39.61/19.67 MAYBE 41.74/20.32 proof of /export/starexec/sandbox/benchmark/theBenchmark.hs 41.74/20.32 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 41.74/20.32 41.74/20.32 41.74/20.32 H-Termination with start terms of the given HASKELL could not be shown: 41.74/20.32 41.74/20.32 (0) HASKELL 41.74/20.32 (1) IFR [EQUIVALENT, 0 ms] 41.74/20.32 (2) HASKELL 41.74/20.32 (3) BR [EQUIVALENT, 0 ms] 41.74/20.32 (4) HASKELL 41.74/20.32 (5) COR [EQUIVALENT, 0 ms] 41.74/20.32 (6) HASKELL 41.74/20.32 (7) NumRed [SOUND, 0 ms] 41.74/20.32 (8) HASKELL 41.74/20.32 (9) Narrow [SOUND, 0 ms] 41.74/20.32 (10) AND 41.74/20.32 (11) QDP 41.74/20.32 (12) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (13) NO 41.74/20.32 (14) QDP 41.74/20.32 (15) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (16) NO 41.74/20.32 (17) QDP 41.74/20.32 (18) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (19) NO 41.74/20.32 (20) QDP 41.74/20.32 (21) QDPSizeChangeProof [EQUIVALENT, 0 ms] 41.74/20.32 (22) YES 41.74/20.32 (23) QDP 41.74/20.32 (24) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (25) NO 41.74/20.32 (26) QDP 41.74/20.32 (27) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (28) NO 41.74/20.32 (29) QDP 41.74/20.32 (30) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (31) NO 41.74/20.32 (32) QDP 41.74/20.32 (33) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (34) NO 41.74/20.32 (35) QDP 41.74/20.32 (36) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (37) NO 41.74/20.32 (38) QDP 41.74/20.32 (39) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (40) NO 41.74/20.32 (41) QDP 41.74/20.32 (42) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (43) NO 41.74/20.32 (44) QDP 41.74/20.32 (45) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (46) QDP 41.74/20.32 (47) QDPOrderProof [EQUIVALENT, 0 ms] 41.74/20.32 (48) QDP 41.74/20.32 (49) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (50) QDP 41.74/20.32 (51) QDPSizeChangeProof [EQUIVALENT, 0 ms] 41.74/20.32 (52) YES 41.74/20.32 (53) QDP 41.74/20.32 (54) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (55) NO 41.74/20.32 (56) QDP 41.74/20.32 (57) TransformationProof [EQUIVALENT, 36 ms] 41.74/20.32 (58) QDP 41.74/20.32 (59) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (60) QDP 41.74/20.32 (61) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (62) QDP 41.74/20.32 (63) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (64) QDP 41.74/20.32 (65) TransformationProof [EQUIVALENT, 6 ms] 41.74/20.32 (66) QDP 41.74/20.32 (67) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (68) QDP 41.74/20.32 (69) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (70) QDP 41.74/20.32 (71) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (72) QDP 41.74/20.32 (73) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (74) QDP 41.74/20.32 (75) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (76) QDP 41.74/20.32 (77) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (78) QDP 41.74/20.32 (79) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (80) QDP 41.74/20.32 (81) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (82) QDP 41.74/20.32 (83) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (84) QDP 41.74/20.32 (85) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (86) QDP 41.74/20.32 (87) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (88) QDP 41.74/20.32 (89) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (90) QDP 41.74/20.32 (91) TransformationProof [EQUIVALENT, 3 ms] 41.74/20.32 (92) QDP 41.74/20.32 (93) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (94) QDP 41.74/20.32 (95) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (96) QDP 41.74/20.32 (97) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (98) QDP 41.74/20.32 (99) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (100) QDP 41.74/20.32 (101) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (102) QDP 41.74/20.32 (103) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (104) QDP 41.74/20.32 (105) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (106) QDP 41.74/20.32 (107) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (108) QDP 41.74/20.32 (109) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (110) QDP 41.74/20.32 (111) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (112) QDP 41.74/20.32 (113) TransformationProof [EQUIVALENT, 3 ms] 41.74/20.32 (114) QDP 41.74/20.32 (115) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (116) QDP 41.74/20.32 (117) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (118) QDP 41.74/20.32 (119) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (120) QDP 41.74/20.32 (121) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (122) QDP 41.74/20.32 (123) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (124) QDP 41.74/20.32 (125) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (126) QDP 41.74/20.32 (127) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (128) QDP 41.74/20.32 (129) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (130) QDP 41.74/20.32 (131) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (132) QDP 41.74/20.32 (133) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (134) QDP 41.74/20.32 (135) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (136) QDP 41.74/20.32 (137) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (138) QDP 41.74/20.32 (139) QDPSizeChangeProof [EQUIVALENT, 0 ms] 41.74/20.32 (140) YES 41.74/20.32 (141) QDP 41.74/20.32 (142) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (143) NO 41.74/20.32 (144) QDP 41.74/20.32 (145) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (146) NO 41.74/20.32 (147) QDP 41.74/20.32 (148) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (149) QDP 41.74/20.32 (150) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (151) QDP 41.74/20.32 (152) UsableRulesProof [EQUIVALENT, 0 ms] 41.74/20.32 (153) QDP 41.74/20.32 (154) QReductionProof [EQUIVALENT, 0 ms] 41.74/20.32 (155) QDP 41.74/20.32 (156) MNOCProof [EQUIVALENT, 0 ms] 41.74/20.32 (157) QDP 41.74/20.32 (158) InductionCalculusProof [EQUIVALENT, 0 ms] 41.74/20.32 (159) QDP 41.74/20.32 (160) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (161) QDP 41.74/20.32 (162) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (163) QDP 41.74/20.32 (164) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (165) QDP 41.74/20.32 (166) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (167) QDP 41.74/20.32 (168) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (169) QDP 41.74/20.32 (170) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (171) QDP 41.74/20.32 (172) TransformationProof [EQUIVALENT, 0 ms] 41.74/20.32 (173) QDP 41.74/20.32 (174) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (175) QDP 41.74/20.32 (176) MNOCProof [EQUIVALENT, 0 ms] 41.74/20.32 (177) QDP 41.74/20.32 (178) InductionCalculusProof [EQUIVALENT, 0 ms] 41.74/20.32 (179) QDP 41.74/20.32 (180) QDP 41.74/20.32 (181) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (182) NO 41.74/20.32 (183) QDP 41.74/20.32 (184) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (185) QDP 41.74/20.32 (186) QDPOrderProof [EQUIVALENT, 0 ms] 41.74/20.32 (187) QDP 41.74/20.32 (188) DependencyGraphProof [EQUIVALENT, 0 ms] 41.74/20.32 (189) QDP 41.74/20.32 (190) QDPSizeChangeProof [EQUIVALENT, 0 ms] 41.74/20.32 (191) YES 41.74/20.32 (192) QDP 41.74/20.32 (193) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (194) NO 41.74/20.32 (195) QDP 41.74/20.32 (196) NonTerminationLoopProof [COMPLETE, 0 ms] 41.74/20.32 (197) NO 41.74/20.32 (198) Narrow [COMPLETE, 0 ms] 41.74/20.32 (199) TRUE 41.74/20.32 41.74/20.32 41.74/20.32 ---------------------------------------- 41.74/20.32 41.74/20.32 (0) 41.74/20.32 Obligation: 41.74/20.32 mainModule Main 41.74/20.32 module Main where { 41.74/20.32 import qualified Prelude; 41.74/20.32 } 41.74/20.32 41.74/20.32 ---------------------------------------- 41.74/20.32 41.74/20.32 (1) IFR (EQUIVALENT) 41.74/20.32 If Reductions: 41.74/20.32 The following If expression 41.74/20.32 "if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero" 41.74/20.32 is transformed to 41.74/20.32 "primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y)); 41.74/20.32 primDivNatS0 x y False = Zero; 41.74/20.32 " 41.74/20.32 The following If expression 41.74/20.32 "if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x" 41.74/20.32 is transformed to 41.74/20.32 "primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y); 41.74/20.32 primModNatS0 x y False = Succ x; 41.74/20.32 " 41.74/20.32 The following If expression 41.74/20.32 "if primGEqNatS x y then primModNatP (primMinusNatS x y) (Succ y) else primMinusNatS y x" 41.74/20.32 is transformed to 41.74/20.32 "primModNatP0 x y True = primModNatP (primMinusNatS x y) (Succ y); 41.74/20.32 primModNatP0 x y False = primMinusNatS y x; 41.74/20.32 " 41.74/20.32 The following If expression 41.74/20.32 "if b then (showChar '(') . p . showChar ')' else p" 41.74/20.32 is transformed to 41.74/20.32 "showParen0 p True = (showChar '(') . p . showChar ')'; 41.74/20.32 showParen0 p False = p; 41.74/20.32 " 41.74/20.32 41.74/20.32 ---------------------------------------- 41.74/20.32 41.74/20.32 (2) 41.74/20.32 Obligation: 41.74/20.32 mainModule Main 41.74/20.32 module Main where { 41.74/20.32 import qualified Prelude; 41.74/20.32 } 41.74/20.32 41.74/20.32 ---------------------------------------- 41.74/20.32 41.74/20.32 (3) BR (EQUIVALENT) 41.74/20.32 Replaced joker patterns by fresh variables and removed binding patterns. 41.74/20.32 ---------------------------------------- 41.74/20.32 41.74/20.32 (4) 41.74/20.32 Obligation: 41.74/20.32 mainModule Main 41.74/20.32 module Main where { 41.74/20.32 import qualified Prelude; 41.74/20.32 } 41.74/20.32 41.74/20.32 ---------------------------------------- 41.74/20.32 41.74/20.32 (5) COR (EQUIVALENT) 41.74/20.32 Cond Reductions: 41.74/20.32 The following Function with conditions 41.74/20.32 "undefined |Falseundefined; 41.74/20.32 " 41.74/20.32 is transformed to 41.74/20.32 "undefined = undefined1; 41.74/20.32 " 41.74/20.32 "undefined0 True = undefined; 41.74/20.32 " 41.74/20.32 "undefined1 = undefined0 False; 41.74/20.32 " 41.74/20.32 41.74/20.32 ---------------------------------------- 41.74/20.32 41.74/20.32 (6) 41.74/20.32 Obligation: 41.74/20.32 mainModule Main 41.74/20.32 module Main where { 41.74/20.32 import qualified Prelude; 41.74/20.32 } 41.74/20.32 41.74/20.32 ---------------------------------------- 41.74/20.32 41.74/20.32 (7) NumRed (SOUND) 41.74/20.32 Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero. 41.74/20.32 ---------------------------------------- 41.74/20.32 41.74/20.32 (8) 41.74/20.32 Obligation: 41.74/20.32 mainModule Main 41.74/20.32 module Main where { 41.74/20.32 import qualified Prelude; 41.74/20.32 } 41.74/20.32 41.74/20.32 ---------------------------------------- 41.74/20.32 41.74/20.32 (9) Narrow (SOUND) 41.74/20.32 Haskell To QDPs 41.74/20.32 41.74/20.32 digraph dp_graph { 41.74/20.32 node [outthreshold=100, inthreshold=100];1[label="show",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 41.74/20.32 3[label="show ww3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 41.74/20.32 4[label="showsPrec (Pos Zero) ww3 []",fontsize=16,color="burlywood",shape="box"];2989[label="ww3/ww30 :% ww31",fontsize=10,color="white",style="solid",shape="box"];4 -> 2989[label="",style="solid", color="burlywood", weight=9]; 41.74/20.32 2989 -> 5[label="",style="solid", color="burlywood", weight=3]; 41.74/20.32 5[label="showsPrec (Pos Zero) (ww30 :% ww31) []",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 41.74/20.32 6 -> 1526[label="",style="dashed", color="red", weight=0]; 41.74/20.32 6[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww30) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww31) []",fontsize=16,color="magenta"];6 -> 1527[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 6 -> 1528[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 6 -> 1529[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 6 -> 1530[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 6 -> 1531[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 6 -> 1532[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1527[label="[]",fontsize=16,color="green",shape="box"];1528[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1529[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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"];1530[label="ww30",fontsize=16,color="green",shape="box"];1531[label="ww31",fontsize=16,color="green",shape="box"];1532[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"];1526[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) ww199",fontsize=16,color="black",shape="triangle"];1526 -> 1539[label="",style="solid", color="black", weight=3]; 41.74/20.32 1539[label="showParen0 ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww199",fontsize=16,color="black",shape="box"];1539 -> 1540[label="",style="solid", color="black", weight=3]; 41.74/20.32 1540[label="showParen0 ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww199",fontsize=16,color="black",shape="box"];1540 -> 1541[label="",style="solid", color="black", weight=3]; 41.74/20.32 1541[label="showParen0 ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww199",fontsize=16,color="black",shape="box"];1541 -> 1542[label="",style="solid", color="black", weight=3]; 41.74/20.32 1542[label="showParen0 ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww199",fontsize=16,color="black",shape="box"];1542 -> 1543[label="",style="solid", color="black", weight=3]; 41.74/20.32 1543[label="showParen0 ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) (LT == GT) ww199",fontsize=16,color="black",shape="box"];1543 -> 1544[label="",style="solid", color="black", weight=3]; 41.74/20.32 1544[label="showParen0 ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) False ww199",fontsize=16,color="black",shape="box"];1544 -> 1545[label="",style="solid", color="black", weight=3]; 41.74/20.32 1545[label="(shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="black",shape="box"];1545 -> 1546[label="",style="solid", color="black", weight=3]; 41.74/20.32 1546[label="shows ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1546 -> 1547[label="",style="solid", color="black", weight=3]; 41.74/20.32 1547[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="blue",shape="box"];2990[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2990[label="",style="solid", color="blue", weight=9]; 41.74/20.32 2990 -> 1548[label="",style="solid", color="blue", weight=3]; 41.74/20.32 2991[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2991[label="",style="solid", color="blue", weight=9]; 41.74/20.32 2991 -> 1549[label="",style="solid", color="blue", weight=3]; 41.74/20.32 2992[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2992[label="",style="solid", color="blue", weight=9]; 41.74/20.32 2992 -> 1550[label="",style="solid", color="blue", weight=3]; 41.74/20.32 2993[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2993[label="",style="solid", color="blue", weight=9]; 41.74/20.32 2993 -> 1551[label="",style="solid", color="blue", weight=3]; 41.74/20.32 2994[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2994[label="",style="solid", color="blue", weight=9]; 41.74/20.32 2994 -> 1552[label="",style="solid", color="blue", weight=3]; 41.74/20.32 2995[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2995[label="",style="solid", color="blue", weight=9]; 41.74/20.32 2995 -> 1553[label="",style="solid", color="blue", weight=3]; 41.74/20.32 2996[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2996[label="",style="solid", color="blue", weight=9]; 41.74/20.32 2996 -> 1554[label="",style="solid", color="blue", weight=3]; 41.74/20.32 2997[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2997[label="",style="solid", color="blue", weight=9]; 41.74/20.32 2997 -> 1555[label="",style="solid", color="blue", weight=3]; 41.74/20.32 2998[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2998[label="",style="solid", color="blue", weight=9]; 41.74/20.32 2998 -> 1556[label="",style="solid", color="blue", weight=3]; 41.74/20.32 2999[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2999[label="",style="solid", color="blue", weight=9]; 41.74/20.32 2999 -> 1557[label="",style="solid", color="blue", weight=3]; 41.74/20.32 3000[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3000[label="",style="solid", color="blue", weight=9]; 41.74/20.32 3000 -> 1558[label="",style="solid", color="blue", weight=3]; 41.74/20.32 3001[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3001[label="",style="solid", color="blue", weight=9]; 41.74/20.32 3001 -> 1559[label="",style="solid", color="blue", weight=3]; 41.74/20.32 3002[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3002[label="",style="solid", color="blue", weight=9]; 41.74/20.32 3002 -> 1560[label="",style="solid", color="blue", weight=3]; 41.74/20.32 3003[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3003[label="",style="solid", color="blue", weight=9]; 41.74/20.32 3003 -> 1561[label="",style="solid", color="blue", weight=3]; 41.74/20.32 3004[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3004[label="",style="solid", color="blue", weight=9]; 41.74/20.32 3004 -> 1562[label="",style="solid", color="blue", weight=3]; 41.74/20.32 3005[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3005[label="",style="solid", color="blue", weight=9]; 41.74/20.32 3005 -> 1563[label="",style="solid", color="blue", weight=3]; 41.74/20.32 3006[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3006[label="",style="solid", color="blue", weight=9]; 41.74/20.32 3006 -> 1564[label="",style="solid", color="blue", weight=3]; 41.74/20.32 3007[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3007[label="",style="solid", color="blue", weight=9]; 41.74/20.32 3007 -> 1565[label="",style="solid", color="blue", weight=3]; 41.74/20.32 1548[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1548 -> 1566[label="",style="solid", color="black", weight=3]; 41.74/20.32 1549[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1549 -> 1567[label="",style="solid", color="black", weight=3]; 41.74/20.32 1550[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1550 -> 1568[label="",style="solid", color="black", weight=3]; 41.74/20.32 1551[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1551 -> 1569[label="",style="solid", color="black", weight=3]; 41.74/20.32 1552[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1552 -> 1570[label="",style="solid", color="black", weight=3]; 41.74/20.32 1553[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1553 -> 1571[label="",style="solid", color="black", weight=3]; 41.74/20.32 1554[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1554 -> 1572[label="",style="solid", color="black", weight=3]; 41.74/20.32 1555[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="burlywood",shape="box"];3008[label="ww194/ww1940 :% ww1941",fontsize=10,color="white",style="solid",shape="box"];1555 -> 3008[label="",style="solid", color="burlywood", weight=9]; 41.74/20.32 3008 -> 1573[label="",style="solid", color="burlywood", weight=3]; 41.74/20.32 1556[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1556 -> 1574[label="",style="solid", color="black", weight=3]; 41.74/20.32 1557[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1557 -> 1575[label="",style="solid", color="black", weight=3]; 41.74/20.32 1558[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1558 -> 1576[label="",style="solid", color="black", weight=3]; 41.74/20.32 1559[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1559 -> 1577[label="",style="solid", color="black", weight=3]; 41.74/20.32 1560[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1560 -> 1578[label="",style="solid", color="black", weight=3]; 41.74/20.32 1561[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1561 -> 1579[label="",style="solid", color="black", weight=3]; 41.74/20.32 1562[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1562 -> 1580[label="",style="solid", color="black", weight=3]; 41.74/20.32 1563[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1563 -> 1581[label="",style="solid", color="black", weight=3]; 41.74/20.32 1564[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1564 -> 1582[label="",style="solid", color="black", weight=3]; 41.74/20.32 1565[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1565 -> 1583[label="",style="solid", color="black", weight=3]; 41.74/20.32 1566 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1566[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1566 -> 1736[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1566 -> 1737[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1567 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1567[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1567 -> 1738[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1567 -> 1739[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1568 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1568[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1568 -> 1740[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1568 -> 1741[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1569 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1569[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1569 -> 1742[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1569 -> 1743[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1570 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1570[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1570 -> 1744[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1570 -> 1745[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1571 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1571[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1571 -> 1746[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1571 -> 1747[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1572 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1572[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1572 -> 1748[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1572 -> 1749[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1573[label="showsPrec (Pos Zero) (ww1940 :% ww1941) ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1573 -> 1591[label="",style="solid", color="black", weight=3]; 41.74/20.32 1574 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1574[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1574 -> 1750[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1574 -> 1751[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1575 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1575[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1575 -> 1752[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1575 -> 1753[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1576 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1576[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1576 -> 1754[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1576 -> 1755[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1577 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1577[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1577 -> 1756[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1577 -> 1757[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1578 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1578[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1578 -> 1758[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1578 -> 1759[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1579 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1579[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1579 -> 1760[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1579 -> 1761[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1580 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1580[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1580 -> 1762[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1580 -> 1763[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1581 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1581[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1581 -> 1764[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1581 -> 1765[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1582 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1582[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1582 -> 1766[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1582 -> 1767[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1583 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1583[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1583 -> 1768[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1583 -> 1769[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1736[label="show ww194",fontsize=16,color="black",shape="triangle"];1736 -> 1959[label="",style="solid", color="black", weight=3]; 41.74/20.32 1737 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1737[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1735[label="ww240 ++ ww200",fontsize=16,color="burlywood",shape="triangle"];3009[label="ww240/ww2400 : ww2401",fontsize=10,color="white",style="solid",shape="box"];1735 -> 3009[label="",style="solid", color="burlywood", weight=9]; 41.74/20.32 3009 -> 1960[label="",style="solid", color="burlywood", weight=3]; 41.74/20.32 3010[label="ww240/[]",fontsize=10,color="white",style="solid",shape="box"];1735 -> 3010[label="",style="solid", color="burlywood", weight=9]; 41.74/20.32 3010 -> 1961[label="",style="solid", color="burlywood", weight=3]; 41.74/20.32 1738[label="show ww194",fontsize=16,color="black",shape="triangle"];1738 -> 1962[label="",style="solid", color="black", weight=3]; 41.74/20.32 1739 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1739[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1740[label="show ww194",fontsize=16,color="black",shape="triangle"];1740 -> 1963[label="",style="solid", color="black", weight=3]; 41.74/20.32 1741 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1741[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1742[label="show ww194",fontsize=16,color="black",shape="triangle"];1742 -> 1964[label="",style="solid", color="black", weight=3]; 41.74/20.32 1743 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1743[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1744[label="show ww194",fontsize=16,color="black",shape="triangle"];1744 -> 1965[label="",style="solid", color="black", weight=3]; 41.74/20.32 1745 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1745[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1746[label="show ww194",fontsize=16,color="black",shape="triangle"];1746 -> 1966[label="",style="solid", color="black", weight=3]; 41.74/20.32 1747 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1747[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1748[label="show ww194",fontsize=16,color="black",shape="triangle"];1748 -> 1967[label="",style="solid", color="black", weight=3]; 41.74/20.32 1749 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1749[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1591 -> 1526[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1591[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1940) . (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 ww1941) ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="magenta"];1591 -> 1609[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1591 -> 1610[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1591 -> 1611[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1591 -> 1612[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1591 -> 1613[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1591 -> 1614[label="",style="dashed", color="magenta", weight=3]; 41.74/20.32 1750[label="show ww194",fontsize=16,color="black",shape="triangle"];1750 -> 1968[label="",style="solid", color="black", weight=3]; 41.74/20.32 1751 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1751[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1752[label="show ww194",fontsize=16,color="black",shape="triangle"];1752 -> 1969[label="",style="solid", color="black", weight=3]; 41.74/20.32 1753 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1753[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1754[label="show ww194",fontsize=16,color="black",shape="triangle"];1754 -> 1970[label="",style="solid", color="black", weight=3]; 41.74/20.32 1755 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.32 1755[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1756[label="show ww194",fontsize=16,color="black",shape="triangle"];1756 -> 1971[label="",style="solid", color="black", weight=3]; 41.74/20.33 1757 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1757[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1758[label="show ww194",fontsize=16,color="black",shape="triangle"];1758 -> 1972[label="",style="solid", color="black", weight=3]; 41.74/20.33 1759 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1759[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1760[label="show ww194",fontsize=16,color="black",shape="triangle"];1760 -> 1973[label="",style="solid", color="black", weight=3]; 41.74/20.33 1761 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1761[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1762[label="show ww194",fontsize=16,color="black",shape="triangle"];1762 -> 1974[label="",style="solid", color="black", weight=3]; 41.74/20.33 