ww21 ++ ww22",fontsize=16,color="magenta"];292 -> 318[label="",style="dashed", color="magenta", weight=3]; 292 -> 319[label="",style="dashed", color="magenta", weight=3]; 293 -> 182[label="",style="dashed", color="red", weight=0]; 293[label="show ww21 ++ ww22",fontsize=16,color="magenta"];293 -> 320[label="",style="dashed", color="magenta", weight=3]; 293 -> 321[label="",style="dashed", color="magenta", weight=3]; 294 -> 182[label="",style="dashed", color="red", weight=0]; 294[label="show ww21 ++ ww22",fontsize=16,color="magenta"];294 -> 322[label="",style="dashed", color="magenta", weight=3]; 294 -> 323[label="",style="dashed", color="magenta", weight=3]; 295[label="showsPrec (Pos Zero) (ww210 :% ww211) ww22",fontsize=16,color="black",shape="box"];295 -> 324[label="",style="solid", color="black", weight=3]; 296 -> 182[label="",style="dashed", color="red", weight=0]; 296[label="show ww21 ++ ww22",fontsize=16,color="magenta"];296 -> 325[label="",style="dashed", color="magenta", weight=3]; 296 -> 326[label="",style="dashed", color="magenta", weight=3]; 297 -> 182[label="",style="dashed", color="red", weight=0]; 297[label="show ww21 ++ ww22",fontsize=16,color="magenta"];297 -> 327[label="",style="dashed", color="magenta", weight=3]; 297 -> 328[label="",style="dashed", color="magenta", weight=3]; 298 -> 182[label="",style="dashed", color="red", weight=0]; 298[label="show ww21 ++ ww22",fontsize=16,color="magenta"];298 -> 329[label="",style="dashed", color="magenta", weight=3]; 298 -> 330[label="",style="dashed", color="magenta", weight=3]; 299 -> 182[label="",style="dashed", color="red", weight=0]; 299[label="show ww21 ++ ww22",fontsize=16,color="magenta"];299 -> 331[label="",style="dashed", color="magenta", weight=3]; 299 -> 332[label="",style="dashed", color="magenta", weight=3]; 300 -> 182[label="",style="dashed", color="red", weight=0]; 300[label="show ww21 ++ ww22",fontsize=16,color="magenta"];300 -> 333[label="",style="dashed", color="magenta", weight=3]; 300 -> 334[label="",style="dashed", color="magenta", weight=3]; 301 -> 182[label="",style="dashed", color="red", weight=0]; 301[label="show ww21 ++ ww22",fontsize=16,color="magenta"];301 -> 335[label="",style="dashed", color="magenta", weight=3]; 301 -> 336[label="",style="dashed", color="magenta", weight=3]; 302 -> 182[label="",style="dashed", color="red", weight=0]; 302[label="show ww21 ++ ww22",fontsize=16,color="magenta"];302 -> 337[label="",style="dashed", color="magenta", weight=3]; 302 -> 338[label="",style="dashed", color="magenta", weight=3]; 303 -> 182[label="",style="dashed", color="red", weight=0]; 303[label="show ww21 ++ ww22",fontsize=16,color="magenta"];303 -> 339[label="",style="dashed", color="magenta", weight=3]; 303 -> 340[label="",style="dashed", color="magenta", weight=3]; 304 -> 182[label="",style="dashed", color="red", weight=0]; 304[label="show ww21 ++ ww22",fontsize=16,color="magenta"];304 -> 341[label="",style="dashed", color="magenta", weight=3]; 304 -> 342[label="",style="dashed", color="magenta", weight=3]; 305 -> 182[label="",style="dashed", color="red", weight=0]; 305[label="show ww21 ++ ww22",fontsize=16,color="magenta"];305 -> 343[label="",style="dashed", color="magenta", weight=3]; 305 -> 344[label="",style="dashed", color="magenta", weight=3]; 373[label="ww1700",fontsize=16,color="green",shape="box"];374[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];372[label="div Pos (Succ ww60) Pos (Succ ww61)",fontsize=16,color="black",shape="triangle"];372 -> 378[label="",style="solid", color="black", weight=3]; 389 -> 400[label="",style="dashed", color="red", weight=0]; 389[label="primIntToChar (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];389 -> 401[label="",style="dashed", color="magenta", weight=3]; 389 -> 402[label="",style="dashed", color="magenta", weight=3]; 310 -> 183[label="",style="dashed", color="red", weight=0]; 310[label="show ww21",fontsize=16,color="magenta"];310 -> 348[label="",style="dashed", color="magenta", weight=3]; 311[label="ww22",fontsize=16,color="green",shape="box"];312 -> 185[label="",style="dashed", color="red", weight=0]; 312[label="show ww21",fontsize=16,color="magenta"];312 -> 349[label="",style="dashed", color="magenta", weight=3]; 313[label="ww22",fontsize=16,color="green",shape="box"];314 -> 187[label="",style="dashed", color="red", weight=0]; 314[label="show