1763 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1763[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1764[label="show ww194",fontsize=16,color="black",shape="triangle"];1764 -> 1975[label="",style="solid", color="black", weight=3]; 41.74/20.33 1765 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1765[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1766[label="show ww194",fontsize=16,color="black",shape="triangle"];1766 -> 1976[label="",style="solid", color="black", weight=3]; 41.74/20.33 1767 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1767[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1768[label="show ww194",fontsize=16,color="black",shape="triangle"];1768 -> 1977[label="",style="solid", color="black", weight=3]; 41.74/20.33 1769 -> 1609[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1769[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1959[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1959 -> 1979[label="",style="solid", color="black", weight=3]; 41.74/20.33 1609[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="black",shape="triangle"];1609 -> 1633[label="",style="solid", color="black", weight=3]; 41.74/20.33 1960[label="(ww2400 : ww2401) ++ ww200",fontsize=16,color="black",shape="box"];1960 -> 1980[label="",style="solid", color="black", weight=3]; 41.74/20.33 1961[label="[] ++ ww200",fontsize=16,color="black",shape="box"];1961 -> 1981[label="",style="solid", color="black", weight=3]; 41.74/20.33 1962[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1962 -> 1982[label="",style="solid", color="black", weight=3]; 41.74/20.33 1963[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1963 -> 1983[label="",style="solid", color="black", weight=3]; 41.74/20.33 1964[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1964 -> 1984[label="",style="solid", color="black", weight=3]; 41.74/20.33 1965[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1965 -> 1985[label="",style="solid", color="black", weight=3]; 41.74/20.33 1966[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1966 -> 1986[label="",style="solid", color="black", weight=3]; 41.74/20.33 1967[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1967 -> 1987[label="",style="solid", color="black", weight=3]; 41.74/20.33 1610[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"];1611[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"];1612[label="ww1940",fontsize=16,color="green",shape="box"];1613[label="ww1941",fontsize=16,color="green",shape="box"];1614[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"];1968[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1968 -> 1988[label="",style="solid", color="black", weight=3]; 41.74/20.33 1969[label="primShowInt ww194",fontsize=16,color="burlywood",shape="triangle"];3011[label="ww194/Pos ww1940",fontsize=10,color="white",style="solid",shape="box"];1969 -> 3011[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3011 -> 1989[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3012[label="ww194/Neg ww1940",fontsize=10,color="white",style="solid",shape="box"];1969 -> 3012[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3012 -> 1990[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 1970[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1970 -> 1991[label="",style="solid", color="black", weight=3]; 41.74/20.33 1971[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1971 -> 1992[label="",style="solid", color="black", weight=3]; 41.74/20.33 1972[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1972 -> 1993[label="",style="solid", color="black", weight=3]; 41.74/20.33 1973[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1973 -> 1994[label="",style="solid", color="black", weight=3]; 41.74/20.33 1974[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1974 -> 1995[label="",style="solid", color="black", weight=3]; 41.74/20.33 1975[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1975 -> 1996[label="",style="solid", color="black", weight=3]; 41.74/20.33 1976[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1976 -> 1997[label="",style="solid", color="black", weight=3]; 41.74/20.33 1977[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1977 -> 1998[label="",style="solid", color="black", weight=3]; 41.74/20.33 1979 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1979[label="show ww194 ++ []",fontsize=16,color="magenta"];1979 -> 2017[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1979 -> 2018[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1633[label="showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : []) (shows ww198 ww199)",fontsize=16,color="black",shape="box"];1633 -> 1669[label="",style="solid", color="black", weight=3]; 41.74/20.33 1980[label="ww2400 : ww2401 ++ ww200",fontsize=16,color="green",shape="box"];1980 -> 2019[label="",style="dashed", color="green", weight=3]; 41.74/20.33 1981[label="ww200",fontsize=16,color="green",shape="box"];1982 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1982[label="show ww194 ++ []",fontsize=16,color="magenta"];1982 -> 2020[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1982 -> 2021[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1983 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1983[label="show ww194 ++ []",fontsize=16,color="magenta"];1983 -> 2022[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1983 -> 2023[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1984 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1984[label="show ww194 ++ []",fontsize=16,color="magenta"];1984 -> 2024[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1984 -> 2025[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1985 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1985[label="show ww194 ++ []",fontsize=16,color="magenta"];1985 -> 2026[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1985 -> 2027[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1986 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1986[label="show ww194 ++ []",fontsize=16,color="magenta"];1986 -> 2028[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1986 -> 2029[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1987 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1987[label="show ww194 ++ []",fontsize=16,color="magenta"];1987 -> 2030[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1987 -> 2031[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1988 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1988[label="show ww194 ++ []",fontsize=16,color="magenta"];1988 -> 2032[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1988 -> 2033[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1989[label="primShowInt (Pos ww1940)",fontsize=16,color="burlywood",shape="box"];3013[label="ww1940/Succ ww19400",fontsize=10,color="white",style="solid",shape="box"];1989 -> 3013[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3013 -> 2034[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3014[label="ww1940/Zero",fontsize=10,color="white",style="solid",shape="box"];1989 -> 3014[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3014 -> 2035[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 1990[label="primShowInt (Neg ww1940)",fontsize=16,color="black",shape="box"];1990 -> 2036[label="",style="solid", color="black", weight=3]; 41.74/20.33 1991 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1991[label="show ww194 ++ []",fontsize=16,color="magenta"];1991 -> 2037[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1991 -> 2038[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1992 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1992[label="show ww194 ++ []",fontsize=16,color="magenta"];1992 -> 2039[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1992 -> 2040[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1993 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1993[label="show ww194 ++ []",fontsize=16,color="magenta"];1993 -> 2041[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1993 -> 2042[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1994 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1994[label="show ww194 ++ []",fontsize=16,color="magenta"];1994 -> 2043[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1994 -> 2044[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1995 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1995[label="show ww194 ++ []",fontsize=16,color="magenta"];1995 -> 2045[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1995 -> 2046[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1996 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1996[label="show ww194 ++ []",fontsize=16,color="magenta"];1996 -> 2047[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1996 -> 2048[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1997 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1997[label="show ww194 ++ []",fontsize=16,color="magenta"];1997 -> 2049[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1997 -> 2050[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1998 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1998[label="show ww194 ++ []",fontsize=16,color="magenta"];1998 -> 2051[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1998 -> 2052[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2017 -> 1736[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2017[label="show ww194",fontsize=16,color="magenta"];2018[label="[]",fontsize=16,color="green",shape="box"];1669 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 1669[label="(++) (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : []) shows ww198 ww199",fontsize=16,color="magenta"];1669 -> 1883[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1669 -> 1884[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2019 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2019[label="ww2401 ++ ww200",fontsize=16,color="magenta"];2019 -> 2071[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2020 -> 1738[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2020[label="show ww194",fontsize=16,color="magenta"];2021[label="[]",fontsize=16,color="green",shape="box"];2022 -> 1740[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2022[label="show ww194",fontsize=16,color="magenta"];2023[label="[]",fontsize=16,color="green",shape="box"];2024 -> 1742[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2024[label="show ww194",fontsize=16,color="magenta"];2025[label="[]",fontsize=16,color="green",shape="box"];2026 -> 1744[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2026[label="show ww194",fontsize=16,color="magenta"];2027[label="[]",fontsize=16,color="green",shape="box"];2028 -> 1746[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2028[label="show ww194",fontsize=16,color="magenta"];2029[label="[]",fontsize=16,color="green",shape="box"];2030 -> 1748[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2030[label="show ww194",fontsize=16,color="magenta"];2031[label="[]",fontsize=16,color="green",shape="box"];2032 -> 1750[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2032[label="show ww194",fontsize=16,color="magenta"];2033[label="[]",fontsize=16,color="green",shape="box"];2034[label="primShowInt (Pos (Succ ww19400))",fontsize=16,color="black",shape="box"];2034 -> 2072[label="",style="solid", color="black", weight=3]; 41.74/20.33 2035[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];2035 -> 2073[label="",style="solid", color="black", weight=3]; 41.74/20.33 2036[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 ww1940)",fontsize=16,color="green",shape="box"];2036 -> 2074[label="",style="dashed", color="green", weight=3]; 41.74/20.33 2037 -> 1754[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2037[label="show ww194",fontsize=16,color="magenta"];2038[label="[]",fontsize=16,color="green",shape="box"];2039 -> 1756[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2039[label="show ww194",fontsize=16,color="magenta"];2040[label="[]",fontsize=16,color="green",shape="box"];2041 -> 1758[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2041[label="show ww194",fontsize=16,color="magenta"];2042[label="[]",fontsize=16,color="green",shape="box"];2043 -> 1760[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2043[label="show ww194",fontsize=16,color="magenta"];2044[label="[]",fontsize=16,color="green",shape="box"];2045 -> 1762[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2045[label="show ww194",fontsize=16,color="magenta"];2046[label="[]",fontsize=16,color="green",shape="box"];2047 -> 1764[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2047[label="show ww194",fontsize=16,color="magenta"];2048[label="[]",fontsize=16,color="green",shape="box"];2049 -> 1766[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2049[label="show ww194",fontsize=16,color="magenta"];2050[label="[]",fontsize=16,color="green",shape="box"];2051 -> 1768[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2051[label="show ww194",fontsize=16,color="magenta"];2052[label="[]",fontsize=16,color="green",shape="box"];1883[label="Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : []",fontsize=16,color="green",shape="box"];1884[label="shows ww198 ww199",fontsize=16,color="black",shape="box"];1884 -> 1978[label="",style="solid", color="black", weight=3]; 41.74/20.33 2071[label="ww2401",fontsize=16,color="green",shape="box"];2072 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2072[label="primShowInt (div Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];2072 -> 2110[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2072 -> 2111[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2073[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"];2074 -> 1969[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2074[label="primShowInt (Pos ww1940)",fontsize=16,color="magenta"];2074 -> 2112[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 1978[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="blue",shape="box"];3015[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3015[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3015 -> 1999[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3016[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3016[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3016 -> 2000[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3017[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3017[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3017 -> 2001[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3018[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3018[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3018 -> 2002[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3019[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3019[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3019 -> 2003[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3020[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3020[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3020 -> 2004[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3021[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3021[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3021 -> 2005[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3022[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3022[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3022 -> 2006[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3023[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3023[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3023 -> 2007[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3024[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3024[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3024 -> 2008[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3025[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3025[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3025 -> 2009[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3026[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3026[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3026 -> 2010[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3027[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3027[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3027 -> 2011[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3028[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3028[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3028 -> 2012[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3029[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3029[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3029 -> 2013[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3030[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3030[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3030 -> 2014[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3031[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3031[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3031 -> 2015[label="",style="solid", color="blue", weight=3]; 41.74/20.33 3032[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3032[label="",style="solid", color="blue", weight=9]; 41.74/20.33 3032 -> 2016[label="",style="solid", color="blue", weight=3]; 41.74/20.33 2110 -> 1969[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2110[label="primShowInt (div Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];2110 -> 2135[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2111[label="toEnum (mod Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];2111 -> 2136[label="",style="dashed", color="green", weight=3]; 41.74/20.33 2112[label="Pos ww1940",fontsize=16,color="green",shape="box"];1999[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];1999 -> 2053[label="",style="solid", color="black", weight=3]; 41.74/20.33 2000[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2000 -> 2054[label="",style="solid", color="black", weight=3]; 41.74/20.33 2001[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2001 -> 2055[label="",style="solid", color="black", weight=3]; 41.74/20.33 2002[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2002 -> 2056[label="",style="solid", color="black", weight=3]; 41.74/20.33 2003[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2003 -> 2057[label="",style="solid", color="black", weight=3]; 41.74/20.33 2004[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2004 -> 2058[label="",style="solid", color="black", weight=3]; 41.74/20.33 2005[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2005 -> 2059[label="",style="solid", color="black", weight=3]; 41.74/20.33 2006[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="burlywood",shape="box"];3033[label="ww198/ww1980 :% ww1981",fontsize=10,color="white",style="solid",shape="box"];2006 -> 3033[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3033 -> 2060[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2007[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2007 -> 2061[label="",style="solid", color="black", weight=3]; 41.74/20.33 2008[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2008 -> 2062[label="",style="solid", color="black", weight=3]; 41.74/20.33 2009[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2009 -> 2063[label="",style="solid", color="black", weight=3]; 41.74/20.33 2010[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2010 -> 2064[label="",style="solid", color="black", weight=3]; 41.74/20.33 2011[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2011 -> 2065[label="",style="solid", color="black", weight=3]; 41.74/20.33 2012[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2012 -> 2066[label="",style="solid", color="black", weight=3]; 41.74/20.33 2013[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2013 -> 2067[label="",style="solid", color="black", weight=3]; 41.74/20.33 2014[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2014 -> 2068[label="",style="solid", color="black", weight=3]; 41.74/20.33 2015[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2015 -> 2069[label="",style="solid", color="black", weight=3]; 41.74/20.33 2016[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2016 -> 2070[label="",style="solid", color="black", weight=3]; 41.74/20.33 2135 -> 2137[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2135[label="div Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];2135 -> 2138[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2135 -> 2139[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2136[label="toEnum (mod Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];2136 -> 2154[label="",style="solid", color="black", weight=3]; 41.74/20.33 2053 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2053[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2053 -> 2075[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2053 -> 2076[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2054 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2054[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2054 -> 2077[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2054 -> 2078[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2055 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2055[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2055 -> 2079[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2055 -> 2080[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2056 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2056[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2056 -> 2081[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2056 -> 2082[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2057 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2057[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2057 -> 2083[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2057 -> 2084[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2058 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2058[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2058 -> 2085[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2058 -> 2086[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2059 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2059[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2059 -> 2087[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2059 -> 2088[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2060[label="showsPrec (Pos Zero) (ww1980 :% ww1981) ww199",fontsize=16,color="black",shape="box"];2060 -> 2089[label="",style="solid", color="black", weight=3]; 41.74/20.33 2061 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2061[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2061 -> 2090[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2061 -> 2091[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2062 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2062[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2062 -> 2092[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2062 -> 2093[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2063 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2063[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2063 -> 2094[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2063 -> 2095[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2064 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2064[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2064 -> 2096[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2064 -> 2097[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2065 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2065[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2065 -> 2098[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2065 -> 2099[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2066 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2066[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2066 -> 2100[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2066 -> 2101[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2067 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2067[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2067 -> 2102[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2067 -> 2103[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2068 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2068[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2068 -> 2104[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2068 -> 2105[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2069 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2069[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2069 -> 2106[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2069 -> 2107[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2070 -> 1735[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2070[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2070 -> 2108[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2070 -> 2109[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2138[label="ww19400",fontsize=16,color="green",shape="box"];2139[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];2137[label="div Pos (Succ ww242) Pos (Succ ww243)",fontsize=16,color="black",shape="triangle"];2137 -> 2143[label="",style="solid", color="black", weight=3]; 41.74/20.33 2154 -> 2165[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2154[label="primIntToChar (mod Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];2154 -> 2166[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2154 -> 2167[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2075 -> 1736[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2075[label="show ww198",fontsize=16,color="magenta"];2075 -> 2113[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2076[label="ww199",fontsize=16,color="green",shape="box"];2077 -> 1738[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2077[label="show ww198",fontsize=16,color="magenta"];2077 -> 2114[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2078[label="ww199",fontsize=16,color="green",shape="box"];2079 -> 1740[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2079[label="show ww198",fontsize=16,color="magenta"];2079 -> 2115[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2080[label="ww199",fontsize=16,color="green",shape="box"];2081 -> 1742[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2081[label="show ww198",fontsize=16,color="magenta"];2081 -> 2116[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2082[label="ww199",fontsize=16,color="green",shape="box"];2083 -> 1744[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2083[label="show ww198",fontsize=16,color="magenta"];2083 -> 2117[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2084[label="ww199",fontsize=16,color="green",shape="box"];2085 -> 1746[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2085[label="show ww198",fontsize=16,color="magenta"];2085 -> 2118[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2086[label="ww199",fontsize=16,color="green",shape="box"];2087 -> 1748[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2087[label="show ww198",fontsize=16,color="magenta"];2087 -> 2119[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2088[label="ww199",fontsize=16,color="green",shape="box"];2089 -> 1526[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2089[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1980) . (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 ww1981) ww199",fontsize=16,color="magenta"];2089 -> 2120[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2089 -> 2121[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2089 -> 2122[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2089 -> 2123[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2089 -> 2124[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2090 -> 1750[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2090[label="show ww198",fontsize=16,color="magenta"];2090 -> 2125[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2091[label="ww199",fontsize=16,color="green",shape="box"];2092 -> 1752[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2092[label="show ww198",fontsize=16,color="magenta"];2092 -> 2126[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2093[label="ww199",fontsize=16,color="green",shape="box"];2094 -> 1754[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2094[label="show ww198",fontsize=16,color="magenta"];2094 -> 2127[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2095[label="ww199",fontsize=16,color="green",shape="box"];2096 -> 1756[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2096[label="show ww198",fontsize=16,color="magenta"];2096 -> 2128[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2097[label="ww199",fontsize=16,color="green",shape="box"];2098 -> 1758[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2098[label="show ww198",fontsize=16,color="magenta"];2098 -> 2129[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2099[label="ww199",fontsize=16,color="green",shape="box"];2100 -> 1760[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2100[label="show ww198",fontsize=16,color="magenta"];2100 -> 2130[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2101[label="ww199",fontsize=16,color="green",shape="box"];2102 -> 1762[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2102[label="show ww198",fontsize=16,color="magenta"];2102 -> 2131[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2103[label="ww199",fontsize=16,color="green",shape="box"];2104 -> 