ww21",fontsize=16,color="magenta"];314 -> 350[label="",style="dashed", color="magenta", weight=3]; 315[label="ww22",fontsize=16,color="green",shape="box"];316 -> 189[label="",style="dashed", color="red", weight=0]; 316[label="show ww21",fontsize=16,color="magenta"];316 -> 351[label="",style="dashed", color="magenta", weight=3]; 317[label="ww22",fontsize=16,color="green",shape="box"];318 -> 191[label="",style="dashed", color="red", weight=0]; 318[label="show ww21",fontsize=16,color="magenta"];318 -> 352[label="",style="dashed", color="magenta", weight=3]; 319[label="ww22",fontsize=16,color="green",shape="box"];320 -> 193[label="",style="dashed", color="red", weight=0]; 320[label="show ww21",fontsize=16,color="magenta"];320 -> 353[label="",style="dashed", color="magenta", weight=3]; 321[label="ww22",fontsize=16,color="green",shape="box"];322 -> 195[label="",style="dashed", color="red", weight=0]; 322[label="show ww21",fontsize=16,color="magenta"];322 -> 354[label="",style="dashed", color="magenta", weight=3]; 323[label="ww22",fontsize=16,color="green",shape="box"];324 -> 24[label="",style="dashed", color="red", weight=0]; 324[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww210) . (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 ww211) ww22",fontsize=16,color="magenta"];324 -> 355[label="",style="dashed", color="magenta", weight=3]; 324 -> 356[label="",style="dashed", color="magenta", weight=3]; 324 -> 357[label="",style="dashed", color="magenta", weight=3]; 324 -> 358[label="",style="dashed", color="magenta", weight=3]; 324 -> 359[label="",style="dashed", color="magenta", weight=3]; 325 -> 197[label="",style="dashed", color="red", weight=0]; 325[label="show ww21",fontsize=16,color="magenta"];325 -> 360[label="",style="dashed", color="magenta", weight=3]; 326[label="ww22",fontsize=16,color="green",shape="box"];327 -> 199[label="",style="dashed", color="red", weight=0]; 327[label="show ww21",fontsize=16,color="magenta"];327 -> 361[label="",style="dashed", color="magenta", weight=3]; 328[label="ww22",fontsize=16,color="green",shape="box"];329 -> 201[label="",style="dashed", color="red", weight=0]; 329[label="show ww21",fontsize=16,color="magenta"];329 -> 362[label="",style="dashed", color="magenta", weight=3]; 330[label="ww22",fontsize=16,color="green",shape="box"];331 -> 203[label="",style="dashed", color="red", weight=0]; 331[label="show ww21",fontsize=16,color="magenta"];331 -> 363[label="",style="dashed", color="magenta", weight=3]; 332[label="ww22",fontsize=16,color="green",shape="box"];333 -> 205[label="",style="dashed", color="red", weight=0]; 333[label="show ww21",fontsize=16,color="magenta"];333 -> 364[label="",style="dashed", color="magenta", weight=3]; 334[label="ww22",fontsize=16,color="green",shape="box"];335 -> 207[label="",style="dashed", color="red", weight=0]; 335[label="show ww21",fontsize=16,color="magenta"];335 -> 365[label="",style="dashed", color="magenta", weight=3]; 336[label="ww22",fontsize=16,color="green",shape="box"];337 -> 209[label="",style="dashed", color="red", weight=0]; 337[label="show ww21",fontsize=16,color="magenta"];337 -> 366[label="",style="dashed", color="magenta", weight=3]; 338[label="ww22",fontsize=16,color="green",shape="box"];339 -> 211[label="",style="dashed", color="red", weight=0]; 339[label="show ww21",fontsize=16,color="magenta"];339 -> 367[label="",style="dashed", color="magenta", weight=3]; 340[label="ww22",fontsize=16,color="green",shape="box"];341 -> 213[label="",style="dashed", color="red", weight=0]; 341[label="show ww21",fontsize=16,color="magenta"];341 -> 368[label="",style="dashed", color="magenta", weight=3]; 342[label="ww22",fontsize=16,color="green",shape="box"];343 -> 215[label="",style="dashed", color="red", weight=0]; 343[label="show ww21",fontsize=16,color="magenta"];343 -> 369[label="",style="dashed", color="magenta", weight=3]; 344[label="ww22",fontsize=16,color="green",shape="box"];378[label="primDivInt (Pos (Succ ww60)) (Pos (Succ ww61))",fontsize=16,color="black",shape="box"];378 -> 388[label="",style="solid", color="black", weight=3]; 401[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];402[label="ww1700",fontsize=16,color="green",shape="box"];400[label="primIntToChar (mod Pos (Succ ww66) Pos (Succ ww67))",fontsize=16,color="black",shape="triangle"];400 -> 403[label="",style="solid", color="black", weight=3]; 