1764[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2104[label="show ww198",fontsize=16,color="magenta"];2104 -> 2132[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2105[label="ww199",fontsize=16,color="green",shape="box"];2106 -> 1766[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2106[label="show ww198",fontsize=16,color="magenta"];2106 -> 2133[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2107[label="ww199",fontsize=16,color="green",shape="box"];2108 -> 1768[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2108[label="show ww198",fontsize=16,color="magenta"];2108 -> 2134[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2109[label="ww199",fontsize=16,color="green",shape="box"];2143[label="primDivInt (Pos (Succ ww242)) (Pos (Succ ww243))",fontsize=16,color="black",shape="box"];2143 -> 2153[label="",style="solid", color="black", weight=3]; 41.74/20.33 2166[label="ww19400",fontsize=16,color="green",shape="box"];2167[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];2165[label="primIntToChar (mod Pos (Succ ww248) Pos (Succ ww249))",fontsize=16,color="black",shape="triangle"];2165 -> 2168[label="",style="solid", color="black", weight=3]; 41.74/20.33 2113[label="ww198",fontsize=16,color="green",shape="box"];2114[label="ww198",fontsize=16,color="green",shape="box"];2115[label="ww198",fontsize=16,color="green",shape="box"];2116[label="ww198",fontsize=16,color="green",shape="box"];2117[label="ww198",fontsize=16,color="green",shape="box"];2118[label="ww198",fontsize=16,color="green",shape="box"];2119[label="ww198",fontsize=16,color="green",shape="box"];2120[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"];2121[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"];2122[label="ww1980",fontsize=16,color="green",shape="box"];2123[label="ww1981",fontsize=16,color="green",shape="box"];2124[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"];2125[label="ww198",fontsize=16,color="green",shape="box"];2126[label="ww198",fontsize=16,color="green",shape="box"];2127[label="ww198",fontsize=16,color="green",shape="box"];2128[label="ww198",fontsize=16,color="green",shape="box"];2129[label="ww198",fontsize=16,color="green",shape="box"];2130[label="ww198",fontsize=16,color="green",shape="box"];2131[label="ww198",fontsize=16,color="green",shape="box"];2132[label="ww198",fontsize=16,color="green",shape="box"];2133[label="ww198",fontsize=16,color="green",shape="box"];2134[label="ww198",fontsize=16,color="green",shape="box"];2153[label="Pos (primDivNatS (Succ ww242) (Succ ww243))",fontsize=16,color="green",shape="box"];2153 -> 2164[label="",style="dashed", color="green", weight=3]; 41.74/20.33 2168[label="primIntToChar (primModInt (Pos (Succ ww248)) (Pos (Succ ww249)))",fontsize=16,color="black",shape="box"];2168 -> 2170[label="",style="solid", color="black", weight=3]; 41.74/20.33 2164[label="primDivNatS (Succ ww242) (Succ ww243)",fontsize=16,color="black",shape="triangle"];2164 -> 2169[label="",style="solid", color="black", weight=3]; 41.74/20.33 2170[label="primIntToChar (Pos (primModNatS (Succ ww248) (Succ ww249)))",fontsize=16,color="black",shape="box"];2170 -> 2173[label="",style="solid", color="black", weight=3]; 41.74/20.33 2169[label="primDivNatS0 ww242 ww243 (primGEqNatS ww242 ww243)",fontsize=16,color="burlywood",shape="box"];3034[label="ww242/Succ ww2420",fontsize=10,color="white",style="solid",shape="box"];2169 -> 3034[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3034 -> 2171[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3035[label="ww242/Zero",fontsize=10,color="white",style="solid",shape="box"];2169 -> 3035[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3035 -> 2172[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2173[label="Char (primModNatS (Succ ww248) (Succ ww249))",fontsize=16,color="green",shape="box"];2173 -> 2178[label="",style="dashed", color="green", weight=3]; 41.74/20.33 2171[label="primDivNatS0 (Succ ww2420) ww243 (primGEqNatS (Succ ww2420) ww243)",fontsize=16,color="burlywood",shape="box"];3036[label="ww243/Succ ww2430",fontsize=10,color="white",style="solid",shape="box"];2171 -> 3036[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3036 -> 2174[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3037[label="ww243/Zero",fontsize=10,color="white",style="solid",shape="box"];2171 -> 3037[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3037 -> 2175[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2172[label="primDivNatS0 Zero ww243 (primGEqNatS Zero ww243)",fontsize=16,color="burlywood",shape="box"];3038[label="ww243/Succ ww2430",fontsize=10,color="white",style="solid",shape="box"];2172 -> 3038[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3038 -> 2176[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3039[label="ww243/Zero",fontsize=10,color="white",style="solid",shape="box"];2172 -> 3039[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3039 -> 2177[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2178[label="primModNatS (Succ ww248) (Succ ww249)",fontsize=16,color="black",shape="triangle"];2178 -> 2183[label="",style="solid", color="black", weight=3]; 41.74/20.33 2174[label="primDivNatS0 (Succ ww2420) (Succ ww2430) (primGEqNatS (Succ ww2420) (Succ ww2430))",fontsize=16,color="black",shape="box"];2174 -> 2179[label="",style="solid", color="black", weight=3]; 41.74/20.33 2175[label="primDivNatS0 (Succ ww2420) Zero (primGEqNatS (Succ ww2420) Zero)",fontsize=16,color="black",shape="box"];2175 -> 2180[label="",style="solid", color="black", weight=3]; 41.74/20.33 2176[label="primDivNatS0 Zero (Succ ww2430) (primGEqNatS Zero (Succ ww2430))",fontsize=16,color="black",shape="box"];2176 -> 2181[label="",style="solid", color="black", weight=3]; 41.74/20.33 2177[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2177 -> 2182[label="",style="solid", color="black", weight=3]; 41.74/20.33 2183[label="primModNatS0 ww248 ww249 (primGEqNatS ww248 ww249)",fontsize=16,color="burlywood",shape="box"];3040[label="ww248/Succ ww2480",fontsize=10,color="white",style="solid",shape="box"];2183 -> 3040[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3040 -> 2189[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3041[label="ww248/Zero",fontsize=10,color="white",style="solid",shape="box"];2183 -> 3041[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3041 -> 2190[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2179 -> 2695[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2179[label="primDivNatS0 (Succ ww2420) (Succ ww2430) (primGEqNatS ww2420 ww2430)",fontsize=16,color="magenta"];2179 -> 2696[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2179 -> 2697[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2179 -> 2698[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2179 -> 2699[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2180[label="primDivNatS0 (Succ ww2420) Zero True",fontsize=16,color="black",shape="box"];2180 -> 2186[label="",style="solid", color="black", weight=3]; 41.74/20.33 2181[label="primDivNatS0 Zero (Succ ww2430) False",fontsize=16,color="black",shape="box"];2181 -> 2187[label="",style="solid", color="black", weight=3]; 41.74/20.33 2182[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2182 -> 2188[label="",style="solid", color="black", weight=3]; 41.74/20.33 2189[label="primModNatS0 (Succ ww2480) ww249 (primGEqNatS (Succ ww2480) ww249)",fontsize=16,color="burlywood",shape="box"];3042[label="ww249/Succ ww2490",fontsize=10,color="white",style="solid",shape="box"];2189 -> 3042[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3042 -> 2197[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3043[label="ww249/Zero",fontsize=10,color="white",style="solid",shape="box"];2189 -> 3043[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3043 -> 2198[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2190[label="primModNatS0 Zero ww249 (primGEqNatS Zero ww249)",fontsize=16,color="burlywood",shape="box"];3044[label="ww249/Succ ww2490",fontsize=10,color="white",style="solid",shape="box"];2190 -> 3044[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3044 -> 2199[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3045[label="ww249/Zero",fontsize=10,color="white",style="solid",shape="box"];2190 -> 3045[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3045 -> 2200[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2696[label="ww2420",fontsize=16,color="green",shape="box"];2697[label="ww2430",fontsize=16,color="green",shape="box"];2698[label="ww2420",fontsize=16,color="green",shape="box"];2699[label="ww2430",fontsize=16,color="green",shape="box"];2695[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS ww294 ww295)",fontsize=16,color="burlywood",shape="triangle"];3046[label="ww294/Succ ww2940",fontsize=10,color="white",style="solid",shape="box"];2695 -> 3046[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3046 -> 2736[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3047[label="ww294/Zero",fontsize=10,color="white",style="solid",shape="box"];2695 -> 3047[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3047 -> 2737[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2186[label="Succ (primDivNatS (primMinusNatS (Succ ww2420) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2186 -> 2195[label="",style="dashed", color="green", weight=3]; 41.74/20.33 2187[label="Zero",fontsize=16,color="green",shape="box"];2188[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2188 -> 2196[label="",style="dashed", color="green", weight=3]; 41.74/20.33 2197[label="primModNatS0 (Succ ww2480) (Succ ww2490) (primGEqNatS (Succ ww2480) (Succ ww2490))",fontsize=16,color="black",shape="box"];2197 -> 2207[label="",style="solid", color="black", weight=3]; 41.74/20.33 2198[label="primModNatS0 (Succ ww2480) Zero (primGEqNatS (Succ ww2480) Zero)",fontsize=16,color="black",shape="box"];2198 -> 2208[label="",style="solid", color="black", weight=3]; 41.74/20.33 2199[label="primModNatS0 Zero (Succ ww2490) (primGEqNatS Zero (Succ ww2490))",fontsize=16,color="black",shape="box"];2199 -> 2209[label="",style="solid", color="black", weight=3]; 41.74/20.33 2200[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2200 -> 2210[label="",style="solid", color="black", weight=3]; 41.74/20.33 2736[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS (Succ ww2940) ww295)",fontsize=16,color="burlywood",shape="box"];3048[label="ww295/Succ ww2950",fontsize=10,color="white",style="solid",shape="box"];2736 -> 3048[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3048 -> 2748[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3049[label="ww295/Zero",fontsize=10,color="white",style="solid",shape="box"];2736 -> 3049[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3049 -> 2749[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2737[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS Zero ww295)",fontsize=16,color="burlywood",shape="box"];3050[label="ww295/Succ ww2950",fontsize=10,color="white",style="solid",shape="box"];2737 -> 3050[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3050 -> 2750[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3051[label="ww295/Zero",fontsize=10,color="white",style="solid",shape="box"];2737 -> 3051[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3051 -> 2751[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2195 -> 2949[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2195[label="primDivNatS (primMinusNatS (Succ ww2420) Zero) (Succ Zero)",fontsize=16,color="magenta"];2195 -> 2950[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2195 -> 2951[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2195 -> 2952[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2196 -> 2949[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2196[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2196 -> 2953[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2196 -> 2954[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2196 -> 2955[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2207 -> 2770[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2207[label="primModNatS0 (Succ ww2480) (Succ ww2490) (primGEqNatS ww2480 ww2490)",fontsize=16,color="magenta"];2207 -> 2771[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2207 -> 2772[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2207 -> 2773[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2207 -> 2774[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2208[label="primModNatS0 (Succ ww2480) Zero True",fontsize=16,color="black",shape="box"];2208 -> 2221[label="",style="solid", color="black", weight=3]; 41.74/20.33 2209[label="primModNatS0 Zero (Succ ww2490) False",fontsize=16,color="black",shape="box"];2209 -> 2222[label="",style="solid", color="black", weight=3]; 41.74/20.33 2210[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2210 -> 2223[label="",style="solid", color="black", weight=3]; 41.74/20.33 2748[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS (Succ ww2940) (Succ ww2950))",fontsize=16,color="black",shape="box"];2748 -> 2762[label="",style="solid", color="black", weight=3]; 41.74/20.33 2749[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS (Succ ww2940) Zero)",fontsize=16,color="black",shape="box"];2749 -> 2763[label="",style="solid", color="black", weight=3]; 41.74/20.33 2750[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS Zero (Succ ww2950))",fontsize=16,color="black",shape="box"];2750 -> 2764[label="",style="solid", color="black", weight=3]; 41.74/20.33 2751[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2751 -> 2765[label="",style="solid", color="black", weight=3]; 41.74/20.33 2950[label="Succ ww2420",fontsize=16,color="green",shape="box"];2951[label="Zero",fontsize=16,color="green",shape="box"];2952[label="Zero",fontsize=16,color="green",shape="box"];2949[label="primDivNatS (primMinusNatS ww306 ww307) (Succ ww308)",fontsize=16,color="burlywood",shape="triangle"];3052[label="ww306/Succ ww3060",fontsize=10,color="white",style="solid",shape="box"];2949 -> 3052[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3052 -> 2974[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3053[label="ww306/Zero",fontsize=10,color="white",style="solid",shape="box"];2949 -> 3053[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3053 -> 2975[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2953[label="Zero",fontsize=16,color="green",shape="box"];2954[label="Zero",fontsize=16,color="green",shape="box"];2955[label="Zero",fontsize=16,color="green",shape="box"];2771[label="ww2480",fontsize=16,color="green",shape="box"];2772[label="ww2490",fontsize=16,color="green",shape="box"];2773[label="ww2490",fontsize=16,color="green",shape="box"];2774[label="ww2480",fontsize=16,color="green",shape="box"];2770[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS ww299 ww300)",fontsize=16,color="burlywood",shape="triangle"];3054[label="ww299/Succ ww2990",fontsize=10,color="white",style="solid",shape="box"];2770 -> 3054[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3054 -> 2811[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3055[label="ww299/Zero",fontsize=10,color="white",style="solid",shape="box"];2770 -> 3055[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3055 -> 2812[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2221 -> 2857[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2221[label="primModNatS (primMinusNatS (Succ ww2480) Zero) (Succ Zero)",fontsize=16,color="magenta"];2221 -> 2858[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2221 -> 2859[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2221 -> 2860[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2222[label="Succ Zero",fontsize=16,color="green",shape="box"];2223 -> 2857[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2223[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2223 -> 2861[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2223 -> 2862[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2223 -> 2863[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2762 -> 2695[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2762[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS ww2940 ww2950)",fontsize=16,color="magenta"];2762 -> 2813[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2762 -> 2814[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2763[label="primDivNatS0 (Succ ww292) (Succ ww293) True",fontsize=16,color="black",shape="triangle"];2763 -> 2815[label="",style="solid", color="black", weight=3]; 41.74/20.33 2764[label="primDivNatS0 (Succ ww292) (Succ ww293) False",fontsize=16,color="black",shape="box"];2764 -> 2816[label="",style="solid", color="black", weight=3]; 41.74/20.33 2765 -> 2763[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2765[label="primDivNatS0 (Succ ww292) (Succ ww293) True",fontsize=16,color="magenta"];2974[label="primDivNatS (primMinusNatS (Succ ww3060) ww307) (Succ ww308)",fontsize=16,color="burlywood",shape="box"];3056[label="ww307/Succ ww3070",fontsize=10,color="white",style="solid",shape="box"];2974 -> 3056[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3056 -> 2976[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3057[label="ww307/Zero",fontsize=10,color="white",style="solid",shape="box"];2974 -> 3057[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3057 -> 2977[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2975[label="primDivNatS (primMinusNatS Zero ww307) (Succ ww308)",fontsize=16,color="burlywood",shape="box"];3058[label="ww307/Succ ww3070",fontsize=10,color="white",style="solid",shape="box"];2975 -> 3058[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3058 -> 2978[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3059[label="ww307/Zero",fontsize=10,color="white",style="solid",shape="box"];2975 -> 3059[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3059 -> 2979[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2811[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS (Succ ww2990) ww300)",fontsize=16,color="burlywood",shape="box"];3060[label="ww300/Succ ww3000",fontsize=10,color="white",style="solid",shape="box"];2811 -> 3060[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3060 -> 2821[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3061[label="ww300/Zero",fontsize=10,color="white",style="solid",shape="box"];2811 -> 3061[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3061 -> 2822[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2812[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS Zero ww300)",fontsize=16,color="burlywood",shape="box"];3062[label="ww300/Succ ww3000",fontsize=10,color="white",style="solid",shape="box"];2812 -> 3062[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3062 -> 2823[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3063[label="ww300/Zero",fontsize=10,color="white",style="solid",shape="box"];2812 -> 3063[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3063 -> 2824[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2858[label="Zero",fontsize=16,color="green",shape="box"];2859[label="Succ ww2480",fontsize=16,color="green",shape="box"];2860[label="Zero",fontsize=16,color="green",shape="box"];2857[label="primModNatS (primMinusNatS ww302 ww303) (Succ ww304)",fontsize=16,color="burlywood",shape="triangle"];3064[label="ww302/Succ ww3020",fontsize=10,color="white",style="solid",shape="box"];2857 -> 3064[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3064 -> 2888[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3065[label="ww302/Zero",fontsize=10,color="white",style="solid",shape="box"];2857 -> 3065[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3065 -> 2889[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2861[label="Zero",fontsize=16,color="green",shape="box"];2862[label="Zero",fontsize=16,color="green",shape="box"];2863[label="Zero",fontsize=16,color="green",shape="box"];2813[label="ww2940",fontsize=16,color="green",shape="box"];2814[label="ww2950",fontsize=16,color="green",shape="box"];2815[label="Succ (primDivNatS (primMinusNatS (Succ ww292) (Succ ww293)) (Succ (Succ ww293)))",fontsize=16,color="green",shape="box"];2815 -> 2825[label="",style="dashed", color="green", weight=3]; 41.74/20.33 2816[label="Zero",fontsize=16,color="green",shape="box"];2976[label="primDivNatS (primMinusNatS (Succ ww3060) (Succ ww3070)) (Succ ww308)",fontsize=16,color="black",shape="box"];2976 -> 2980[label="",style="solid", color="black", weight=3]; 41.74/20.33 2977[label="primDivNatS (primMinusNatS (Succ ww3060) Zero) (Succ ww308)",fontsize=16,color="black",shape="box"];2977 -> 2981[label="",style="solid", color="black", weight=3]; 41.74/20.33 2978[label="primDivNatS (primMinusNatS Zero (Succ ww3070)) (Succ ww308)",fontsize=16,color="black",shape="box"];2978 -> 2982[label="",style="solid", color="black", weight=3]; 41.74/20.33 2979[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww308)",fontsize=16,color="black",shape="box"];2979 -> 2983[label="",style="solid", color="black", weight=3]; 41.74/20.33 2821[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS (Succ ww2990) (Succ ww3000))",fontsize=16,color="black",shape="box"];2821 -> 2832[label="",style="solid", color="black", weight=3]; 41.74/20.33 2822[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS (Succ ww2990) Zero)",fontsize=16,color="black",shape="box"];2822 -> 2833[label="",style="solid", color="black", weight=3]; 41.74/20.33 2823[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS Zero (Succ ww3000))",fontsize=16,color="black",shape="box"];2823 -> 2834[label="",style="solid", color="black", weight=3]; 41.74/20.33 2824[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2824 -> 2835[label="",style="solid", color="black", weight=3]; 41.74/20.33 2888[label="primModNatS (primMinusNatS (Succ ww3020) ww303) (Succ ww304)",fontsize=16,color="burlywood",shape="box"];3066[label="ww303/Succ ww3030",fontsize=10,color="white",style="solid",shape="box"];2888 -> 3066[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3066 -> 2894[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3067[label="ww303/Zero",fontsize=10,color="white",style="solid",shape="box"];2888 -> 3067[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3067 -> 2895[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2889[label="primModNatS (primMinusNatS Zero ww303) (Succ ww304)",fontsize=16,color="burlywood",shape="box"];3068[label="ww303/Succ ww3030",fontsize=10,color="white",style="solid",shape="box"];2889 -> 3068[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3068 -> 2896[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 3069[label="ww303/Zero",fontsize=10,color="white",style="solid",shape="box"];2889 -> 3069[label="",style="solid", color="burlywood", weight=9]; 41.74/20.33 3069 -> 2897[label="",style="solid", color="burlywood", weight=3]; 41.74/20.33 2825 -> 2949[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2825[label="primDivNatS (primMinusNatS (Succ ww292) (Succ ww293)) (Succ (Succ ww293))",fontsize=16,color="magenta"];2825 -> 2956[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2825 -> 2957[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2825 -> 2958[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2980 -> 2949[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2980[label="primDivNatS (primMinusNatS ww3060 ww3070) (Succ ww308)",fontsize=16,color="magenta"];2980 -> 2984[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2980 -> 2985[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2981 -> 2164[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2981[label="primDivNatS (Succ ww3060) (Succ ww308)",fontsize=16,color="magenta"];2981 -> 2986[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2981 -> 2987[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2982[label="primDivNatS Zero (Succ ww308)",fontsize=16,color="black",shape="triangle"];2982 -> 2988[label="",style="solid", color="black", weight=3]; 41.74/20.33 2983 -> 2982[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2983[label="primDivNatS Zero (Succ ww308)",fontsize=16,color="magenta"];2832 -> 2770[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2832[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS ww2990 ww3000)",fontsize=16,color="magenta"];2832 -> 2841[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2832 -> 2842[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2833[label="primModNatS0 (Succ ww297) (Succ ww298) True",fontsize=16,color="black",shape="triangle"];2833 -> 2843[label="",style="solid", color="black", weight=3]; 41.74/20.33 2834[label="primModNatS0 (Succ ww297) (Succ ww298) False",fontsize=16,color="black",shape="box"];2834 -> 2844[label="",style="solid", color="black", weight=3]; 41.74/20.33 2835 -> 2833[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2835[label="primModNatS0 (Succ ww297) (Succ ww298) True",fontsize=16,color="magenta"];2894[label="primModNatS (primMinusNatS (Succ ww3020) (Succ ww3030)) (Succ ww304)",fontsize=16,color="black",shape="box"];2894 -> 2904[label="",style="solid", color="black", weight=3]; 41.74/20.33 2895[label="primModNatS (primMinusNatS (Succ ww3020) Zero) (Succ ww304)",fontsize=16,color="black",shape="box"];2895 -> 2905[label="",style="solid", color="black", weight=3]; 41.74/20.33 2896[label="primModNatS (primMinusNatS Zero (Succ ww3030)) (Succ ww304)",fontsize=16,color="black",shape="box"];2896 -> 2906[label="",style="solid", color="black", weight=3]; 41.74/20.33 2897[label="primModNatS (primMinusNatS Zero Zero) (Succ ww304)",fontsize=16,color="black",shape="box"];2897 -> 2907[label="",style="solid", color="black", weight=3]; 41.74/20.33 2956[label="Succ ww292",fontsize=16,color="green",shape="box"];2957[label="Succ ww293",fontsize=16,color="green",shape="box"];2958[label="Succ ww293",fontsize=16,color="green",shape="box"];2984[label="ww3060",fontsize=16,color="green",shape="box"];2985[label="ww3070",fontsize=16,color="green",shape="box"];2986[label="ww3060",fontsize=16,color="green",shape="box"];2987[label="ww308",fontsize=16,color="green",shape="box"];2988[label="Zero",fontsize=16,color="green",shape="box"];2841[label="ww2990",fontsize=16,color="green",shape="box"];2842[label="ww3000",fontsize=16,color="green",shape="box"];2843 -> 2857[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2843[label="primModNatS (primMinusNatS (Succ ww297) (Succ ww298)) (Succ (Succ ww298))",fontsize=16,color="magenta"];2843 -> 2870[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2843 -> 2871[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2843 -> 2872[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2844[label="Succ (Succ ww297)",fontsize=16,color="green",shape="box"];2904 -> 2857[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2904[label="primModNatS (primMinusNatS ww3020 ww3030) (Succ ww304)",fontsize=16,color="magenta"];2904 -> 2912[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2904 -> 2913[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2905 -> 2178[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2905[label="primModNatS (Succ ww3020) (Succ ww304)",fontsize=16,color="magenta"];2905 -> 2914[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2905 -> 2915[label="",style="dashed", color="magenta", weight=3]; 41.74/20.33 2906[label="primModNatS Zero (Succ ww304)",fontsize=16,color="black",shape="triangle"];2906 -> 2916[label="",style="solid", color="black", weight=3]; 41.74/20.33 2907 -> 2906[label="",style="dashed", color="red", weight=0]; 41.74/20.33 2907[label="primModNatS Zero (Succ ww304)",fontsize=16,color="magenta"];2870[label="Succ ww298",fontsize=16,color="green",shape="box"];2871[label="Succ ww297",fontsize=16,color="green",shape="box"];2872[label="Succ ww298",fontsize=16,color="green",shape="box"];2912[label="ww3030",fontsize=16,color="green",shape="box"];2913[label="ww3020",fontsize=16,color="green",shape="box"];2914[label="ww3020",fontsize=16,color="green",shape="box"];2915[label="ww304",fontsize=16,color="green",shape="box"];2916[label="Zero",fontsize=16,color="green",shape="box"];} 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (10) 41.74/20.33 Complex Obligation (AND) 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (11) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_show2(ww194) -> new_show2(ww194) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (12) NonTerminationLoopProof (COMPLETE) 41.74/20.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 41.74/20.33 Found a loop by semiunifying a rule from P directly. 41.74/20.33 41.74/20.33 s = new_show2(ww194) evaluates to t =new_show2(ww194) 41.74/20.33 41.74/20.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 41.74/20.33 * Matcher: [ ] 41.74/20.33 * Semiunifier: [ ] 41.74/20.33 41.74/20.33 -------------------------------------------------------------------------------- 41.74/20.33 Rewriting sequence 41.74/20.33 41.74/20.33 The DP semiunifies directly so there is only one rewrite step from new_show2(ww194) to new_show2(ww194). 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (13) 41.74/20.33 NO 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (14) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_show8(ww194, h, ba) -> new_show8(ww194, h, ba) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (15) NonTerminationLoopProof (COMPLETE) 41.74/20.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 41.74/20.33 Found a loop by semiunifying a rule from P directly. 41.74/20.33 41.74/20.33 s = new_show8(ww194, h, ba) evaluates to t =new_show8(ww194, h, ba) 41.74/20.33 41.74/20.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 41.74/20.33 * Matcher: [ ] 41.74/20.33 * Semiunifier: [ ] 41.74/20.33 41.74/20.33 -------------------------------------------------------------------------------- 41.74/20.33 Rewriting sequence 41.74/20.33 41.74/20.33 The DP semiunifies directly so there is only one rewrite step from new_show8(ww194, h, ba) to new_show8(ww194, h, ba). 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (16) 41.74/20.33 NO 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (17) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_show11(ww194) -> new_show11(ww194) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (18) NonTerminationLoopProof (COMPLETE) 41.74/20.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 41.74/20.33 Found a loop by semiunifying a rule from P directly. 41.74/20.33 41.74/20.33 s = new_show11(ww194) evaluates to t =new_show11(ww194) 41.74/20.33 41.74/20.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 41.74/20.33 * Matcher: [ ] 41.74/20.33 * Semiunifier: [ ] 41.74/20.33 41.74/20.33 -------------------------------------------------------------------------------- 41.74/20.33 Rewriting sequence 41.74/20.33 41.74/20.33 The DP semiunifies directly so there is only one rewrite step from new_show11(ww194) to new_show11(ww194). 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (19) 41.74/20.33 NO 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (20) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_psPs(:(ww2400, ww2401), ww200) -> new_psPs(ww2401, ww200) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (21) QDPSizeChangeProof (EQUIVALENT) 41.74/20.33 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. 41.74/20.33 41.74/20.33 From the DPs we obtained the following set of size-change graphs: 41.74/20.33 *new_psPs(:(ww2400, ww2401), ww200) -> new_psPs(ww2401, ww200) 41.74/20.33 The graph contains the following edges 1 > 1, 2 >= 2 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (22) 41.74/20.33 YES 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (23) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_show(ww194) -> new_show(ww194) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (24) NonTerminationLoopProof (COMPLETE) 41.74/20.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 41.74/20.33 Found a loop by semiunifying a rule from P directly. 41.74/20.33 41.74/20.33 s = new_show(ww194) evaluates to t =new_show(ww194) 41.74/20.33 41.74/20.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 41.74/20.33 * Matcher: [ ] 41.74/20.33 * Semiunifier: [ ] 41.74/20.33 41.74/20.33 -------------------------------------------------------------------------------- 41.74/20.33 Rewriting sequence 41.74/20.33 41.74/20.33 The DP semiunifies directly so there is only one rewrite step from new_show(ww194) to new_show(ww194). 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (25) 41.74/20.33 NO 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (26) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_show3(ww194, h, ba) -> new_show3(ww194, h, ba) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (27) NonTerminationLoopProof (COMPLETE) 41.74/20.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 41.74/20.33 Found a loop by semiunifying a rule from P directly. 41.74/20.33 41.74/20.33 s = new_show3(ww194, h, ba) evaluates to t =new_show3(ww194, h, ba) 41.74/20.33 41.74/20.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 41.74/20.33 * Matcher: [ ] 41.74/20.33 * Semiunifier: [ ] 41.74/20.33 41.74/20.33 -------------------------------------------------------------------------------- 41.74/20.33 Rewriting sequence 41.74/20.33 41.74/20.33 The DP semiunifies directly so there is only one rewrite step from new_show3(ww194, h, ba) to new_show3(ww194, h, ba). 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (28) 41.74/20.33 NO 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (29) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_show6(ww194, h, ba, bb) -> new_show6(ww194, h, ba, bb) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (30) NonTerminationLoopProof (COMPLETE) 41.74/20.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 41.74/20.33 Found a loop by semiunifying a rule from P directly. 41.74/20.33 41.74/20.33 s = new_show6(ww194, h, ba, bb) evaluates to t =new_show6(ww194, h, ba, bb) 41.74/20.33 41.74/20.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 41.74/20.33 * Matcher: [ ] 41.74/20.33 * Semiunifier: [ ] 41.74/20.33 41.74/20.33 -------------------------------------------------------------------------------- 41.74/20.33 Rewriting sequence 41.74/20.33 41.74/20.33 The DP semiunifies directly so there is only one rewrite step from new_show6(ww194, h, ba, bb) to new_show6(ww194, h, ba, bb). 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (31) 41.74/20.33 NO 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (32) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_show14(ww194, h) -> new_show14(ww194, h) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (33) NonTerminationLoopProof (COMPLETE) 41.74/20.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 41.74/20.33 Found a loop by semiunifying a rule from P directly. 41.74/20.33 41.74/20.33 s = new_show14(ww194, h) evaluates to t =new_show14(ww194, h) 41.74/20.33 41.74/20.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 41.74/20.33 * Matcher: [ ] 41.74/20.33 * Semiunifier: [ ] 41.74/20.33 41.74/20.33 -------------------------------------------------------------------------------- 41.74/20.33 Rewriting sequence 41.74/20.33 41.74/20.33 The DP semiunifies directly so there is only one rewrite step from new_show14(ww194, h) to new_show14(ww194, h). 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (34) 41.74/20.33 NO 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (35) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_show4(ww194) -> new_show4(ww194) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (36) NonTerminationLoopProof (COMPLETE) 41.74/20.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 41.74/20.33 Found a loop by semiunifying a rule from P directly. 41.74/20.33 41.74/20.33 s = new_show4(ww194) evaluates to t =new_show4(ww194) 41.74/20.33 41.74/20.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 41.74/20.33 * Matcher: [ ] 41.74/20.33 * Semiunifier: [ ] 41.74/20.33 41.74/20.33 -------------------------------------------------------------------------------- 41.74/20.33 Rewriting sequence 41.74/20.33 41.74/20.33 The DP semiunifies directly so there is only one rewrite step from new_show4(ww194) to new_show4(ww194). 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (37) 41.74/20.33 NO 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (38) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_show10(ww194) -> new_show10(ww194) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (39) NonTerminationLoopProof (COMPLETE) 41.74/20.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 41.74/20.33 Found a loop by semiunifying a rule from P directly. 41.74/20.33 41.74/20.33 s = new_show10(ww194) evaluates to t =new_show10(ww194) 41.74/20.33 41.74/20.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 41.74/20.33 * Matcher: [ ] 41.74/20.33 * Semiunifier: [ ] 41.74/20.33 41.74/20.33 -------------------------------------------------------------------------------- 41.74/20.33 Rewriting sequence 41.74/20.33 41.74/20.33 The DP semiunifies directly so there is only one rewrite step from new_show10(ww194) to new_show10(ww194). 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (40) 41.74/20.33 NO 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (41) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_show9(ww194) -> new_show9(ww194) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (42) NonTerminationLoopProof (COMPLETE) 41.74/20.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 41.74/20.33 Found a loop by semiunifying a rule from P directly. 41.74/20.33 41.74/20.33 s = new_show9(ww194) evaluates to t =new_show9(ww194) 41.74/20.33 41.74/20.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 41.74/20.33 * Matcher: [ ] 41.74/20.33 * Semiunifier: [ ] 41.74/20.33 41.74/20.33 -------------------------------------------------------------------------------- 41.74/20.33 Rewriting sequence 41.74/20.33 41.74/20.33 The DP semiunifies directly so there is only one rewrite step from new_show9(ww194) to new_show9(ww194). 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (43) 41.74/20.33 NO 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (44) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_primDivNatS0(ww292, ww293, Zero, Zero) -> new_primDivNatS00(ww292, ww293) 41.74/20.33 new_primDivNatS00(ww292, ww293) -> new_primDivNatS(Succ(ww292), Succ(ww293), Succ(ww293)) 41.74/20.33 new_primDivNatS(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS(ww3060, ww3070, ww308) 41.74/20.33 new_primDivNatS1(Succ(ww2420), Zero) -> new_primDivNatS(Succ(ww2420), Zero, Zero) 41.74/20.33 new_primDivNatS0(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS0(ww292, ww293, ww2940, ww2950) 41.74/20.33 new_primDivNatS0(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS(Succ(ww292), Succ(ww293), Succ(ww293)) 41.74/20.33 new_primDivNatS1(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS0(ww2420, ww2430, ww2420, ww2430) 41.74/20.33 new_primDivNatS1(Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero) 41.74/20.33 new_primDivNatS(Succ(ww3060), Zero, ww308) -> new_primDivNatS1(ww3060, ww308) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (45) DependencyGraphProof (EQUIVALENT) 41.74/20.33 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (46) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_primDivNatS00(ww292, ww293) -> new_primDivNatS(Succ(ww292), Succ(ww293), Succ(ww293)) 41.74/20.33 new_primDivNatS(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS(ww3060, ww3070, ww308) 41.74/20.33 new_primDivNatS(Succ(ww3060), Zero, ww308) -> new_primDivNatS1(ww3060, ww308) 41.74/20.33 new_primDivNatS1(Succ(ww2420), Zero) -> new_primDivNatS(Succ(ww2420), Zero, Zero) 41.74/20.33 new_primDivNatS1(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS0(ww2420, ww2430, ww2420, ww2430) 41.74/20.33 new_primDivNatS0(ww292, ww293, Zero, Zero) -> new_primDivNatS00(ww292, ww293) 41.74/20.33 new_primDivNatS0(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS0(ww292, ww293, ww2940, ww2950) 41.74/20.33 new_primDivNatS0(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS(Succ(ww292), Succ(ww293), Succ(ww293)) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (47) QDPOrderProof (EQUIVALENT) 41.74/20.33 We use the reduction pair processor [LPAR04,JAR06]. 41.74/20.33 41.74/20.33 41.74/20.33 The following pairs can be oriented strictly and are deleted. 41.74/20.33 41.74/20.33 new_primDivNatS(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS(ww3060, ww3070, ww308) 41.74/20.33 new_primDivNatS1(Succ(ww2420), Zero) -> new_primDivNatS(Succ(ww2420), Zero, Zero) 41.74/20.33 new_primDivNatS1(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS0(ww2420, ww2430, ww2420, ww2430) 41.74/20.33 The remaining pairs can at least be oriented weakly. 41.74/20.33 Used ordering: Polynomial interpretation [POLO]: 41.74/20.33 41.74/20.33 POL(Succ(x_1)) = 1 + x_1 41.74/20.33 POL(Zero) = 0 41.74/20.33 POL(new_primDivNatS(x_1, x_2, x_3)) = x_1 41.74/20.33 POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 41.74/20.33 POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1 41.74/20.33 POL(new_primDivNatS1(x_1, x_2)) = 1 + x_1 41.74/20.33 41.74/20.33 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 41.74/20.33 none 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (48) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_primDivNatS00(ww292, ww293) -> new_primDivNatS(Succ(ww292), Succ(ww293), Succ(ww293)) 41.74/20.33 new_primDivNatS(Succ(ww3060), Zero, ww308) -> new_primDivNatS1(ww3060, ww308) 41.74/20.33 new_primDivNatS0(ww292, ww293, Zero, Zero) -> new_primDivNatS00(ww292, ww293) 41.74/20.33 new_primDivNatS0(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS0(ww292, ww293, ww2940, ww2950) 41.74/20.33 new_primDivNatS0(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS(Succ(ww292), Succ(ww293), Succ(ww293)) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (49) DependencyGraphProof (EQUIVALENT) 41.74/20.33 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (50) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_primDivNatS0(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS0(ww292, ww293, ww2940, ww2950) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (51) QDPSizeChangeProof (EQUIVALENT) 41.74/20.33 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. 41.74/20.33 41.74/20.33 From the DPs we obtained the following set of size-change graphs: 41.74/20.33 *new_primDivNatS0(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS0(ww292, ww293, ww2940, ww2950) 41.74/20.33 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (52) 41.74/20.33 YES 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (53) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_show13(ww194) -> new_show13(ww194) 41.74/20.33 41.74/20.33 R is empty. 41.74/20.33 Q is empty. 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (54) NonTerminationLoopProof (COMPLETE) 41.74/20.33 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 41.74/20.33 Found a loop by semiunifying a rule from P directly. 41.74/20.33 41.74/20.33 s = new_show13(ww194) evaluates to t =new_show13(ww194) 41.74/20.33 41.74/20.33 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 41.74/20.33 * Matcher: [ ] 41.74/20.33 * Semiunifier: [ ] 41.74/20.33 41.74/20.33 -------------------------------------------------------------------------------- 41.74/20.33 Rewriting sequence 41.74/20.33 41.74/20.33 The DP semiunifies directly so there is only one rewrite step from new_show13(ww194) to new_show13(ww194). 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (55) 41.74/20.33 NO 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (56) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 41.74/20.33 The TRS R consists of the following rules: 41.74/20.33 41.74/20.33 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 41.74/20.33 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 41.74/20.33 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 41.74/20.33 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 41.74/20.33 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 41.74/20.33 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 41.74/20.33 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 41.74/20.33 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 41.74/20.33 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 41.74/20.33 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 41.74/20.33 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 41.74/20.33 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 41.74/20.33 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 41.74/20.33 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 41.74/20.33 new_primModNatS4(ww304) -> Zero 41.74/20.33 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.33 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 41.74/20.33 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 41.74/20.33 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 41.74/20.33 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 41.74/20.33 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 41.74/20.33 new_psPs0([], ww200) -> ww200 41.74/20.33 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 41.74/20.33 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.33 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 41.74/20.33 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 41.74/20.33 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 41.74/20.33 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 41.74/20.33 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 41.74/20.33 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 41.74/20.33 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 41.74/20.33 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 41.74/20.33 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 41.74/20.33 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 41.74/20.33 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 41.74/20.33 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 41.74/20.33 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.33 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 41.74/20.33 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.33 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 41.74/20.33 new_show23(ww194) -> new_primShowInt0(ww194) 41.74/20.33 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 41.74/20.33 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 41.74/20.33 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 41.74/20.33 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 41.74/20.33 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 41.74/20.33 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 41.74/20.33 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 41.74/20.33 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 41.74/20.33 new_primDivNatS4(ww308) -> Zero 41.74/20.33 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 41.74/20.33 41.74/20.33 The set Q consists of the following terms: 41.74/20.33 41.74/20.33 new_psPs0([], x0) 41.74/20.33 new_show22(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Succ(x2), Zero) 41.74/20.33 new_showsPrec(x0, x1, ty_IOError) 41.74/20.33 new_primModNatS3(Zero, Succ(x0), x1) 41.74/20.33 new_showsPrec(x0, x1, ty_Bool) 41.74/20.33 new_showsPrec(x0, x1, app(ty_[], x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 41.74/20.33 new_show15(x0, x1) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 41.74/20.33 new_psPs0(:(x0, x1), x2) 41.74/20.33 new_primShowInt0(Pos(Succ(x0))) 41.74/20.33 new_show27(x0, x1, x2) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 41.74/20.33 new_primDivNatS3(Zero, Succ(x0)) 41.74/20.33 new_showsPrec(x0, x1, ty_Float) 41.74/20.33 new_primDivNatS3(Succ(x0), Succ(x1)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 41.74/20.33 new_primDivNatS3(Succ(x0), Zero) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 41.74/20.33 new_pt0(x0, x1, x2, x3, x4, x5) 41.74/20.33 new_show19(x0) 41.74/20.33 new_primModNatS3(Zero, Zero, x0) 41.74/20.33 new_primDivNatS2(Zero, Succ(x0), x1) 41.74/20.33 new_primModNatS2(Zero, Succ(x0)) 41.74/20.33 new_show31(x0) 41.74/20.33 new_show29(x0) 41.74/20.33 new_show21(x0, x1, x2) 41.74/20.33 new_primModNatS2(Succ(x0), Zero) 41.74/20.33 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 41.74/20.33 new_showsPrec(x0, x1, ty_Double) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 41.74/20.33 new_primDivNatS2(Succ(x0), Zero, x1) 41.74/20.33 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 41.74/20.33 new_showsPrec(x0, x1, ty_HugsException) 41.74/20.33 new_showsPrec(x0, x1, ty_Char) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 41.74/20.33 new_primModNatS01(x0, x1, Zero, Zero) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 41.74/20.33 new_primDivNatS01(x0, x1) 41.74/20.33 new_primShowInt0(Neg(x0)) 41.74/20.33 new_show17(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 41.74/20.33 new_primModNatS2(Zero, Zero) 41.74/20.33 new_primModNatS4(x0) 41.74/20.33 new_show30(x0, x1) 41.74/20.33 new_showsPrec(x0, x1, ty_Int) 41.74/20.33 new_show24(x0, x1, x2, x3) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 41.74/20.33 new_primDivNatS4(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 41.74/20.33 new_primShowInt0(Pos(Zero)) 41.74/20.33 new_show16(x0) 41.74/20.33 new_show26(x0) 41.74/20.33 new_showsPrec(x0, x1, ty_Integer) 41.74/20.33 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 41.74/20.33 new_primModNatS02(x0, x1) 41.74/20.33 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 41.74/20.33 new_showsPrec(x0, x1, app(ty_IO, x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 41.74/20.33 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 41.74/20.33 new_div(x0, x1) 41.74/20.33 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 41.74/20.33 new_primIntToChar(x0, x1) 41.74/20.33 new_primDivNatS2(Succ(x0), Succ(x1), x2) 41.74/20.33 new_show18(x0) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 41.74/20.33 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 41.74/20.33 new_primDivNatS2(Zero, Zero, x0) 41.74/20.33 new_show20(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Zero, Zero) 41.74/20.33 new_primModNatS01(x0, x1, Zero, Succ(x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 41.74/20.33 new_show25(x0, x1) 41.74/20.33 new_show23(x0) 41.74/20.33 new_primModNatS2(Succ(x0), Succ(x1)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 41.74/20.33 new_primModNatS3(Succ(x0), Succ(x1), x2) 41.74/20.33 new_show28(x0) 41.74/20.33 new_showsPrec(x0, x1, ty_IOErrorKind) 41.74/20.33 new_primModNatS01(x0, x1, Succ(x2), Zero) 41.74/20.33 new_primModNatS3(Succ(x0), Zero, x1) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 41.74/20.33 new_showsPrec(x0, x1, ty_@0) 41.74/20.33 new_primDivNatS3(Zero, Zero) 41.74/20.33 new_showsPrec(x0, x1, ty_Ordering) 41.74/20.33 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (57) TransformationProof (EQUIVALENT) 41.74/20.33 By rewriting [LPAR04] the rule new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) at position [5] we obtained the following new rules [LPAR04]: 41.74/20.33 41.74/20.33 (new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, be)), be, be),new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, be)), be, be)) 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (58) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, be)), be, be) 41.74/20.33 41.74/20.33 The TRS R consists of the following rules: 41.74/20.33 41.74/20.33 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 41.74/20.33 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 41.74/20.33 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 41.74/20.33 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 41.74/20.33 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 41.74/20.33 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 41.74/20.33 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 41.74/20.33 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 41.74/20.33 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 41.74/20.33 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 41.74/20.33 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 41.74/20.33 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 41.74/20.33 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 41.74/20.33 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 41.74/20.33 new_primModNatS4(ww304) -> Zero 41.74/20.33 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.33 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 41.74/20.33 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 41.74/20.33 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 41.74/20.33 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 41.74/20.33 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 41.74/20.33 new_psPs0([], ww200) -> ww200 41.74/20.33 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 41.74/20.33 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.33 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 41.74/20.33 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 41.74/20.33 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 41.74/20.33 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 41.74/20.33 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 41.74/20.33 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 41.74/20.33 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 41.74/20.33 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 41.74/20.33 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 41.74/20.33 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 41.74/20.33 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 41.74/20.33 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 41.74/20.33 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.33 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 41.74/20.33 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.33 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 41.74/20.33 new_show23(ww194) -> new_primShowInt0(ww194) 41.74/20.33 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 41.74/20.33 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 41.74/20.33 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 41.74/20.33 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 41.74/20.33 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 41.74/20.33 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 41.74/20.33 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 41.74/20.33 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 41.74/20.33 new_primDivNatS4(ww308) -> Zero 41.74/20.33 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 41.74/20.33 41.74/20.33 The set Q consists of the following terms: 41.74/20.33 41.74/20.33 new_psPs0([], x0) 41.74/20.33 new_show22(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Succ(x2), Zero) 41.74/20.33 new_showsPrec(x0, x1, ty_IOError) 41.74/20.33 new_primModNatS3(Zero, Succ(x0), x1) 41.74/20.33 new_showsPrec(x0, x1, ty_Bool) 41.74/20.33 new_showsPrec(x0, x1, app(ty_[], x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 41.74/20.33 new_show15(x0, x1) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 41.74/20.33 new_psPs0(:(x0, x1), x2) 41.74/20.33 new_primShowInt0(Pos(Succ(x0))) 41.74/20.33 new_show27(x0, x1, x2) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 41.74/20.33 new_primDivNatS3(Zero, Succ(x0)) 41.74/20.33 new_showsPrec(x0, x1, ty_Float) 41.74/20.33 new_primDivNatS3(Succ(x0), Succ(x1)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 41.74/20.33 new_primDivNatS3(Succ(x0), Zero) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 41.74/20.33 new_pt0(x0, x1, x2, x3, x4, x5) 41.74/20.33 new_show19(x0) 41.74/20.33 new_primModNatS3(Zero, Zero, x0) 41.74/20.33 new_primDivNatS2(Zero, Succ(x0), x1) 41.74/20.33 new_primModNatS2(Zero, Succ(x0)) 41.74/20.33 new_show31(x0) 41.74/20.33 new_show29(x0) 41.74/20.33 new_show21(x0, x1, x2) 41.74/20.33 new_primModNatS2(Succ(x0), Zero) 41.74/20.33 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 41.74/20.33 new_showsPrec(x0, x1, ty_Double) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 41.74/20.33 new_primDivNatS2(Succ(x0), Zero, x1) 41.74/20.33 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 41.74/20.33 new_showsPrec(x0, x1, ty_HugsException) 41.74/20.33 new_showsPrec(x0, x1, ty_Char) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 41.74/20.33 new_primModNatS01(x0, x1, Zero, Zero) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 41.74/20.33 new_primDivNatS01(x0, x1) 41.74/20.33 new_primShowInt0(Neg(x0)) 41.74/20.33 new_show17(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 41.74/20.33 new_primModNatS2(Zero, Zero) 41.74/20.33 new_primModNatS4(x0) 41.74/20.33 new_show30(x0, x1) 41.74/20.33 new_showsPrec(x0, x1, ty_Int) 41.74/20.33 new_show24(x0, x1, x2, x3) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 41.74/20.33 new_primDivNatS4(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 41.74/20.33 new_primShowInt0(Pos(Zero)) 41.74/20.33 new_show16(x0) 41.74/20.33 new_show26(x0) 41.74/20.33 new_showsPrec(x0, x1, ty_Integer) 41.74/20.33 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 41.74/20.33 new_primModNatS02(x0, x1) 41.74/20.33 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 41.74/20.33 new_showsPrec(x0, x1, app(ty_IO, x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 41.74/20.33 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 41.74/20.33 new_div(x0, x1) 41.74/20.33 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 41.74/20.33 new_primIntToChar(x0, x1) 41.74/20.33 new_primDivNatS2(Succ(x0), Succ(x1), x2) 41.74/20.33 new_show18(x0) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 41.74/20.33 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 41.74/20.33 new_primDivNatS2(Zero, Zero, x0) 41.74/20.33 new_show20(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Zero, Zero) 41.74/20.33 new_primModNatS01(x0, x1, Zero, Succ(x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 41.74/20.33 new_show25(x0, x1) 41.74/20.33 new_show23(x0) 41.74/20.33 new_primModNatS2(Succ(x0), Succ(x1)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 41.74/20.33 new_primModNatS3(Succ(x0), Succ(x1), x2) 41.74/20.33 new_show28(x0) 41.74/20.33 new_showsPrec(x0, x1, ty_IOErrorKind) 41.74/20.33 new_primModNatS01(x0, x1, Succ(x2), Zero) 41.74/20.33 new_primModNatS3(Succ(x0), Zero, x1) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 41.74/20.33 new_showsPrec(x0, x1, ty_@0) 41.74/20.33 new_primDivNatS3(Zero, Zero) 41.74/20.33 new_showsPrec(x0, x1, ty_Ordering) 41.74/20.33 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (59) TransformationProof (EQUIVALENT) 41.74/20.33 By rewriting [LPAR04] the rule new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, be)), be, be) at position [5] we obtained the following new rules [LPAR04]: 41.74/20.33 41.74/20.33 (new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), new_psPs0(:(Char(Succ(ww196)), :(Char(Succ(ww197)), [])), new_showsPrec(ww198, ww199, be))), be, be),new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), new_psPs0(:(Char(Succ(ww196)), :(Char(Succ(ww197)), [])), new_showsPrec(ww198, ww199, be))), be, be)) 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (60) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), new_psPs0(:(Char(Succ(ww196)), :(Char(Succ(ww197)), [])), new_showsPrec(ww198, ww199, be))), be, be) 41.74/20.33 41.74/20.33 The TRS R consists of the following rules: 41.74/20.33 41.74/20.33 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 41.74/20.33 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 41.74/20.33 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 41.74/20.33 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 41.74/20.33 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 41.74/20.33 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 41.74/20.33 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 41.74/20.33 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 41.74/20.33 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 41.74/20.33 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 41.74/20.33 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 41.74/20.33 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 41.74/20.33 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 41.74/20.33 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 41.74/20.33 new_primModNatS4(ww304) -> Zero 41.74/20.33 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.33 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 41.74/20.33 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 41.74/20.33 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 41.74/20.33 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 41.74/20.33 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 41.74/20.33 new_psPs0([], ww200) -> ww200 41.74/20.33 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 41.74/20.33 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.33 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 41.74/20.33 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 41.74/20.33 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 41.74/20.33 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 41.74/20.33 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 41.74/20.33 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 41.74/20.33 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 41.74/20.33 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 41.74/20.33 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 41.74/20.33 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 41.74/20.33 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 41.74/20.33 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 41.74/20.33 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.33 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 41.74/20.33 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.33 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 41.74/20.33 new_show23(ww194) -> new_primShowInt0(ww194) 41.74/20.33 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 41.74/20.33 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 41.74/20.33 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 41.74/20.33 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 41.74/20.33 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 41.74/20.33 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 41.74/20.33 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 41.74/20.33 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 41.74/20.33 new_primDivNatS4(ww308) -> Zero 41.74/20.33 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 41.74/20.33 41.74/20.33 The set Q consists of the following terms: 41.74/20.33 41.74/20.33 new_psPs0([], x0) 41.74/20.33 new_show22(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Succ(x2), Zero) 41.74/20.33 new_showsPrec(x0, x1, ty_IOError) 41.74/20.33 new_primModNatS3(Zero, Succ(x0), x1) 41.74/20.33 new_showsPrec(x0, x1, ty_Bool) 41.74/20.33 new_showsPrec(x0, x1, app(ty_[], x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 41.74/20.33 new_show15(x0, x1) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 41.74/20.33 new_psPs0(:(x0, x1), x2) 41.74/20.33 new_primShowInt0(Pos(Succ(x0))) 41.74/20.33 new_show27(x0, x1, x2) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 41.74/20.33 new_primDivNatS3(Zero, Succ(x0)) 41.74/20.33 new_showsPrec(x0, x1, ty_Float) 41.74/20.33 new_primDivNatS3(Succ(x0), Succ(x1)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 41.74/20.33 new_primDivNatS3(Succ(x0), Zero) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 41.74/20.33 new_pt0(x0, x1, x2, x3, x4, x5) 41.74/20.33 new_show19(x0) 41.74/20.33 new_primModNatS3(Zero, Zero, x0) 41.74/20.33 new_primDivNatS2(Zero, Succ(x0), x1) 41.74/20.33 new_primModNatS2(Zero, Succ(x0)) 41.74/20.33 new_show31(x0) 41.74/20.33 new_show29(x0) 41.74/20.33 new_show21(x0, x1, x2) 41.74/20.33 new_primModNatS2(Succ(x0), Zero) 41.74/20.33 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 41.74/20.33 new_showsPrec(x0, x1, ty_Double) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 41.74/20.33 new_primDivNatS2(Succ(x0), Zero, x1) 41.74/20.33 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 41.74/20.33 new_showsPrec(x0, x1, ty_HugsException) 41.74/20.33 new_showsPrec(x0, x1, ty_Char) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 41.74/20.33 new_primModNatS01(x0, x1, Zero, Zero) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 41.74/20.33 new_primDivNatS01(x0, x1) 41.74/20.33 new_primShowInt0(Neg(x0)) 41.74/20.33 new_show17(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 41.74/20.33 new_primModNatS2(Zero, Zero) 41.74/20.33 new_primModNatS4(x0) 41.74/20.33 new_show30(x0, x1) 41.74/20.33 new_showsPrec(x0, x1, ty_Int) 41.74/20.33 new_show24(x0, x1, x2, x3) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 41.74/20.33 new_primDivNatS4(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 41.74/20.33 new_primShowInt0(Pos(Zero)) 41.74/20.33 new_show16(x0) 41.74/20.33 new_show26(x0) 41.74/20.33 new_showsPrec(x0, x1, ty_Integer) 41.74/20.33 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 41.74/20.33 new_primModNatS02(x0, x1) 41.74/20.33 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 41.74/20.33 new_showsPrec(x0, x1, app(ty_IO, x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 41.74/20.33 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 41.74/20.33 new_div(x0, x1) 41.74/20.33 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 41.74/20.33 new_primIntToChar(x0, x1) 41.74/20.33 new_primDivNatS2(Succ(x0), Succ(x1), x2) 41.74/20.33 new_show18(x0) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 41.74/20.33 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 41.74/20.33 new_primDivNatS2(Zero, Zero, x0) 41.74/20.33 new_show20(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Zero, Zero) 41.74/20.33 new_primModNatS01(x0, x1, Zero, Succ(x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 41.74/20.33 new_show25(x0, x1) 41.74/20.33 new_show23(x0) 41.74/20.33 new_primModNatS2(Succ(x0), Succ(x1)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 41.74/20.33 new_primModNatS3(Succ(x0), Succ(x1), x2) 41.74/20.33 new_show28(x0) 41.74/20.33 new_showsPrec(x0, x1, ty_IOErrorKind) 41.74/20.33 new_primModNatS01(x0, x1, Succ(x2), Zero) 41.74/20.33 new_primModNatS3(Succ(x0), Zero, x1) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 41.74/20.33 new_showsPrec(x0, x1, ty_@0) 41.74/20.33 new_primDivNatS3(Zero, Zero) 41.74/20.33 new_showsPrec(x0, x1, ty_Ordering) 41.74/20.33 41.74/20.33 We have to consider all minimal (P,Q,R)-chains. 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (61) TransformationProof (EQUIVALENT) 41.74/20.33 By rewriting [LPAR04] the rule new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), new_psPs0(:(Char(Succ(ww196)), :(Char(Succ(ww197)), [])), new_showsPrec(ww198, ww199, be))), be, be) at position [5,1] we obtained the following new rules [LPAR04]: 41.74/20.33 41.74/20.33 (new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), new_psPs0(:(Char(Succ(ww197)), []), new_showsPrec(ww198, ww199, be)))), be, be),new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), new_psPs0(:(Char(Succ(ww197)), []), new_showsPrec(ww198, ww199, be)))), be, be)) 41.74/20.33 41.74/20.33 41.74/20.33 ---------------------------------------- 41.74/20.33 41.74/20.33 (62) 41.74/20.33 Obligation: 41.74/20.33 Q DP problem: 41.74/20.33 The TRS P consists of the following rules: 41.74/20.33 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.33 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), new_psPs0(:(Char(Succ(ww197)), []), new_showsPrec(ww198, ww199, be)))), be, be) 41.74/20.33 41.74/20.33 The TRS R consists of the following rules: 41.74/20.33 41.74/20.33 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 41.74/20.33 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 41.74/20.33 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 41.74/20.33 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 41.74/20.33 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 41.74/20.33 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 41.74/20.33 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 41.74/20.33 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 41.74/20.33 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 41.74/20.33 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 41.74/20.33 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 41.74/20.33 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 41.74/20.33 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 41.74/20.33 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 41.74/20.33 new_primModNatS4(ww304) -> Zero 41.74/20.33 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.33 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 41.74/20.33 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 41.74/20.33 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 41.74/20.33 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 41.74/20.33 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 41.74/20.33 new_psPs0([], ww200) -> ww200 41.74/20.33 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 41.74/20.33 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.33 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 41.74/20.33 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 41.74/20.33 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 41.74/20.33 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 41.74/20.33 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 41.74/20.33 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 41.74/20.33 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 41.74/20.33 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 41.74/20.33 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 41.74/20.33 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 41.74/20.33 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 41.74/20.33 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 41.74/20.33 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 41.74/20.33 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.33 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 41.74/20.33 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.33 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 41.74/20.33 new_show23(ww194) -> new_primShowInt0(ww194) 41.74/20.33 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 41.74/20.33 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 41.74/20.33 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 41.74/20.33 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.33 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 41.74/20.33 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 41.74/20.33 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 41.74/20.33 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 41.74/20.33 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 41.74/20.33 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 41.74/20.33 new_primDivNatS4(ww308) -> Zero 41.74/20.33 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 41.74/20.33 41.74/20.33 The set Q consists of the following terms: 41.74/20.33 41.74/20.33 new_psPs0([], x0) 41.74/20.33 new_show22(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Succ(x2), Zero) 41.74/20.33 new_showsPrec(x0, x1, ty_IOError) 41.74/20.33 new_primModNatS3(Zero, Succ(x0), x1) 41.74/20.33 new_showsPrec(x0, x1, ty_Bool) 41.74/20.33 new_showsPrec(x0, x1, app(ty_[], x2)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 41.74/20.33 new_show15(x0, x1) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 41.74/20.33 new_psPs0(:(x0, x1), x2) 41.74/20.33 new_primShowInt0(Pos(Succ(x0))) 41.74/20.33 new_show27(x0, x1, x2) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 41.74/20.33 new_primDivNatS3(Zero, Succ(x0)) 41.74/20.33 new_showsPrec(x0, x1, ty_Float) 41.74/20.33 new_primDivNatS3(Succ(x0), Succ(x1)) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 41.74/20.33 new_primDivNatS3(Succ(x0), Zero) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 41.74/20.33 new_pt0(x0, x1, x2, x3, x4, x5) 41.74/20.33 new_show19(x0) 41.74/20.33 new_primModNatS3(Zero, Zero, x0) 41.74/20.33 new_primDivNatS2(Zero, Succ(x0), x1) 41.74/20.33 new_primModNatS2(Zero, Succ(x0)) 41.74/20.33 new_show31(x0) 41.74/20.33 new_show29(x0) 41.74/20.33 new_show21(x0, x1, x2) 41.74/20.33 new_primModNatS2(Succ(x0), Zero) 41.74/20.33 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 41.74/20.33 new_showsPrec(x0, x1, ty_Double) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 41.74/20.33 new_primDivNatS2(Succ(x0), Zero, x1) 41.74/20.33 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 41.74/20.33 new_showsPrec(x0, x1, ty_HugsException) 41.74/20.33 new_showsPrec(x0, x1, ty_Char) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 41.74/20.33 new_primModNatS01(x0, x1, Zero, Zero) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 41.74/20.33 new_primDivNatS01(x0, x1) 41.74/20.33 new_primShowInt0(Neg(x0)) 41.74/20.33 new_show17(x0) 41.74/20.33 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 41.74/20.33 new_primModNatS2(Zero, Zero) 41.74/20.33 new_primModNatS4(x0) 41.74/20.33 new_show30(x0, x1) 41.74/20.33 new_showsPrec(x0, x1, ty_Int) 41.74/20.33 new_show24(x0, x1, x2, x3) 41.74/20.33 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 41.74/20.34 new_primDivNatS4(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 41.74/20.34 new_primShowInt0(Pos(Zero)) 41.74/20.34 new_show16(x0) 41.74/20.34 new_show26(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_Integer) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 41.74/20.34 new_primModNatS02(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 41.74/20.34 new_showsPrec(x0, x1, app(ty_IO, x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 41.74/20.34 new_div(x0, x1) 41.74/20.34 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 41.74/20.34 new_primIntToChar(x0, x1) 41.74/20.34 new_primDivNatS2(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show18(x0) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 41.74/20.34 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 41.74/20.34 new_primDivNatS2(Zero, Zero, x0) 41.74/20.34 new_show20(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Zero) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 41.74/20.34 new_show25(x0, x1) 41.74/20.34 new_show23(x0) 41.74/20.34 new_primModNatS2(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 41.74/20.34 new_primModNatS3(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show28(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_IOErrorKind) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Zero) 41.74/20.34 new_primModNatS3(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, ty_@0) 41.74/20.34 new_primDivNatS3(Zero, Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_Ordering) 41.74/20.34 41.74/20.34 We have to consider all minimal (P,Q,R)-chains. 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (63) TransformationProof (EQUIVALENT) 41.74/20.34 By rewriting [LPAR04] the rule new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), new_psPs0(:(Char(Succ(ww197)), []), new_showsPrec(ww198, ww199, be)))), be, be) at position [5,1,1] we obtained the following new rules [LPAR04]: 41.74/20.34 41.74/20.34 (new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_psPs0([], new_showsPrec(ww198, ww199, be))))), be, be),new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_psPs0([], new_showsPrec(ww198, ww199, be))))), be, be)) 41.74/20.34 41.74/20.34 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (64) 41.74/20.34 Obligation: 41.74/20.34 Q DP problem: 41.74/20.34 The TRS P consists of the following rules: 41.74/20.34 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_psPs0([], new_showsPrec(ww198, ww199, be))))), be, be) 41.74/20.34 41.74/20.34 The TRS R consists of the following rules: 41.74/20.34 41.74/20.34 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 41.74/20.34 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 41.74/20.34 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 41.74/20.34 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 41.74/20.34 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 41.74/20.34 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 41.74/20.34 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 41.74/20.34 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 41.74/20.34 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 41.74/20.34 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 41.74/20.34 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 41.74/20.34 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 41.74/20.34 new_primModNatS4(ww304) -> Zero 41.74/20.34 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.34 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 41.74/20.34 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 41.74/20.34 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 41.74/20.34 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 41.74/20.34 new_psPs0([], ww200) -> ww200 41.74/20.34 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 41.74/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.34 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 41.74/20.34 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 41.74/20.34 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 41.74/20.34 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 41.74/20.34 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 41.74/20.34 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 41.74/20.34 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 41.74/20.34 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 41.74/20.34 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 41.74/20.34 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 41.74/20.34 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 41.74/20.34 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 41.74/20.34 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.34 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 41.74/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.34 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 41.74/20.34 new_show23(ww194) -> new_primShowInt0(ww194) 41.74/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 41.74/20.34 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 41.74/20.34 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 41.74/20.34 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 41.74/20.34 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 41.74/20.34 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 41.74/20.34 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 41.74/20.34 new_primDivNatS4(ww308) -> Zero 41.74/20.34 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 41.74/20.34 41.74/20.34 The set Q consists of the following terms: 41.74/20.34 41.74/20.34 new_psPs0([], x0) 41.74/20.34 new_show22(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Succ(x2), Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_IOError) 41.74/20.34 new_primModNatS3(Zero, Succ(x0), x1) 41.74/20.34 new_showsPrec(x0, x1, ty_Bool) 41.74/20.34 new_showsPrec(x0, x1, app(ty_[], x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 41.74/20.34 new_show15(x0, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 41.74/20.34 new_psPs0(:(x0, x1), x2) 41.74/20.34 new_primShowInt0(Pos(Succ(x0))) 41.74/20.34 new_show27(x0, x1, x2) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 41.74/20.34 new_primDivNatS3(Zero, Succ(x0)) 41.74/20.34 new_showsPrec(x0, x1, ty_Float) 41.74/20.34 new_primDivNatS3(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 41.74/20.34 new_primDivNatS3(Succ(x0), Zero) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 41.74/20.34 new_pt0(x0, x1, x2, x3, x4, x5) 41.74/20.34 new_show19(x0) 41.74/20.34 new_primModNatS3(Zero, Zero, x0) 41.74/20.34 new_primDivNatS2(Zero, Succ(x0), x1) 41.74/20.34 new_primModNatS2(Zero, Succ(x0)) 41.74/20.34 new_show31(x0) 41.74/20.34 new_show29(x0) 41.74/20.34 new_show21(x0, x1, x2) 41.74/20.34 new_primModNatS2(Succ(x0), Zero) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 41.74/20.34 new_showsPrec(x0, x1, ty_Double) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 41.74/20.34 new_primDivNatS2(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 41.74/20.34 new_showsPrec(x0, x1, ty_HugsException) 41.74/20.34 new_showsPrec(x0, x1, ty_Char) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Zero) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 41.74/20.34 new_primDivNatS01(x0, x1) 41.74/20.34 new_primShowInt0(Neg(x0)) 41.74/20.34 new_show17(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 41.74/20.34 new_primModNatS2(Zero, Zero) 41.74/20.34 new_primModNatS4(x0) 41.74/20.34 new_show30(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, ty_Int) 41.74/20.34 new_show24(x0, x1, x2, x3) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 41.74/20.34 new_primDivNatS4(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 41.74/20.34 new_primShowInt0(Pos(Zero)) 41.74/20.34 new_show16(x0) 41.74/20.34 new_show26(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_Integer) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 41.74/20.34 new_primModNatS02(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 41.74/20.34 new_showsPrec(x0, x1, app(ty_IO, x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 41.74/20.34 new_div(x0, x1) 41.74/20.34 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 41.74/20.34 new_primIntToChar(x0, x1) 41.74/20.34 new_primDivNatS2(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show18(x0) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 41.74/20.34 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 41.74/20.34 new_primDivNatS2(Zero, Zero, x0) 41.74/20.34 new_show20(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Zero) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 41.74/20.34 new_show25(x0, x1) 41.74/20.34 new_show23(x0) 41.74/20.34 new_primModNatS2(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 41.74/20.34 new_primModNatS3(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show28(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_IOErrorKind) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Zero) 41.74/20.34 new_primModNatS3(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, ty_@0) 41.74/20.34 new_primDivNatS3(Zero, Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_Ordering) 41.74/20.34 41.74/20.34 We have to consider all minimal (P,Q,R)-chains. 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (65) TransformationProof (EQUIVALENT) 41.74/20.34 By rewriting [LPAR04] the rule new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_psPs0([], new_showsPrec(ww198, ww199, be))))), be, be) at position [5,1,1,1] we obtained the following new rules [LPAR04]: 41.74/20.34 41.74/20.34 (new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be),new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be)) 41.74/20.34 41.74/20.34 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (66) 41.74/20.34 Obligation: 41.74/20.34 Q DP problem: 41.74/20.34 The TRS P consists of the following rules: 41.74/20.34 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 41.74/20.34 41.74/20.34 The TRS R consists of the following rules: 41.74/20.34 41.74/20.34 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 41.74/20.34 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 41.74/20.34 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 41.74/20.34 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 41.74/20.34 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 41.74/20.34 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 41.74/20.34 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 41.74/20.34 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 41.74/20.34 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 41.74/20.34 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 41.74/20.34 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 41.74/20.34 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 41.74/20.34 new_primModNatS4(ww304) -> Zero 41.74/20.34 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.34 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 41.74/20.34 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 41.74/20.34 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 41.74/20.34 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 41.74/20.34 new_psPs0([], ww200) -> ww200 41.74/20.34 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 41.74/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.34 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 41.74/20.34 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 41.74/20.34 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 41.74/20.34 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 41.74/20.34 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 41.74/20.34 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 41.74/20.34 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 41.74/20.34 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 41.74/20.34 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 41.74/20.34 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 41.74/20.34 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 41.74/20.34 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 41.74/20.34 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.34 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 41.74/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.34 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 41.74/20.34 new_show23(ww194) -> new_primShowInt0(ww194) 41.74/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 41.74/20.34 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 41.74/20.34 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 41.74/20.34 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 41.74/20.34 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 41.74/20.34 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 41.74/20.34 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 41.74/20.34 new_primDivNatS4(ww308) -> Zero 41.74/20.34 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 41.74/20.34 41.74/20.34 The set Q consists of the following terms: 41.74/20.34 41.74/20.34 new_psPs0([], x0) 41.74/20.34 new_show22(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Succ(x2), Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_IOError) 41.74/20.34 new_primModNatS3(Zero, Succ(x0), x1) 41.74/20.34 new_showsPrec(x0, x1, ty_Bool) 41.74/20.34 new_showsPrec(x0, x1, app(ty_[], x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 41.74/20.34 new_show15(x0, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 41.74/20.34 new_psPs0(:(x0, x1), x2) 41.74/20.34 new_primShowInt0(Pos(Succ(x0))) 41.74/20.34 new_show27(x0, x1, x2) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 41.74/20.34 new_primDivNatS3(Zero, Succ(x0)) 41.74/20.34 new_showsPrec(x0, x1, ty_Float) 41.74/20.34 new_primDivNatS3(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 41.74/20.34 new_primDivNatS3(Succ(x0), Zero) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 41.74/20.34 new_pt0(x0, x1, x2, x3, x4, x5) 41.74/20.34 new_show19(x0) 41.74/20.34 new_primModNatS3(Zero, Zero, x0) 41.74/20.34 new_primDivNatS2(Zero, Succ(x0), x1) 41.74/20.34 new_primModNatS2(Zero, Succ(x0)) 41.74/20.34 new_show31(x0) 41.74/20.34 new_show29(x0) 41.74/20.34 new_show21(x0, x1, x2) 41.74/20.34 new_primModNatS2(Succ(x0), Zero) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 41.74/20.34 new_showsPrec(x0, x1, ty_Double) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 41.74/20.34 new_primDivNatS2(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 41.74/20.34 new_showsPrec(x0, x1, ty_HugsException) 41.74/20.34 new_showsPrec(x0, x1, ty_Char) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Zero) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 41.74/20.34 new_primDivNatS01(x0, x1) 41.74/20.34 new_primShowInt0(Neg(x0)) 41.74/20.34 new_show17(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 41.74/20.34 new_primModNatS2(Zero, Zero) 41.74/20.34 new_primModNatS4(x0) 41.74/20.34 new_show30(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, ty_Int) 41.74/20.34 new_show24(x0, x1, x2, x3) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 41.74/20.34 new_primDivNatS4(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 41.74/20.34 new_primShowInt0(Pos(Zero)) 41.74/20.34 new_show16(x0) 41.74/20.34 new_show26(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_Integer) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 41.74/20.34 new_primModNatS02(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 41.74/20.34 new_showsPrec(x0, x1, app(ty_IO, x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 41.74/20.34 new_div(x0, x1) 41.74/20.34 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 41.74/20.34 new_primIntToChar(x0, x1) 41.74/20.34 new_primDivNatS2(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show18(x0) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 41.74/20.34 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 41.74/20.34 new_primDivNatS2(Zero, Zero, x0) 41.74/20.34 new_show20(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Zero) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 41.74/20.34 new_show25(x0, x1) 41.74/20.34 new_show23(x0) 41.74/20.34 new_primModNatS2(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 41.74/20.34 new_primModNatS3(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show28(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_IOErrorKind) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Zero) 41.74/20.34 new_primModNatS3(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, ty_@0) 41.74/20.34 new_primDivNatS3(Zero, Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_Ordering) 41.74/20.34 41.74/20.34 We have to consider all minimal (P,Q,R)-chains. 