348[label="ww21",fontsize=16,color="green",shape="box"];349[label="ww21",fontsize=16,color="green",shape="box"];350[label="ww21",fontsize=16,color="green",shape="box"];351[label="ww21",fontsize=16,color="green",shape="box"];352[label="ww21",fontsize=16,color="green",shape="box"];353[label="ww21",fontsize=16,color="green",shape="box"];354[label="ww21",fontsize=16,color="green",shape="box"];355[label="ww210",fontsize=16,color="green",shape="box"];356[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"];357[label="ww211",fontsize=16,color="green",shape="box"];358[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"];359[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"];360[label="ww21",fontsize=16,color="green",shape="box"];361[label="ww21",fontsize=16,color="green",shape="box"];362[label="ww21",fontsize=16,color="green",shape="box"];363[label="ww21",fontsize=16,color="green",shape="box"];364[label="ww21",fontsize=16,color="green",shape="box"];365[label="ww21",fontsize=16,color="green",shape="box"];366[label="ww21",fontsize=16,color="green",shape="box"];367[label="ww21",fontsize=16,color="green",shape="box"];368[label="ww21",fontsize=16,color="green",shape="box"];369[label="ww21",fontsize=16,color="green",shape="box"];388[label="Pos (primDivNatS (Succ ww60) (Succ ww61))",fontsize=16,color="green",shape="box"];388 -> 399[label="",style="dashed", color="green", weight=3]; 403[label="primIntToChar (primModInt (Pos (Succ ww66)) (Pos (Succ ww67)))",fontsize=16,color="black",shape="box"];403 -> 405[label="",style="solid", color="black", weight=3]; 399[label="primDivNatS (Succ ww60) (Succ ww61)",fontsize=16,color="black",shape="triangle"];399 -> 404[label="",style="solid", color="black", weight=3]; 405[label="primIntToChar (Pos (primModNatS (Succ ww66) (Succ ww67)))",fontsize=16,color="black",shape="box"];405 -> 408[label="",style="solid", color="black", weight=3]; 404[label="primDivNatS0 ww60 ww61 (primGEqNatS ww60 ww61)",fontsize=16,color="burlywood",shape="box"];1269[label="ww60/Succ ww600",fontsize=10,color="white",style="solid",shape="box"];404 -> 1269[label="",style="solid", color="burlywood", weight=9]; 1269 -> 406[label="",style="solid", color="burlywood", weight=3]; 1270[label="ww60/Zero",fontsize=10,color="white",style="solid",shape="box"];404 -> 1270[label="",style="solid", color="burlywood", weight=9]; 1270 -> 407[label="",style="solid", color="burlywood", weight=3]; 408[label="Char (primModNatS (Succ ww66) (Succ ww67))",fontsize=16,color="green",shape="box"];408 -> 413[label="",style="dashed", color="green", weight=3]; 406[label="primDivNatS0 (Succ ww600) ww61 (primGEqNatS (Succ ww600) ww61)",fontsize=16,color="burlywood",shape="box"];1271[label="ww61/Succ ww610",fontsize=10,color="white",style="solid",shape="box"];406 -> 1271[label="",style="solid", color="burlywood", weight=9]; 1271 -> 409[label="",style="solid", color="burlywood", weight=3]; 1272[label="ww61/Zero",fontsize=10,color="white",style="solid",shape="box"];406 -> 1272[label="",style="solid", color="burlywood", weight=9]; 1272 -> 410[label="",style="solid", color="burlywood", weight=3]; 407[label="primDivNatS0 Zero ww61 (primGEqNatS Zero ww61)",fontsize=16,color="burlywood",shape="box"];1273[label="ww61/Succ ww610",fontsize=10,color="white",style="solid",shape="box"];407 -> 1273[label="",style="solid", color="burlywood", weight=9]; 1273 -> 411[label="",style="solid", color="burlywood", weight=3]; 1274[label="ww61/Zero",fontsize=10,color="white",style="solid",shape="box"];407 -> 1274[label="",style="solid", color="burlywood", weight=9]; 1274 -> 412[label="",style="solid", color="burlywood", weight=3]; 413[label="primModNatS (Succ ww66) (Succ ww67)",fontsize=16,color="black",shape="triangle"];413 -> 418[label="",style="solid", color="black", weight=3]; 409[label="primDivNatS0 (Succ ww600) (Succ ww610) (primGEqNatS (Succ ww600) (Succ ww610))",fontsize=16,color="black",shape="box"];409 -> 414[label="",style="solid", color="black", weight=3]; 410[label="primDivNatS0 (Succ ww600) Zero (primGEqNatS (Succ ww600) Zero)",fontsize=16,color="black",shape="box"];410 -> 415[label="",style="solid", color="black", weight=3]; 411[label="primDivNatS0 Zero (Succ ww610) (primGEqNatS Zero (Succ ww610))",fontsize=16,color="black",shape="box"];411 -> 416[label="",style="solid", color="black", weight=3]; 