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (67) TransformationProof (EQUIVALENT) 41.74/20.34 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 41.74/20.34 41.74/20.34 (new_showParen(z5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, app(ty_IO, x6)),new_showParen(z5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, app(ty_IO, x6))) 41.74/20.34 (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))) 41.74/20.34 41.74/20.34 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (68) 41.74/20.34 Obligation: 41.74/20.34 Q DP problem: 41.74/20.34 The TRS P consists of the following rules: 41.74/20.34 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 41.74/20.34 new_showParen(z5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, app(ty_IO, x6)) 41.74/20.34 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)) 41.74/20.34 41.74/20.34 The TRS R consists of the following rules: 41.74/20.34 41.74/20.34 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 41.74/20.34 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 41.74/20.34 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 41.74/20.34 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 41.74/20.34 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 41.74/20.34 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 41.74/20.34 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 41.74/20.34 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 41.74/20.34 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 41.74/20.34 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 41.74/20.34 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 41.74/20.34 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 41.74/20.34 new_primModNatS4(ww304) -> Zero 41.74/20.34 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.34 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 41.74/20.34 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 41.74/20.34 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 41.74/20.34 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 41.74/20.34 new_psPs0([], ww200) -> ww200 41.74/20.34 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 41.74/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.34 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 41.74/20.34 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 41.74/20.34 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 41.74/20.34 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 41.74/20.34 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 41.74/20.34 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 41.74/20.34 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 41.74/20.34 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 41.74/20.34 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 41.74/20.34 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 41.74/20.34 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 41.74/20.34 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 41.74/20.34 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.34 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 41.74/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.34 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 41.74/20.34 new_show23(ww194) -> new_primShowInt0(ww194) 41.74/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 41.74/20.34 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 41.74/20.34 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 41.74/20.34 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 41.74/20.34 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 41.74/20.34 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 41.74/20.34 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 41.74/20.34 new_primDivNatS4(ww308) -> Zero 41.74/20.34 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 41.74/20.34 41.74/20.34 The set Q consists of the following terms: 41.74/20.34 41.74/20.34 new_psPs0([], x0) 41.74/20.34 new_show22(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Succ(x2), Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_IOError) 41.74/20.34 new_primModNatS3(Zero, Succ(x0), x1) 41.74/20.34 new_showsPrec(x0, x1, ty_Bool) 41.74/20.34 new_showsPrec(x0, x1, app(ty_[], x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 41.74/20.34 new_show15(x0, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 41.74/20.34 new_psPs0(:(x0, x1), x2) 41.74/20.34 new_primShowInt0(Pos(Succ(x0))) 41.74/20.34 new_show27(x0, x1, x2) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 41.74/20.34 new_primDivNatS3(Zero, Succ(x0)) 41.74/20.34 new_showsPrec(x0, x1, ty_Float) 41.74/20.34 new_primDivNatS3(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 41.74/20.34 new_primDivNatS3(Succ(x0), Zero) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 41.74/20.34 new_pt0(x0, x1, x2, x3, x4, x5) 41.74/20.34 new_show19(x0) 41.74/20.34 new_primModNatS3(Zero, Zero, x0) 41.74/20.34 new_primDivNatS2(Zero, Succ(x0), x1) 41.74/20.34 new_primModNatS2(Zero, Succ(x0)) 41.74/20.34 new_show31(x0) 41.74/20.34 new_show29(x0) 41.74/20.34 new_show21(x0, x1, x2) 41.74/20.34 new_primModNatS2(Succ(x0), Zero) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 41.74/20.34 new_showsPrec(x0, x1, ty_Double) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 41.74/20.34 new_primDivNatS2(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 41.74/20.34 new_showsPrec(x0, x1, ty_HugsException) 41.74/20.34 new_showsPrec(x0, x1, ty_Char) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Zero) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 41.74/20.34 new_primDivNatS01(x0, x1) 41.74/20.34 new_primShowInt0(Neg(x0)) 41.74/20.34 new_show17(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 41.74/20.34 new_primModNatS2(Zero, Zero) 41.74/20.34 new_primModNatS4(x0) 41.74/20.34 new_show30(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, ty_Int) 41.74/20.34 new_show24(x0, x1, x2, x3) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 41.74/20.34 new_primDivNatS4(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 41.74/20.34 new_primShowInt0(Pos(Zero)) 41.74/20.34 new_show16(x0) 41.74/20.34 new_show26(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_Integer) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 41.74/20.34 new_primModNatS02(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 41.74/20.34 new_showsPrec(x0, x1, app(ty_IO, x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 41.74/20.34 new_div(x0, x1) 41.74/20.34 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 41.74/20.34 new_primIntToChar(x0, x1) 41.74/20.34 new_primDivNatS2(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show18(x0) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 41.74/20.34 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 41.74/20.34 new_primDivNatS2(Zero, Zero, x0) 41.74/20.34 new_show20(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Zero) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 41.74/20.34 new_show25(x0, x1) 41.74/20.34 new_show23(x0) 41.74/20.34 new_primModNatS2(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 41.74/20.34 new_primModNatS3(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show28(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_IOErrorKind) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Zero) 41.74/20.34 new_primModNatS3(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, ty_@0) 41.74/20.34 new_primDivNatS3(Zero, Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_Ordering) 41.74/20.34 41.74/20.34 We have to consider all minimal (P,Q,R)-chains. 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (69) DependencyGraphProof (EQUIVALENT) 41.74/20.34 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (70) 41.74/20.34 Obligation: 41.74/20.34 Q DP problem: 41.74/20.34 The TRS P consists of the following rules: 41.74/20.34 41.74/20.34 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 41.74/20.34 41.74/20.34 The TRS R consists of the following rules: 41.74/20.34 41.74/20.34 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 41.74/20.34 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 41.74/20.34 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 41.74/20.34 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 41.74/20.34 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 41.74/20.34 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 41.74/20.34 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 41.74/20.34 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 41.74/20.34 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 41.74/20.34 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 41.74/20.34 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 41.74/20.34 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 41.74/20.34 new_primModNatS4(ww304) -> Zero 41.74/20.34 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.34 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 41.74/20.34 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 41.74/20.34 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 41.74/20.34 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 41.74/20.34 new_psPs0([], ww200) -> ww200 41.74/20.34 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 41.74/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.34 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 41.74/20.34 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 41.74/20.34 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 41.74/20.34 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 41.74/20.34 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 41.74/20.34 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 41.74/20.34 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 41.74/20.34 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 41.74/20.34 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 41.74/20.34 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 41.74/20.34 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 41.74/20.34 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 41.74/20.34 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.34 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 41.74/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.34 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 41.74/20.34 new_show23(ww194) -> new_primShowInt0(ww194) 41.74/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 41.74/20.34 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 41.74/20.34 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 41.74/20.34 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 41.74/20.34 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 41.74/20.34 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 41.74/20.34 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 41.74/20.34 new_primDivNatS4(ww308) -> Zero 41.74/20.34 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 41.74/20.34 41.74/20.34 The set Q consists of the following terms: 41.74/20.34 41.74/20.34 new_psPs0([], x0) 41.74/20.34 new_show22(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Succ(x2), Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_IOError) 41.74/20.34 new_primModNatS3(Zero, Succ(x0), x1) 41.74/20.34 new_showsPrec(x0, x1, ty_Bool) 41.74/20.34 new_showsPrec(x0, x1, app(ty_[], x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 41.74/20.34 new_show15(x0, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 41.74/20.34 new_psPs0(:(x0, x1), x2) 41.74/20.34 new_primShowInt0(Pos(Succ(x0))) 41.74/20.34 new_show27(x0, x1, x2) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 41.74/20.34 new_primDivNatS3(Zero, Succ(x0)) 41.74/20.34 new_showsPrec(x0, x1, ty_Float) 41.74/20.34 new_primDivNatS3(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 41.74/20.34 new_primDivNatS3(Succ(x0), Zero) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 41.74/20.34 new_pt0(x0, x1, x2, x3, x4, x5) 41.74/20.34 new_show19(x0) 41.74/20.34 new_primModNatS3(Zero, Zero, x0) 41.74/20.34 new_primDivNatS2(Zero, Succ(x0), x1) 41.74/20.34 new_primModNatS2(Zero, Succ(x0)) 41.74/20.34 new_show31(x0) 41.74/20.34 new_show29(x0) 41.74/20.34 new_show21(x0, x1, x2) 41.74/20.34 new_primModNatS2(Succ(x0), Zero) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 41.74/20.34 new_showsPrec(x0, x1, ty_Double) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 41.74/20.34 new_primDivNatS2(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 41.74/20.34 new_showsPrec(x0, x1, ty_HugsException) 41.74/20.34 new_showsPrec(x0, x1, ty_Char) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Zero) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 41.74/20.34 new_primDivNatS01(x0, x1) 41.74/20.34 new_primShowInt0(Neg(x0)) 41.74/20.34 new_show17(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 41.74/20.34 new_primModNatS2(Zero, Zero) 41.74/20.34 new_primModNatS4(x0) 41.74/20.34 new_show30(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, ty_Int) 41.74/20.34 new_show24(x0, x1, x2, x3) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 41.74/20.34 new_primDivNatS4(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 41.74/20.34 new_primShowInt0(Pos(Zero)) 41.74/20.34 new_show16(x0) 41.74/20.34 new_show26(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_Integer) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 41.74/20.34 new_primModNatS02(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 41.74/20.34 new_showsPrec(x0, x1, app(ty_IO, x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 41.74/20.34 new_div(x0, x1) 41.74/20.34 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 41.74/20.34 new_primIntToChar(x0, x1) 41.74/20.34 new_primDivNatS2(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show18(x0) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 41.74/20.34 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 41.74/20.34 new_primDivNatS2(Zero, Zero, x0) 41.74/20.34 new_show20(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Zero) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 41.74/20.34 new_show25(x0, x1) 41.74/20.34 new_show23(x0) 41.74/20.34 new_primModNatS2(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 41.74/20.34 new_primModNatS3(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show28(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_IOErrorKind) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Zero) 41.74/20.34 new_primModNatS3(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, ty_@0) 41.74/20.34 new_primDivNatS3(Zero, Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_Ordering) 41.74/20.34 41.74/20.34 We have to consider all minimal (P,Q,R)-chains. 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (71) TransformationProof (EQUIVALENT) 41.74/20.34 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 41.74/20.34 41.74/20.34 (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError)) 41.74/20.34 (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)) 41.74/20.34 41.74/20.34 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (72) 41.74/20.34 Obligation: 41.74/20.34 Q DP problem: 41.74/20.34 The TRS P consists of the following rules: 41.74/20.34 41.74/20.34 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 41.74/20.34 new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, ty_IOError) 41.74/20.34 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) 41.74/20.34 41.74/20.34 The TRS R consists of the following rules: 41.74/20.34 41.74/20.34 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 41.74/20.34 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 41.74/20.34 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 41.74/20.34 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 41.74/20.34 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 41.74/20.34 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 41.74/20.34 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 41.74/20.34 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 41.74/20.34 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 41.74/20.34 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 41.74/20.34 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 41.74/20.34 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 41.74/20.34 new_primModNatS4(ww304) -> Zero 41.74/20.34 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.34 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 41.74/20.34 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 41.74/20.34 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 41.74/20.34 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 41.74/20.34 new_psPs0([], ww200) -> ww200 41.74/20.34 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 41.74/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.34 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 41.74/20.34 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 41.74/20.34 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 41.74/20.34 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 41.74/20.34 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 41.74/20.34 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 41.74/20.34 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 41.74/20.34 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 41.74/20.34 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 41.74/20.34 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 41.74/20.34 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 41.74/20.34 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 41.74/20.34 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.34 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 41.74/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.34 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 41.74/20.34 new_show23(ww194) -> new_primShowInt0(ww194) 41.74/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 41.74/20.34 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 41.74/20.34 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 41.74/20.34 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 41.74/20.34 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 41.74/20.34 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 41.74/20.34 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 41.74/20.34 new_primDivNatS4(ww308) -> Zero 41.74/20.34 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 41.74/20.34 41.74/20.34 The set Q consists of the following terms: 41.74/20.34 41.74/20.34 new_psPs0([], x0) 41.74/20.34 new_show22(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Succ(x2), Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_IOError) 41.74/20.34 new_primModNatS3(Zero, Succ(x0), x1) 41.74/20.34 new_showsPrec(x0, x1, ty_Bool) 41.74/20.34 new_showsPrec(x0, x1, app(ty_[], x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 41.74/20.34 new_show15(x0, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 41.74/20.34 new_psPs0(:(x0, x1), x2) 41.74/20.34 new_primShowInt0(Pos(Succ(x0))) 41.74/20.34 new_show27(x0, x1, x2) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 41.74/20.34 new_primDivNatS3(Zero, Succ(x0)) 41.74/20.34 new_showsPrec(x0, x1, ty_Float) 41.74/20.34 new_primDivNatS3(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 41.74/20.34 new_primDivNatS3(Succ(x0), Zero) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 41.74/20.34 new_pt0(x0, x1, x2, x3, x4, x5) 41.74/20.34 new_show19(x0) 41.74/20.34 new_primModNatS3(Zero, Zero, x0) 41.74/20.34 new_primDivNatS2(Zero, Succ(x0), x1) 41.74/20.34 new_primModNatS2(Zero, Succ(x0)) 41.74/20.34 new_show31(x0) 41.74/20.34 new_show29(x0) 41.74/20.34 new_show21(x0, x1, x2) 41.74/20.34 new_primModNatS2(Succ(x0), Zero) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 41.74/20.34 new_showsPrec(x0, x1, ty_Double) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 41.74/20.34 new_primDivNatS2(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 41.74/20.34 new_showsPrec(x0, x1, ty_HugsException) 41.74/20.34 new_showsPrec(x0, x1, ty_Char) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Zero) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 41.74/20.34 new_primDivNatS01(x0, x1) 41.74/20.34 new_primShowInt0(Neg(x0)) 41.74/20.34 new_show17(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 41.74/20.34 new_primModNatS2(Zero, Zero) 41.74/20.34 new_primModNatS4(x0) 41.74/20.34 new_show30(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, ty_Int) 41.74/20.34 new_show24(x0, x1, x2, x3) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 41.74/20.34 new_primDivNatS4(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 41.74/20.34 new_primShowInt0(Pos(Zero)) 41.74/20.34 new_show16(x0) 41.74/20.34 new_show26(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_Integer) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 41.74/20.34 new_primModNatS02(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 41.74/20.34 new_showsPrec(x0, x1, app(ty_IO, x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 41.74/20.34 new_div(x0, x1) 41.74/20.34 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 41.74/20.34 new_primIntToChar(x0, x1) 41.74/20.34 new_primDivNatS2(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show18(x0) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 41.74/20.34 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 41.74/20.34 new_primDivNatS2(Zero, Zero, x0) 41.74/20.34 new_show20(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Zero) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 41.74/20.34 new_show25(x0, x1) 41.74/20.34 new_show23(x0) 41.74/20.34 new_primModNatS2(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 41.74/20.34 new_primModNatS3(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show28(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_IOErrorKind) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Zero) 41.74/20.34 new_primModNatS3(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, ty_@0) 41.74/20.34 new_primDivNatS3(Zero, Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_Ordering) 41.74/20.34 41.74/20.34 We have to consider all minimal (P,Q,R)-chains. 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (73) DependencyGraphProof (EQUIVALENT) 41.74/20.34 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (74) 41.74/20.34 Obligation: 41.74/20.34 Q DP problem: 41.74/20.34 The TRS P consists of the following rules: 41.74/20.34 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 41.74/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 41.74/20.34 41.74/20.34 The TRS R consists of the following rules: 41.74/20.34 41.74/20.34 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 41.74/20.34 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 41.74/20.34 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 41.74/20.34 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 41.74/20.34 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 41.74/20.34 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 41.74/20.34 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 41.74/20.34 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 41.74/20.34 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 41.74/20.34 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 41.74/20.34 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 41.74/20.34 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 41.74/20.34 new_primModNatS4(ww304) -> Zero 41.74/20.34 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.34 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 41.74/20.34 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 41.74/20.34 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 41.74/20.34 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 41.74/20.34 new_psPs0([], ww200) -> ww200 41.74/20.34 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 41.74/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 41.74/20.34 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 41.74/20.34 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 41.74/20.34 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 41.74/20.34 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 41.74/20.34 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 41.74/20.34 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 41.74/20.34 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 41.74/20.34 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 41.74/20.34 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 41.74/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 41.74/20.34 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 41.74/20.34 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 41.74/20.34 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 41.74/20.34 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.34 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 41.74/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 41.74/20.34 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 41.74/20.34 new_show23(ww194) -> new_primShowInt0(ww194) 41.74/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 41.74/20.34 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 41.74/20.34 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 41.74/20.34 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 41.74/20.34 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 41.74/20.34 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 41.74/20.34 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 41.74/20.34 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 41.74/20.34 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 41.74/20.34 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 41.74/20.34 new_primDivNatS4(ww308) -> Zero 41.74/20.34 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 41.74/20.34 41.74/20.34 The set Q consists of the following terms: 41.74/20.34 41.74/20.34 new_psPs0([], x0) 41.74/20.34 new_show22(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Succ(x2), Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_IOError) 41.74/20.34 new_primModNatS3(Zero, Succ(x0), x1) 41.74/20.34 new_showsPrec(x0, x1, ty_Bool) 41.74/20.34 new_showsPrec(x0, x1, app(ty_[], x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 41.74/20.34 new_show15(x0, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 41.74/20.34 new_psPs0(:(x0, x1), x2) 41.74/20.34 new_primShowInt0(Pos(Succ(x0))) 41.74/20.34 new_show27(x0, x1, x2) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 41.74/20.34 new_primDivNatS3(Zero, Succ(x0)) 41.74/20.34 new_showsPrec(x0, x1, ty_Float) 41.74/20.34 new_primDivNatS3(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 41.74/20.34 new_primDivNatS3(Succ(x0), Zero) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 41.74/20.34 new_pt0(x0, x1, x2, x3, x4, x5) 41.74/20.34 new_show19(x0) 41.74/20.34 new_primModNatS3(Zero, Zero, x0) 41.74/20.34 new_primDivNatS2(Zero, Succ(x0), x1) 41.74/20.34 new_primModNatS2(Zero, Succ(x0)) 41.74/20.34 new_show31(x0) 41.74/20.34 new_show29(x0) 41.74/20.34 new_show21(x0, x1, x2) 41.74/20.34 new_primModNatS2(Succ(x0), Zero) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 41.74/20.34 new_showsPrec(x0, x1, ty_Double) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 41.74/20.34 new_primDivNatS2(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 41.74/20.34 new_showsPrec(x0, x1, ty_HugsException) 41.74/20.34 new_showsPrec(x0, x1, ty_Char) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Zero) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 41.74/20.34 new_primDivNatS01(x0, x1) 41.74/20.34 new_primShowInt0(Neg(x0)) 41.74/20.34 new_show17(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 41.74/20.34 new_primModNatS2(Zero, Zero) 41.74/20.34 new_primModNatS4(x0) 41.74/20.34 new_show30(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, ty_Int) 41.74/20.34 new_show24(x0, x1, x2, x3) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 41.74/20.34 new_primDivNatS4(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 41.74/20.34 new_primShowInt0(Pos(Zero)) 41.74/20.34 new_show16(x0) 41.74/20.34 new_show26(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_Integer) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 41.74/20.34 new_primModNatS02(x0, x1) 41.74/20.34 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 41.74/20.34 new_showsPrec(x0, x1, app(ty_IO, x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 41.74/20.34 new_div(x0, x1) 41.74/20.34 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 41.74/20.34 new_primIntToChar(x0, x1) 41.74/20.34 new_primDivNatS2(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show18(x0) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 41.74/20.34 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 41.74/20.34 new_primDivNatS2(Zero, Zero, x0) 41.74/20.34 new_show20(x0) 41.74/20.34 new_primDivNatS02(x0, x1, Zero, Zero) 41.74/20.34 new_primModNatS01(x0, x1, Zero, Succ(x2)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 41.74/20.34 new_show25(x0, x1) 41.74/20.34 new_show23(x0) 41.74/20.34 new_primModNatS2(Succ(x0), Succ(x1)) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 41.74/20.34 new_primModNatS3(Succ(x0), Succ(x1), x2) 41.74/20.34 new_show28(x0) 41.74/20.34 new_showsPrec(x0, x1, ty_IOErrorKind) 41.74/20.34 new_primModNatS01(x0, x1, Succ(x2), Zero) 41.74/20.34 new_primModNatS3(Succ(x0), Zero, x1) 41.74/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 41.74/20.34 new_showsPrec(x0, x1, ty_@0) 41.74/20.34 new_primDivNatS3(Zero, Zero) 41.74/20.34 new_showsPrec(x0, x1, ty_Ordering) 41.74/20.34 41.74/20.34 We have to consider all minimal (P,Q,R)-chains. 41.74/20.34 ---------------------------------------- 41.74/20.34 41.74/20.34 (75) TransformationProof (EQUIVALENT) 41.74/20.34 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 41.74/20.34 41.74/20.34 (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)) 42.09/20.34 (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)) 42.09/20.34 42.09/20.34 42.09/20.34 ---------------------------------------- 42.09/20.34 42.09/20.34 (76) 42.09/20.34 Obligation: 42.09/20.34 Q DP problem: 42.09/20.34 The TRS P consists of the following rules: 42.09/20.34 42.09/20.34 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.34 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) 42.09/20.34 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) 42.09/20.34 42.09/20.34 The TRS R consists of the following rules: 42.09/20.34 42.09/20.34 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.34 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.34 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.34 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.34 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.34 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.34 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.34 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.34 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.34 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.34 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.34 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.34 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.34 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.34 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.34 new_primModNatS4(ww304) -> Zero 42.09/20.34 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.34 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.34 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.34 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.34 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.34 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.34 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.34 new_psPs0([], ww200) -> ww200 42.09/20.34 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.34 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.34 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.34 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.34 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.34 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.34 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.34 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.34 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.34 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.34 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.34 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.34 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.34 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.34 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.34 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.34 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.34 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.34 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.34 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.34 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.34 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.34 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.34 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.34 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.34 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.34 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.34 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.34 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.34 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.34 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.34 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.34 new_primDivNatS4(ww308) -> Zero 42.09/20.34 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.34 42.09/20.34 The set Q consists of the following terms: 42.09/20.34 42.09/20.34 new_psPs0([], x0) 42.09/20.34 new_show22(x0) 42.09/20.34 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.34 new_showsPrec(x0, x1, ty_IOError) 42.09/20.34 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.34 new_showsPrec(x0, x1, ty_Bool) 42.09/20.34 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.34 new_show15(x0, x1) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.34 new_psPs0(:(x0, x1), x2) 42.09/20.34 new_primShowInt0(Pos(Succ(x0))) 42.09/20.34 new_show27(x0, x1, x2) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.34 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.34 new_showsPrec(x0, x1, ty_Float) 42.09/20.34 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.34 new_primDivNatS3(Succ(x0), Zero) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.34 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.34 new_show19(x0) 42.09/20.34 new_primModNatS3(Zero, Zero, x0) 42.09/20.34 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.34 new_primModNatS2(Zero, Succ(x0)) 42.09/20.34 new_show31(x0) 42.09/20.34 new_show29(x0) 42.09/20.34 new_show21(x0, x1, x2) 42.09/20.34 new_primModNatS2(Succ(x0), Zero) 42.09/20.34 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.34 new_showsPrec(x0, x1, ty_Double) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.34 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.34 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.34 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.34 new_showsPrec(x0, x1, ty_Char) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.34 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.34 new_primDivNatS01(x0, x1) 42.09/20.34 new_primShowInt0(Neg(x0)) 42.09/20.34 new_show17(x0) 42.09/20.34 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.34 new_primModNatS2(Zero, Zero) 42.09/20.34 new_primModNatS4(x0) 42.09/20.34 new_show30(x0, x1) 42.09/20.34 new_showsPrec(x0, x1, ty_Int) 42.09/20.34 new_show24(x0, x1, x2, x3) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.34 new_primDivNatS4(x0) 42.09/20.34 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.34 new_primShowInt0(Pos(Zero)) 42.09/20.34 new_show16(x0) 42.09/20.34 new_show26(x0) 42.09/20.34 new_showsPrec(x0, x1, ty_Integer) 42.09/20.34 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.34 new_primModNatS02(x0, x1) 42.09/20.34 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.34 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.34 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.34 new_div(x0, x1) 42.09/20.34 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.34 new_primIntToChar(x0, x1) 42.09/20.34 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.34 new_show18(x0) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.34 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.34 new_primDivNatS2(Zero, Zero, x0) 42.09/20.34 new_show20(x0) 42.09/20.34 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.34 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.34 new_show25(x0, x1) 42.09/20.34 new_show23(x0) 42.09/20.34 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.34 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.34 new_show28(x0) 42.09/20.34 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.34 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.34 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.34 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.34 new_showsPrec(x0, x1, ty_@0) 42.09/20.34 new_primDivNatS3(Zero, Zero) 42.09/20.34 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.34 42.09/20.34 We have to consider all minimal (P,Q,R)-chains. 42.09/20.34 ---------------------------------------- 42.09/20.34 42.09/20.34 (77) DependencyGraphProof (EQUIVALENT) 42.09/20.34 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.34 ---------------------------------------- 42.09/20.34 42.09/20.34 (78) 42.09/20.34 Obligation: 42.09/20.34 Q DP problem: 42.09/20.34 The TRS P consists of the following rules: 42.09/20.34 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.34 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.34 42.09/20.34 The TRS R consists of the following rules: 42.09/20.34 42.09/20.34 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.34 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.34 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.34 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.34 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.34 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.34 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.34 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.34 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.34 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.34 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.34 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.34 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.34 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.34 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.34 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.34 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.34 new_primModNatS4(ww304) -> Zero 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.35 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.35 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.35 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.35 new_psPs0([], ww200) -> ww200 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.35 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.35 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.35 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.35 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.35 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.35 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.35 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.35 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.35 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.35 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.35 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.35 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.35 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.35 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.35 new_primDivNatS4(ww308) -> Zero 42.09/20.35 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.35 42.09/20.35 The set Q consists of the following terms: 42.09/20.35 42.09/20.35 new_psPs0([], x0) 42.09/20.35 new_show22(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_IOError) 42.09/20.35 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Bool) 42.09/20.35 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.35 new_show15(x0, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.35 new_psPs0(:(x0, x1), x2) 42.09/20.35 new_primShowInt0(Pos(Succ(x0))) 42.09/20.35 new_show27(x0, x1, x2) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.35 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.35 new_showsPrec(x0, x1, ty_Float) 42.09/20.35 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.35 new_primDivNatS3(Succ(x0), Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.35 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.35 new_show19(x0) 42.09/20.35 new_primModNatS3(Zero, Zero, x0) 42.09/20.35 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.35 new_primModNatS2(Zero, Succ(x0)) 42.09/20.35 new_show31(x0) 42.09/20.35 new_show29(x0) 42.09/20.35 new_show21(x0, x1, x2) 42.09/20.35 new_primModNatS2(Succ(x0), Zero) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_showsPrec(x0, x1, ty_Double) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.35 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.35 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.35 new_showsPrec(x0, x1, ty_Char) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.35 new_primDivNatS01(x0, x1) 42.09/20.35 new_primShowInt0(Neg(x0)) 42.09/20.35 new_show17(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_primModNatS2(Zero, Zero) 42.09/20.35 new_primModNatS4(x0) 42.09/20.35 new_show30(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Int) 42.09/20.35 new_show24(x0, x1, x2, x3) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.35 new_primDivNatS4(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.35 new_primShowInt0(Pos(Zero)) 42.09/20.35 new_show16(x0) 42.09/20.35 new_show26(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_Integer) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.35 new_primModNatS02(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.35 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.35 new_div(x0, x1) 42.09/20.35 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.35 new_primIntToChar(x0, x1) 42.09/20.35 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show18(x0) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.35 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.35 new_primDivNatS2(Zero, Zero, x0) 42.09/20.35 new_show20(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.35 new_show25(x0, x1) 42.09/20.35 new_show23(x0) 42.09/20.35 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.35 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show28(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.35 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, ty_@0) 42.09/20.35 new_primDivNatS3(Zero, Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.35 42.09/20.35 We have to consider all minimal (P,Q,R)-chains. 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (79) TransformationProof (EQUIVALENT) 42.09/20.35 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.35 42.09/20.35 (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)) 42.09/20.35 (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)) 42.09/20.35 42.09/20.35 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (80) 42.09/20.35 Obligation: 42.09/20.35 Q DP problem: 42.09/20.35 The TRS P consists of the following rules: 42.09/20.35 42.09/20.35 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.35 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) 42.09/20.35 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) 42.09/20.35 42.09/20.35 The TRS R consists of the following rules: 42.09/20.35 42.09/20.35 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.35 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.35 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.35 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.35 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.35 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.35 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.35 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.35 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.35 new_primModNatS4(ww304) -> Zero 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.35 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.35 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.35 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.35 new_psPs0([], ww200) -> ww200 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.35 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.35 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.35 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.35 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.35 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.35 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.35 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.35 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.35 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.35 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.35 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.35 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.35 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.35 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.35 new_primDivNatS4(ww308) -> Zero 42.09/20.35 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.35 42.09/20.35 The set Q consists of the following terms: 42.09/20.35 42.09/20.35 new_psPs0([], x0) 42.09/20.35 new_show22(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_IOError) 42.09/20.35 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Bool) 42.09/20.35 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.35 new_show15(x0, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.35 new_psPs0(:(x0, x1), x2) 42.09/20.35 new_primShowInt0(Pos(Succ(x0))) 42.09/20.35 new_show27(x0, x1, x2) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.35 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.35 new_showsPrec(x0, x1, ty_Float) 42.09/20.35 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.35 new_primDivNatS3(Succ(x0), Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.35 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.35 new_show19(x0) 42.09/20.35 new_primModNatS3(Zero, Zero, x0) 42.09/20.35 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.35 new_primModNatS2(Zero, Succ(x0)) 42.09/20.35 new_show31(x0) 42.09/20.35 new_show29(x0) 42.09/20.35 new_show21(x0, x1, x2) 42.09/20.35 new_primModNatS2(Succ(x0), Zero) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_showsPrec(x0, x1, ty_Double) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.35 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.35 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.35 new_showsPrec(x0, x1, ty_Char) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.35 new_primDivNatS01(x0, x1) 42.09/20.35 new_primShowInt0(Neg(x0)) 42.09/20.35 new_show17(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_primModNatS2(Zero, Zero) 42.09/20.35 new_primModNatS4(x0) 42.09/20.35 new_show30(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Int) 42.09/20.35 new_show24(x0, x1, x2, x3) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.35 new_primDivNatS4(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.35 new_primShowInt0(Pos(Zero)) 42.09/20.35 new_show16(x0) 42.09/20.35 new_show26(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_Integer) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.35 new_primModNatS02(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.35 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.35 new_div(x0, x1) 42.09/20.35 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.35 new_primIntToChar(x0, x1) 42.09/20.35 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show18(x0) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.35 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.35 new_primDivNatS2(Zero, Zero, x0) 42.09/20.35 new_show20(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.35 new_show25(x0, x1) 42.09/20.35 new_show23(x0) 42.09/20.35 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.35 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show28(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.35 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, ty_@0) 42.09/20.35 new_primDivNatS3(Zero, Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.35 42.09/20.35 We have to consider all minimal (P,Q,R)-chains. 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (81) DependencyGraphProof (EQUIVALENT) 42.09/20.35 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (82) 42.09/20.35 Obligation: 42.09/20.35 Q DP problem: 42.09/20.35 The TRS P consists of the following rules: 42.09/20.35 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.35 42.09/20.35 The TRS R consists of the following rules: 42.09/20.35 42.09/20.35 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.35 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.35 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.35 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.35 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.35 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.35 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.35 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.35 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.35 new_primModNatS4(ww304) -> Zero 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.35 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.35 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.35 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.35 new_psPs0([], ww200) -> ww200 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.35 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.35 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.35 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.35 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.35 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.35 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.35 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.35 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.35 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.35 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.35 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.35 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.35 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.35 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.35 new_primDivNatS4(ww308) -> Zero 42.09/20.35 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.35 42.09/20.35 The set Q consists of the following terms: 42.09/20.35 42.09/20.35 new_psPs0([], x0) 42.09/20.35 new_show22(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_IOError) 42.09/20.35 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Bool) 42.09/20.35 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.35 new_show15(x0, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.35 new_psPs0(:(x0, x1), x2) 42.09/20.35 new_primShowInt0(Pos(Succ(x0))) 42.09/20.35 new_show27(x0, x1, x2) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.35 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.35 new_showsPrec(x0, x1, ty_Float) 42.09/20.35 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.35 new_primDivNatS3(Succ(x0), Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.35 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.35 new_show19(x0) 42.09/20.35 new_primModNatS3(Zero, Zero, x0) 42.09/20.35 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.35 new_primModNatS2(Zero, Succ(x0)) 42.09/20.35 new_show31(x0) 42.09/20.35 new_show29(x0) 42.09/20.35 new_show21(x0, x1, x2) 42.09/20.35 new_primModNatS2(Succ(x0), Zero) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_showsPrec(x0, x1, ty_Double) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.35 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.35 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.35 new_showsPrec(x0, x1, ty_Char) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.35 new_primDivNatS01(x0, x1) 42.09/20.35 new_primShowInt0(Neg(x0)) 42.09/20.35 new_show17(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_primModNatS2(Zero, Zero) 42.09/20.35 new_primModNatS4(x0) 42.09/20.35 new_show30(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Int) 42.09/20.35 new_show24(x0, x1, x2, x3) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.35 new_primDivNatS4(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.35 new_primShowInt0(Pos(Zero)) 42.09/20.35 new_show16(x0) 42.09/20.35 new_show26(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_Integer) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.35 new_primModNatS02(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.35 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.35 new_div(x0, x1) 42.09/20.35 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.35 new_primIntToChar(x0, x1) 42.09/20.35 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show18(x0) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.35 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.35 new_primDivNatS2(Zero, Zero, x0) 42.09/20.35 new_show20(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.35 new_show25(x0, x1) 42.09/20.35 new_show23(x0) 42.09/20.35 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.35 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show28(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.35 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, ty_@0) 42.09/20.35 new_primDivNatS3(Zero, Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.35 42.09/20.35 We have to consider all minimal (P,Q,R)-chains. 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (83) TransformationProof (EQUIVALENT) 42.09/20.35 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.35 42.09/20.35 (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))) 42.09/20.35 (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))) 42.09/20.35 42.09/20.35 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (84) 42.09/20.35 Obligation: 42.09/20.35 Q DP problem: 42.09/20.35 The TRS P consists of the following rules: 42.09/20.35 42.09/20.35 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.35 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)) 42.09/20.35 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)) 42.09/20.35 42.09/20.35 The TRS R consists of the following rules: 42.09/20.35 42.09/20.35 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.35 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.35 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.35 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.35 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.35 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.35 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.35 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.35 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.35 new_primModNatS4(ww304) -> Zero 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.35 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.35 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.35 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.35 new_psPs0([], ww200) -> ww200 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.35 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.35 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.35 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.35 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.35 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.35 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.35 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.35 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.35 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.35 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.35 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.35 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.35 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.35 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.35 new_primDivNatS4(ww308) -> Zero 42.09/20.35 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.35 42.09/20.35 The set Q consists of the following terms: 42.09/20.35 42.09/20.35 new_psPs0([], x0) 42.09/20.35 new_show22(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_IOError) 42.09/20.35 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Bool) 42.09/20.35 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.35 new_show15(x0, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.35 new_psPs0(:(x0, x1), x2) 42.09/20.35 new_primShowInt0(Pos(Succ(x0))) 42.09/20.35 new_show27(x0, x1, x2) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.35 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.35 new_showsPrec(x0, x1, ty_Float) 42.09/20.35 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.35 new_primDivNatS3(Succ(x0), Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.35 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.35 new_show19(x0) 42.09/20.35 new_primModNatS3(Zero, Zero, x0) 42.09/20.35 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.35 new_primModNatS2(Zero, Succ(x0)) 42.09/20.35 new_show31(x0) 42.09/20.35 new_show29(x0) 42.09/20.35 new_show21(x0, x1, x2) 42.09/20.35 new_primModNatS2(Succ(x0), Zero) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_showsPrec(x0, x1, ty_Double) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.35 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.35 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.35 new_showsPrec(x0, x1, ty_Char) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.35 new_primDivNatS01(x0, x1) 42.09/20.35 new_primShowInt0(Neg(x0)) 42.09/20.35 new_show17(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_primModNatS2(Zero, Zero) 42.09/20.35 new_primModNatS4(x0) 42.09/20.35 new_show30(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Int) 42.09/20.35 new_show24(x0, x1, x2, x3) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.35 new_primDivNatS4(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.35 new_primShowInt0(Pos(Zero)) 42.09/20.35 new_show16(x0) 42.09/20.35 new_show26(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_Integer) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.35 new_primModNatS02(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.35 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.35 new_div(x0, x1) 42.09/20.35 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.35 new_primIntToChar(x0, x1) 42.09/20.35 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show18(x0) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.35 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.35 new_primDivNatS2(Zero, Zero, x0) 42.09/20.35 new_show20(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.35 new_show25(x0, x1) 42.09/20.35 new_show23(x0) 42.09/20.35 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.35 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show28(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.35 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, ty_@0) 42.09/20.35 new_primDivNatS3(Zero, Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.35 42.09/20.35 We have to consider all minimal (P,Q,R)-chains. 