412[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];412 -> 417[label="",style="solid", color="black", weight=3]; 418[label="primModNatS0 ww66 ww67 (primGEqNatS ww66 ww67)",fontsize=16,color="burlywood",shape="box"];1275[label="ww66/Succ ww660",fontsize=10,color="white",style="solid",shape="box"];418 -> 1275[label="",style="solid", color="burlywood", weight=9]; 1275 -> 424[label="",style="solid", color="burlywood", weight=3]; 1276[label="ww66/Zero",fontsize=10,color="white",style="solid",shape="box"];418 -> 1276[label="",style="solid", color="burlywood", weight=9]; 1276 -> 425[label="",style="solid", color="burlywood", weight=3]; 414 -> 930[label="",style="dashed", color="red", weight=0]; 414[label="primDivNatS0 (Succ ww600) (Succ ww610) (primGEqNatS ww600 ww610)",fontsize=16,color="magenta"];414 -> 931[label="",style="dashed", color="magenta", weight=3]; 414 -> 932[label="",style="dashed", color="magenta", weight=3]; 414 -> 933[label="",style="dashed", color="magenta", weight=3]; 414 -> 934[label="",style="dashed", color="magenta", weight=3]; 415[label="primDivNatS0 (Succ ww600) Zero True",fontsize=16,color="black",shape="box"];415 -> 421[label="",style="solid", color="black", weight=3]; 416[label="primDivNatS0 Zero (Succ ww610) False",fontsize=16,color="black",shape="box"];416 -> 422[label="",style="solid", color="black", weight=3]; 417[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];417 -> 423[label="",style="solid", color="black", weight=3]; 424[label="primModNatS0 (Succ ww660) ww67 (primGEqNatS (Succ ww660) ww67)",fontsize=16,color="burlywood",shape="box"];1277[label="ww67/Succ ww670",fontsize=10,color="white",style="solid",shape="box"];424 -> 1277[label="",style="solid", color="burlywood", weight=9]; 1277 -> 432[label="",style="solid", color="burlywood", weight=3]; 1278[label="ww67/Zero",fontsize=10,color="white",style="solid",shape="box"];424 -> 1278[label="",style="solid", color="burlywood", weight=9]; 1278 -> 433[label="",style="solid", color="burlywood", weight=3]; 425[label="primModNatS0 Zero ww67 (primGEqNatS Zero ww67)",fontsize=16,color="burlywood",shape="box"];1279[label="ww67/Succ ww670",fontsize=10,color="white",style="solid",shape="box"];425 -> 1279[label="",style="solid", color="burlywood", weight=9]; 1279 -> 434[label="",style="solid", color="burlywood", weight=3]; 1280[label="ww67/Zero",fontsize=10,color="white",style="solid",shape="box"];425 -> 1280[label="",style="solid", color="burlywood", weight=9]; 1280 -> 435[label="",style="solid", color="burlywood", weight=3]; 931[label="ww610",fontsize=16,color="green",shape="box"];932[label="ww600",fontsize=16,color="green",shape="box"];933[label="ww600",fontsize=16,color="green",shape="box"];934[label="ww610",fontsize=16,color="green",shape="box"];930[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS ww112 ww113)",fontsize=16,color="burlywood",shape="triangle"];1281[label="ww112/Succ ww1120",fontsize=10,color="white",style="solid",shape="box"];930 -> 1281[label="",style="solid", color="burlywood", weight=9]; 1281 -> 971[label="",style="solid", color="burlywood", weight=3]; 1282[label="ww112/Zero",fontsize=10,color="white",style="solid",shape="box"];930 -> 1282[label="",style="solid", color="burlywood", weight=9]; 1282 -> 972[label="",style="solid", color="burlywood", weight=3]; 421[label="Succ (primDivNatS (primMinusNatS (Succ ww600) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];421 -> 430[label="",style="dashed", color="green", weight=3]; 422[label="Zero",fontsize=16,color="green",shape="box"];423[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];423 -> 431[label="",style="dashed", color="green", weight=3]; 432[label="primModNatS0 (Succ ww660) (Succ ww670) (primGEqNatS (Succ ww660) (Succ ww670))",fontsize=16,color="black",shape="box"];432 -> 442[label="",style="solid", color="black", weight=3]; 433[label="primModNatS0 (Succ ww660) Zero (primGEqNatS (Succ ww660) Zero)",fontsize=16,color="black",shape="box"];433 -> 443[label="",style="solid", color="black", weight=3]; 434[label="primModNatS0 Zero (Succ ww670) (primGEqNatS Zero (Succ ww670))",fontsize=16,color="black",shape="box"];434 -> 444[label="",style="solid", color="black", weight=3]; 435[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];435 -> 445[label="",style="solid", color="black", weight=3]; 971[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS (Succ ww1120) ww113)",fontsize=16,color="burlywood",shape="box"];1283[label="ww113/Succ ww1130",fontsize=10,color="white",style="solid",shape="box"];971 -> 1283[label="",style="solid", color="burlywood", weight=9]; 1283 -> 983[label="",style="solid", color="burlywood", weight=3]; 1284[label="ww113/Zero",fontsize=10,color="white",style="solid",shape="box"];971 -> 1284[label="",style="solid", color="burlywood", weight=9]; 1284 -> 984[label="",style="solid", color="burlywood", weight=3]; 972[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS Zero ww113)",fontsize=16,color="burlywood",shape="box"];1285[label="ww113/Succ ww1130",fontsize=10,color="white",style="solid",shape="box"];972 -> 1285[label="",style="solid", color="burlywood", weight=9]; 1285 -> 985[label="",style="solid", color="burlywood", weight=3]; 1286[label="ww113/Zero",fontsize=10,color="white",style="solid",shape="box"];972 -> 1286[label="",style="solid", color="burlywood", weight=9]; 1286 -> 986[label="",style="solid", color="burlywood", weight=3]; 430 -> 1184[label="",style="dashed", color="red", weight=0]; 430[label="primDivNatS (primMinusNatS (Succ ww600) Zero) (Succ Zero)",fontsize=16,color="magenta"];430 -> 1185[label="",style="dashed", color="magenta", weight=3]; 430 -> 1186[label="",style="dashed", color="magenta", weight=3]; 430 -> 1187[label="",style="dashed", color="magenta", weight=3]; 431 -> 1184[label="",style="dashed", color="red", weight=0]; 431[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];431 -> 1188[label="",style="dashed", color="magenta", weight=3]; 431 -> 1189[label="",style="dashed", color="magenta", weight=3]; 431 -> 1190[label="",style="dashed", color="magenta", weight=3]; 442 -> 1005[label="",style="dashed", color="red", weight=0]; 442[label="primModNatS0 (Succ ww660) (Succ ww670) (primGEqNatS ww660 ww670)",fontsize=16,color="magenta"];442 -> 1006[label="",style="dashed", color="magenta", weight=3]; 442 -> 1007[label="",style="dashed", color="magenta", weight=3]; 442 -> 1008[label="",style="dashed", color="magenta", weight=3]; 442 -> 1009[label="",style="dashed", color="magenta", weight=3]; 443[label="primModNatS0 (Succ ww660) Zero True",fontsize=16,color="black",shape="box"];443 -> 456[label="",style="solid", color="black", weight=3]; 444[label="primModNatS0 Zero (Succ ww670) False",fontsize=16,color="black",shape="box"];444 -> 457[label="",style="solid", color="black", weight=3]; 445[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];445 -> 458[label="",style="solid", color="black", weight=3]; 983[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS (Succ ww1120) (Succ ww1130))",fontsize=16,color="black",shape="box"];983 -> 997[label="",style="solid", color="black", weight=3]; 984[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS (Succ ww1120) Zero)",fontsize=16,color="black",shape="box"];984 -> 998[label="",style="solid", color="black", weight=3]; 985[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS Zero (Succ ww1130))",fontsize=16,color="black",shape="box"];985 -> 999[label="",style="solid", color="black", weight=3]; 986[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];986 -> 1000[label="",style="solid", color="black", weight=3]; 1185[label="Succ ww600",fontsize=16,color="green",shape="box"];1186[label="Zero",fontsize=16,color="green",shape="box"];1187[label="Zero",fontsize=16,color="green",shape="box"];1184[label="primDivNatS (primMinusNatS ww124 ww125) (Succ ww126)",fontsize=16,color="burlywood",shape="triangle"];1287[label="ww124/Succ ww1240",fontsize=10,color="white",style="solid",shape="box"];1184 -> 1287[label="",style="solid", color="burlywood", weight=9]; 1287 -> 1209[label="",style="solid", color="burlywood", weight=3]; 1288[label="ww124/Zero",fontsize=10,color="white",style="solid",shape="box"];1184 -> 1288[label="",style="solid", color="burlywood", weight=9]; 1288 -> 1210[label="",style="solid", color="burlywood", weight=3]; 1188[label="Zero",fontsize=16,color="green",shape="box"];1189[label="Zero",fontsize=16,color="green",shape="box"];1190[label="Zero",fontsize=16,color="green",shape="box"];1006[label="ww660",fontsize=16,color="green",shape="box"];1007[label="ww670",fontsize=16,color="green",shape="box"];1008[label="ww660",fontsize=16,color="green",shape="box"];1009[label="ww670",fontsize=16,color="green",shape="box"];1005[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS ww117 ww118)",fontsize=16,color="burlywood",shape="triangle"];1289[label="ww117/Succ ww1170",fontsize=10,color="white",style="solid",shape="box"];1005 -> 1289[label="",style="solid", color="burlywood", weight=9]; 1289 -> 1046[label="",style="solid", color="burlywood", weight=3]; 1290[label="ww117/Zero",fontsize=10,color="white",style="solid",shape="box"];1005 -> 1290[label="",style="solid", color="burlywood", weight=9]; 1290 -> 1047[label="",style="solid", color="burlywood", weight=3]; 456 -> 1092[label="",style="dashed", color="red", weight=0]; 456[label="primModNatS (primMinusNatS (Succ ww660) Zero) (Succ Zero)",fontsize=16,color="magenta"];456 -> 1093[label="",style="dashed", color="magenta", weight=3]; 456 -> 1094[label="",style="dashed", color="magenta", weight=3]; 456 -> 1095[label="",style="dashed", color="magenta", weight=3]; 457[label="Succ Zero",fontsize=16,color="green",shape="box"];458 -> 1092[label="",style="dashed", color="red", weight=0]; 458[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];458 -> 1096[label="",style="dashed", color="magenta", weight=3]; 458 -> 1097[label="",style="dashed", color="magenta", weight=3]; 458 -> 1098[label="",style="dashed", color="magenta", weight=3]; 997 -> 930[label="",style="dashed", color="red", weight=0]; 997[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS ww1120 ww1130)",fontsize=16,color="magenta"];997 -> 1048[label="",style="dashed", color="magenta", weight=3]; 997 -> 1049[label="",style="dashed", color="magenta", weight=3]; 998[label="primDivNatS0 (Succ ww110) (Succ ww111) True",fontsize=16,color="black",shape="triangle"];998 -> 1050[label="",style="solid", color="black", weight=3]; 999[label="primDivNatS0 (Succ ww110) (Succ ww111) False",fontsize=16,color="black",shape="box"];999 -> 1051[label="",style="solid", color="black", weight=3]; 1000 -> 998[label="",style="dashed", color="red", weight=0]; 1000[label="primDivNatS0 (Succ ww110) (Succ ww111) True",fontsize=16,color="magenta"];1209[label="primDivNatS (primMinusNatS (Succ ww1240) ww125) (Succ ww126)",fontsize=16,color="burlywood",shape="box"];1291[label="ww125/Succ ww1250",fontsize=10,color="white",style="solid",shape="box"];1209 -> 1291[label="",style="solid", color="burlywood", weight=9]; 1291 -> 1211[label="",style="solid", color="burlywood", weight=3]; 1292[label="ww125/Zero",fontsize=10,color="white",style="solid",shape="box"];1209 -> 1292[label="",style="solid", color="burlywood", weight=9]; 1292 -> 1212[label="",style="solid", color="burlywood", weight=3]; 1210[label="primDivNatS (primMinusNatS Zero ww125) (Succ ww126)",fontsize=16,color="burlywood",shape="box"];1293[label="ww125/Succ ww1250",fontsize=10,color="white",style="solid",shape="box"];1210 -> 1293[label="",style="solid", color="burlywood", weight=9]; 1293 -> 1213[label="",style="solid", color="burlywood", weight=3]; 1294[label="ww125/Zero",fontsize=10,color="white",style="solid",shape="box"];1210 -> 1294[label="",style="solid", color="burlywood", weight=9]; 1294 -> 1214[label="",style="solid", color="burlywood", weight=3]; 1046[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS (Succ ww1170) ww118)",fontsize=16,color="burlywood",shape="box"];1295[label="ww118/Succ ww1180",fontsize=10,color="white",style="solid",shape="box"];1046 -> 1295[label="",style="solid", color="burlywood", weight=9]; 1295 -> 1056[label="",style="solid", color="burlywood", weight=3]; 1296[label="ww118/Zero",fontsize=10,color="white",style="solid",shape="box"];1046 -> 1296[label="",style="solid", color="burlywood", weight=9]; 1296 -> 1057[label="",style="solid", color="burlywood", weight=3]; 1047[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS Zero ww118)",fontsize=16,color="burlywood",shape="box"];1297[label="ww118/Succ ww1180",fontsize=10,color="white",style="solid",shape="box"];1047 -> 1297[label="",style="solid", color="burlywood", weight=9]; 1297 -> 1058[label="",style="solid", color="burlywood", weight=3]; 1298[label="ww118/Zero",fontsize=10,color="white",style="solid",shape="box"];1047 -> 1298[label="",style="solid", color="burlywood", weight=9]; 1298 -> 1059[label="",style="solid", color="burlywood", weight=3]; 1093[label="Succ ww660",fontsize=16,color="green",shape="box"];1094[label="Zero",fontsize=16,color="green",shape="box"];1095[label="Zero",fontsize=16,color="green",shape="box"];1092[label="primModNatS (primMinusNatS ww120 ww121) (Succ ww122)",fontsize=16,color="burlywood",shape="triangle"];1299[label="ww120/Succ ww1200",fontsize=10,color="white",style="solid",shape="box"];1092 -> 1299[label="",style="solid", color="burlywood", weight=9]; 1299 -> 1123[label="",style="solid", color="burlywood", weight=3]; 1300[label="ww120/Zero",fontsize=10,color="white",style="solid",shape="box"];1092 -> 1300[label="",style="solid", color="burlywood", weight=9]; 1300 -> 1124[label="",style="solid", color="burlywood", weight=3]; 1096[label="Zero",fontsize=16,color="green",shape="box"];1097[label="Zero",fontsize=16,color="green",shape="box"];1098[label="Zero",fontsize=16,color="green",shape="box"];1048[label="ww1130",fontsize=16,color="green",shape="box"];1049[label="ww1120",fontsize=16,color="green",shape="box"];1050[label="Succ (primDivNatS (primMinusNatS (Succ ww110) (Succ ww111)) (Succ (Succ ww111)))",fontsize=16,color="green",shape="box"];1050 -> 1060[label="",style="dashed", color="green", weight=3]; 1051[label="Zero",fontsize=16,color="green",shape="box"];1211[label="primDivNatS (primMinusNatS (Succ ww1240) (Succ ww1250)) (Succ ww126)",fontsize=16,color="black",shape="box"];1211 -> 1215[label="",style="solid", color="black", weight=3]; 1212[label="primDivNatS (primMinusNatS (Succ ww1240) Zero) (Succ ww126)",fontsize=16,color="black",shape="box"];1212 -> 1216[label="",style="solid", color="black", weight=3]; 1213[label="primDivNatS (primMinusNatS Zero (Succ ww1250)) (Succ ww126)",fontsize=16,color="black",shape="box"];1213 -> 1217[label="",style="solid", color="black", weight=3]; 1214[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww126)",fontsize=16,color="black",shape="box"];1214 -> 1218[label="",style="solid", color="black", weight=3]; 1056[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS (Succ ww1170) (Succ ww1180))",fontsize=16,color="black",shape="box"];1056 -> 1067[label="",style="solid", color="black", weight=3]; 1057[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS (Succ ww1170) Zero)",fontsize=16,color="black",shape="box"];1057 -> 1068[label="",style="solid", color="black", weight=3]; 1058[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS Zero (Succ ww1180))",fontsize=16,color="black",shape="box"];1058 -> 1069[label="",style="solid", color="black", weight=3]; 1059[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1059 -> 1070[label="",style="solid", color="black", weight=3]; 1123[label="primModNatS (primMinusNatS (Succ ww1200) ww121) (Succ ww122)",fontsize=16,color="burlywood",shape="box"];1301[label="ww121/Succ ww1210",fontsize=10,color="white",style="solid",shape="box"];1123 -> 1301[label="",style="solid", color="burlywood", weight=9]; 1301 -> 1129[label="",style="solid", color="burlywood", weight=3]; 1302[label="ww121/Zero",fontsize=10,color="white",style="solid",shape="box"];1123 -> 1302[label="",style="solid", color="burlywood", weight=9]; 1302 -> 1130[label="",style="solid", color="burlywood", weight=3]; 1124[label="primModNatS (primMinusNatS Zero ww121) (Succ ww122)",fontsize=16,color="burlywood",shape="box"];1303[label="ww121/Succ ww1210",fontsize=10,color="white",style="solid",shape="box"];1124 -> 1303[label="",style="solid", color="burlywood", weight=9]; 1303 -> 1131[label="",style="solid", color="burlywood", weight=3]; 1304[label="ww121/Zero",fontsize=10,color="white",style="solid",shape="box"];1124 -> 1304[label="",style="solid", color="burlywood", weight=9]; 1304 -> 1132[label="",style="solid", color="burlywood", weight=3]; 1060 -> 1184[label="",style="dashed", color="red", weight=0]; 1060[label="primDivNatS (primMinusNatS (Succ ww110) (Succ ww111)) (Succ (Succ ww111))",fontsize=16,color="magenta"];1060 -> 1191[label="",style="dashed", color="magenta", weight=3]; 1060 -> 1192[label="",style="dashed", color="magenta", weight=3]; 1060 -> 1193[label="",style="dashed", color="magenta", weight=3]; 1215 -> 1184[label="",style="dashed", color="red", weight=0]; 1215[label="primDivNatS (primMinusNatS ww1240 ww1250) (Succ ww126)",fontsize=16,color="magenta"];1215 -> 1219[label="",style="dashed", color="magenta", weight=3]; 1215 -> 1220[label="",style="dashed", color="magenta", weight=3]; 1216 -> 399[label="",style="dashed", color="red", weight=0]; 1216[label="primDivNatS (Succ ww1240) (Succ ww126)",fontsize=16,color="magenta"];1216 -> 1221[label="",style="dashed", color="magenta", weight=3]; 1216 -> 1222[label="",style="dashed", color="magenta", weight=3]; 1217[label="primDivNatS Zero (Succ ww126)",fontsize=16,color="black",shape="triangle"];1217 -> 1223[label="",style="solid", color="black", weight=3]; 1218 -> 1217[label="",style="dashed", color="red", weight=0]; 1218[label="primDivNatS Zero (Succ ww126)",fontsize=16,color="magenta"];1067 -> 1005[label="",style="dashed", color="red", weight=0]; 1067[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS ww1170 ww1180)",fontsize=16,color="magenta"];1067 -> 1076[label="",style="dashed", color="magenta", weight=3]; 1067 -> 1077[label="",style="dashed", color="magenta", weight=3]; 1068[label="primModNatS0 (Succ ww115) (Succ ww116) True",fontsize=16,color="black",shape="triangle"];1068 -> 1078[label="",style="solid", color="black", weight=3]; 1069[label="primModNatS0 (Succ ww115) (Succ ww116) False",fontsize=16,color="black",shape="box"];1069 -> 1079[label="",style="solid", color="black", weight=3]; 1070 -> 1068[label="",style="dashed", color="red", weight=0]; 1070[label="primModNatS0 (Succ ww115) (Succ ww116) True",fontsize=16,color="magenta"];1129[label="primModNatS (primMinusNatS (Succ ww1200) (Succ ww1210)) (Succ ww122)",fontsize=16,color="black",shape="box"];1129 -> 1139[label="",style="solid", color="black", weight=3]; 1130[label="primModNatS (primMinusNatS (Succ ww1200) Zero) (Succ ww122)",fontsize=16,color="black",shape="box"];1130 -> 1140[label="",style="solid", color="black", weight=3]; 1131[label="primModNatS (primMinusNatS Zero (Succ ww1210)) (Succ ww122)",fontsize=16,color="black",shape="box"];1131 -> 1141[label="",style="solid", color="black", weight=3]; 1132[label="primModNatS (primMinusNatS Zero Zero) (Succ ww122)",fontsize=16,color="black",shape="box"];1132 -> 1142[label="",style="solid", color="black", weight=3]; 1191[label="Succ ww110",fontsize=16,color="green",shape="box"];1192[label="Succ ww111",fontsize=16,color="green",shape="box"];1193[label="Succ ww111",fontsize=16,color="green",shape="box"];1219[label="ww1240",fontsize=16,color="green",shape="box"];1220[label="ww1250",fontsize=16,color="green",shape="box"];1221[label="ww1240",fontsize=16,color="green",shape="box"];1222[label="ww126",fontsize=16,color="green",shape="box"];1223[label="Zero",fontsize=16,color="green",shape="box"];1076[label="ww1170",fontsize=16,color="green",shape="box"];1077[label="ww1180",fontsize=16,color="green",shape="box"];1078 -> 1092[label="",style="dashed", color="red", weight=0]; 1078[label="primModNatS (primMinusNatS (Succ ww115) (Succ ww116)) (Succ (Succ ww116))",fontsize=16,color="magenta"];1078 -> 1105[label="",style="dashed", color="magenta", weight=3]; 1078 -> 1106[label="",style="dashed", color="magenta", weight=3]; 1078 -> 1107[label="",style="dashed", color="magenta", weight=3]; 1079[label="Succ (Succ ww115)",fontsize=16,color="green",shape="box"];1139 -> 1092[label="",style="dashed", color="red", weight=0]; 1139[label="primModNatS (primMinusNatS ww1200 ww1210) (Succ ww122)",fontsize=16,color="magenta"];1139 -> 1147[label="",style="dashed", color="magenta", weight=3]; 1139 -> 1148[label="",style="dashed", color="magenta", weight=3]; 1140 -> 413[label="",style="dashed", color="red", weight=0]; 1140[label="primModNatS (Succ ww1200) (Succ ww122)",fontsize=16,color="magenta"];1140 -> 1149[label="",style="dashed", color="magenta", weight=3]; 1140 -> 1150[label="",style="dashed", color="magenta", weight=3]; 1141[label="primModNatS Zero (Succ ww122)",fontsize=16,color="black",shape="triangle"];1141 -> 1151[label="",style="solid", color="black", weight=3]; 1142 -> 1141[label="",style="dashed", color="red", weight=0]; 1142[label="primModNatS Zero (Succ ww122)",fontsize=16,color="magenta"];1105[label="Succ ww115",fontsize=16,color="green",shape="box"];1106[label="Succ ww116",fontsize=16,color="green",shape="box"];1107[label="Succ ww116",fontsize=16,color="green",shape="box"];1147[label="ww1200",fontsize=16,color="green",shape="box"];1148[label="ww1210",fontsize=16,color="green",shape="box"];1149[label="ww122",fontsize=16,color="green",shape="box"];1150[label="ww1200",fontsize=16,color="green",shape="box"];1151[label="Zero",fontsize=16,color="green",shape="box"];} ---------------------------------------- (151) TRUE