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (85) DependencyGraphProof (EQUIVALENT) 42.09/20.35 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (86) 42.09/20.35 Obligation: 42.09/20.35 Q DP problem: 42.09/20.35 The TRS P consists of the following rules: 42.09/20.35 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.35 42.09/20.35 The TRS R consists of the following rules: 42.09/20.35 42.09/20.35 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.35 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.35 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.35 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.35 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.35 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.35 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.35 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.35 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.35 new_primModNatS4(ww304) -> Zero 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.35 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.35 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.35 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.35 new_psPs0([], ww200) -> ww200 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.35 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.35 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.35 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.35 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.35 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.35 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.35 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.35 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.35 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.35 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.35 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.35 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.35 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.35 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.35 new_primDivNatS4(ww308) -> Zero 42.09/20.35 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.35 42.09/20.35 The set Q consists of the following terms: 42.09/20.35 42.09/20.35 new_psPs0([], x0) 42.09/20.35 new_show22(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_IOError) 42.09/20.35 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Bool) 42.09/20.35 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.35 new_show15(x0, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.35 new_psPs0(:(x0, x1), x2) 42.09/20.35 new_primShowInt0(Pos(Succ(x0))) 42.09/20.35 new_show27(x0, x1, x2) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.35 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.35 new_showsPrec(x0, x1, ty_Float) 42.09/20.35 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.35 new_primDivNatS3(Succ(x0), Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.35 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.35 new_show19(x0) 42.09/20.35 new_primModNatS3(Zero, Zero, x0) 42.09/20.35 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.35 new_primModNatS2(Zero, Succ(x0)) 42.09/20.35 new_show31(x0) 42.09/20.35 new_show29(x0) 42.09/20.35 new_show21(x0, x1, x2) 42.09/20.35 new_primModNatS2(Succ(x0), Zero) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_showsPrec(x0, x1, ty_Double) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.35 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.35 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.35 new_showsPrec(x0, x1, ty_Char) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.35 new_primDivNatS01(x0, x1) 42.09/20.35 new_primShowInt0(Neg(x0)) 42.09/20.35 new_show17(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_primModNatS2(Zero, Zero) 42.09/20.35 new_primModNatS4(x0) 42.09/20.35 new_show30(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Int) 42.09/20.35 new_show24(x0, x1, x2, x3) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.35 new_primDivNatS4(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.35 new_primShowInt0(Pos(Zero)) 42.09/20.35 new_show16(x0) 42.09/20.35 new_show26(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_Integer) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.35 new_primModNatS02(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.35 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.35 new_div(x0, x1) 42.09/20.35 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.35 new_primIntToChar(x0, x1) 42.09/20.35 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show18(x0) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.35 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.35 new_primDivNatS2(Zero, Zero, x0) 42.09/20.35 new_show20(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.35 new_show25(x0, x1) 42.09/20.35 new_show23(x0) 42.09/20.35 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.35 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show28(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.35 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, ty_@0) 42.09/20.35 new_primDivNatS3(Zero, Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.35 42.09/20.35 We have to consider all minimal (P,Q,R)-chains. 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (87) TransformationProof (EQUIVALENT) 42.09/20.35 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.35 42.09/20.35 (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)) 42.09/20.35 (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)) 42.09/20.35 42.09/20.35 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (88) 42.09/20.35 Obligation: 42.09/20.35 Q DP problem: 42.09/20.35 The TRS P consists of the following rules: 42.09/20.35 42.09/20.35 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.35 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) 42.09/20.35 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) 42.09/20.35 42.09/20.35 The TRS R consists of the following rules: 42.09/20.35 42.09/20.35 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.35 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.35 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.35 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.35 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.35 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.35 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.35 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.35 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.35 new_primModNatS4(ww304) -> Zero 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.35 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.35 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.35 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.35 new_psPs0([], ww200) -> ww200 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.35 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.35 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.35 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.35 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.35 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.35 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.35 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.35 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.35 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.35 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.35 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.35 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.35 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.35 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.35 new_primDivNatS4(ww308) -> Zero 42.09/20.35 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.35 42.09/20.35 The set Q consists of the following terms: 42.09/20.35 42.09/20.35 new_psPs0([], x0) 42.09/20.35 new_show22(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_IOError) 42.09/20.35 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Bool) 42.09/20.35 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.35 new_show15(x0, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.35 new_psPs0(:(x0, x1), x2) 42.09/20.35 new_primShowInt0(Pos(Succ(x0))) 42.09/20.35 new_show27(x0, x1, x2) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.35 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.35 new_showsPrec(x0, x1, ty_Float) 42.09/20.35 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.35 new_primDivNatS3(Succ(x0), Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.35 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.35 new_show19(x0) 42.09/20.35 new_primModNatS3(Zero, Zero, x0) 42.09/20.35 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.35 new_primModNatS2(Zero, Succ(x0)) 42.09/20.35 new_show31(x0) 42.09/20.35 new_show29(x0) 42.09/20.35 new_show21(x0, x1, x2) 42.09/20.35 new_primModNatS2(Succ(x0), Zero) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_showsPrec(x0, x1, ty_Double) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.35 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.35 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.35 new_showsPrec(x0, x1, ty_Char) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.35 new_primDivNatS01(x0, x1) 42.09/20.35 new_primShowInt0(Neg(x0)) 42.09/20.35 new_show17(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_primModNatS2(Zero, Zero) 42.09/20.35 new_primModNatS4(x0) 42.09/20.35 new_show30(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Int) 42.09/20.35 new_show24(x0, x1, x2, x3) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.35 new_primDivNatS4(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.35 new_primShowInt0(Pos(Zero)) 42.09/20.35 new_show16(x0) 42.09/20.35 new_show26(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_Integer) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.35 new_primModNatS02(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.35 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.35 new_div(x0, x1) 42.09/20.35 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.35 new_primIntToChar(x0, x1) 42.09/20.35 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show18(x0) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.35 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.35 new_primDivNatS2(Zero, Zero, x0) 42.09/20.35 new_show20(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.35 new_show25(x0, x1) 42.09/20.35 new_show23(x0) 42.09/20.35 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.35 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show28(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.35 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, ty_@0) 42.09/20.35 new_primDivNatS3(Zero, Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.35 42.09/20.35 We have to consider all minimal (P,Q,R)-chains. 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (89) DependencyGraphProof (EQUIVALENT) 42.09/20.35 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (90) 42.09/20.35 Obligation: 42.09/20.35 Q DP problem: 42.09/20.35 The TRS P consists of the following rules: 42.09/20.35 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.35 42.09/20.35 The TRS R consists of the following rules: 42.09/20.35 42.09/20.35 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.35 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.35 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.35 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.35 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.35 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.35 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.35 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.35 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.35 new_primModNatS4(ww304) -> Zero 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.35 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.35 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.35 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.35 new_psPs0([], ww200) -> ww200 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.35 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.35 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.35 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.35 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.35 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.35 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.35 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.35 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.35 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.35 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.35 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.35 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.35 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.35 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.35 new_primDivNatS4(ww308) -> Zero 42.09/20.35 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.35 42.09/20.35 The set Q consists of the following terms: 42.09/20.35 42.09/20.35 new_psPs0([], x0) 42.09/20.35 new_show22(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_IOError) 42.09/20.35 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Bool) 42.09/20.35 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.35 new_show15(x0, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.35 new_psPs0(:(x0, x1), x2) 42.09/20.35 new_primShowInt0(Pos(Succ(x0))) 42.09/20.35 new_show27(x0, x1, x2) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.35 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.35 new_showsPrec(x0, x1, ty_Float) 42.09/20.35 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.35 new_primDivNatS3(Succ(x0), Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.35 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.35 new_show19(x0) 42.09/20.35 new_primModNatS3(Zero, Zero, x0) 42.09/20.35 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.35 new_primModNatS2(Zero, Succ(x0)) 42.09/20.35 new_show31(x0) 42.09/20.35 new_show29(x0) 42.09/20.35 new_show21(x0, x1, x2) 42.09/20.35 new_primModNatS2(Succ(x0), Zero) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_showsPrec(x0, x1, ty_Double) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.35 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.35 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.35 new_showsPrec(x0, x1, ty_Char) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.35 new_primDivNatS01(x0, x1) 42.09/20.35 new_primShowInt0(Neg(x0)) 42.09/20.35 new_show17(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_primModNatS2(Zero, Zero) 42.09/20.35 new_primModNatS4(x0) 42.09/20.35 new_show30(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Int) 42.09/20.35 new_show24(x0, x1, x2, x3) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.35 new_primDivNatS4(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.35 new_primShowInt0(Pos(Zero)) 42.09/20.35 new_show16(x0) 42.09/20.35 new_show26(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_Integer) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.35 new_primModNatS02(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.35 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.35 new_div(x0, x1) 42.09/20.35 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.35 new_primIntToChar(x0, x1) 42.09/20.35 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show18(x0) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.35 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.35 new_primDivNatS2(Zero, Zero, x0) 42.09/20.35 new_show20(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.35 new_show25(x0, x1) 42.09/20.35 new_show23(x0) 42.09/20.35 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.35 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show28(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.35 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, ty_@0) 42.09/20.35 new_primDivNatS3(Zero, Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.35 42.09/20.35 We have to consider all minimal (P,Q,R)-chains. 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (91) TransformationProof (EQUIVALENT) 42.09/20.35 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.35 42.09/20.35 (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)) 42.09/20.35 (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)) 42.09/20.35 42.09/20.35 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (92) 42.09/20.35 Obligation: 42.09/20.35 Q DP problem: 42.09/20.35 The TRS P consists of the following rules: 42.09/20.35 42.09/20.35 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.35 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) 42.09/20.35 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) 42.09/20.35 42.09/20.35 The TRS R consists of the following rules: 42.09/20.35 42.09/20.35 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.35 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.35 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.35 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.35 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.35 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.35 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.35 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.35 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.35 new_primModNatS4(ww304) -> Zero 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.35 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.35 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.35 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.35 new_psPs0([], ww200) -> ww200 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.35 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.35 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.35 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.35 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.35 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.35 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.35 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.35 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.35 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.35 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.35 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.35 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.35 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.35 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.35 new_primDivNatS4(ww308) -> Zero 42.09/20.35 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.35 42.09/20.35 The set Q consists of the following terms: 42.09/20.35 42.09/20.35 new_psPs0([], x0) 42.09/20.35 new_show22(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_IOError) 42.09/20.35 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Bool) 42.09/20.35 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.35 new_show15(x0, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.35 new_psPs0(:(x0, x1), x2) 42.09/20.35 new_primShowInt0(Pos(Succ(x0))) 42.09/20.35 new_show27(x0, x1, x2) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.35 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.35 new_showsPrec(x0, x1, ty_Float) 42.09/20.35 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.35 new_primDivNatS3(Succ(x0), Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.35 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.35 new_show19(x0) 42.09/20.35 new_primModNatS3(Zero, Zero, x0) 42.09/20.35 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.35 new_primModNatS2(Zero, Succ(x0)) 42.09/20.35 new_show31(x0) 42.09/20.35 new_show29(x0) 42.09/20.35 new_show21(x0, x1, x2) 42.09/20.35 new_primModNatS2(Succ(x0), Zero) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_showsPrec(x0, x1, ty_Double) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.35 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.35 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.35 new_showsPrec(x0, x1, ty_Char) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.35 new_primDivNatS01(x0, x1) 42.09/20.35 new_primShowInt0(Neg(x0)) 42.09/20.35 new_show17(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.35 new_primModNatS2(Zero, Zero) 42.09/20.35 new_primModNatS4(x0) 42.09/20.35 new_show30(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Int) 42.09/20.35 new_show24(x0, x1, x2, x3) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.35 new_primDivNatS4(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.35 new_primShowInt0(Pos(Zero)) 42.09/20.35 new_show16(x0) 42.09/20.35 new_show26(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_Integer) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.35 new_primModNatS02(x0, x1) 42.09/20.35 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.35 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.35 new_div(x0, x1) 42.09/20.35 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.35 new_primIntToChar(x0, x1) 42.09/20.35 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show18(x0) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.35 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.35 new_primDivNatS2(Zero, Zero, x0) 42.09/20.35 new_show20(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.35 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.35 new_show25(x0, x1) 42.09/20.35 new_show23(x0) 42.09/20.35 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.35 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.35 new_show28(x0) 42.09/20.35 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.35 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.35 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.35 new_showsPrec(x0, x1, ty_@0) 42.09/20.35 new_primDivNatS3(Zero, Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.35 42.09/20.35 We have to consider all minimal (P,Q,R)-chains. 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (93) DependencyGraphProof (EQUIVALENT) 42.09/20.35 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.35 ---------------------------------------- 42.09/20.35 42.09/20.35 (94) 42.09/20.35 Obligation: 42.09/20.35 Q DP problem: 42.09/20.35 The TRS P consists of the following rules: 42.09/20.35 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.35 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.35 42.09/20.35 The TRS R consists of the following rules: 42.09/20.35 42.09/20.35 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.35 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.35 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.35 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.35 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.35 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.35 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.35 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.35 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.35 new_primModNatS4(ww304) -> Zero 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.35 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.35 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.35 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.35 new_psPs0([], ww200) -> ww200 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.35 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.35 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.35 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.35 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.35 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.35 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.35 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.35 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.35 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.35 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.35 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.35 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.35 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.35 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.35 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.35 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.35 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.35 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.35 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.35 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.35 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.35 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.35 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.35 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.35 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.35 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.35 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.35 new_primDivNatS4(ww308) -> Zero 42.09/20.35 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.35 42.09/20.35 The set Q consists of the following terms: 42.09/20.35 42.09/20.35 new_psPs0([], x0) 42.09/20.35 new_show22(x0) 42.09/20.35 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.35 new_showsPrec(x0, x1, ty_IOError) 42.09/20.35 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.35 new_showsPrec(x0, x1, ty_Bool) 42.09/20.35 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.35 new_show15(x0, x1) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.35 new_psPs0(:(x0, x1), x2) 42.09/20.35 new_primShowInt0(Pos(Succ(x0))) 42.09/20.35 new_show27(x0, x1, x2) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.35 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.35 new_showsPrec(x0, x1, ty_Float) 42.09/20.35 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.35 new_primDivNatS3(Succ(x0), Zero) 42.09/20.35 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.35 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.35 new_show19(x0) 42.09/20.35 new_primModNatS3(Zero, Zero, x0) 42.09/20.35 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.35 new_primModNatS2(Zero, Succ(x0)) 42.09/20.35 new_show31(x0) 42.09/20.35 new_show29(x0) 42.09/20.35 new_show21(x0, x1, x2) 42.09/20.36 new_primModNatS2(Succ(x0), Zero) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_showsPrec(x0, x1, ty_Double) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.36 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.36 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.36 new_showsPrec(x0, x1, ty_Char) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.36 new_primDivNatS01(x0, x1) 42.09/20.36 new_primShowInt0(Neg(x0)) 42.09/20.36 new_show17(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_primModNatS2(Zero, Zero) 42.09/20.36 new_primModNatS4(x0) 42.09/20.36 new_show30(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Int) 42.09/20.36 new_show24(x0, x1, x2, x3) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.36 new_primDivNatS4(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.36 new_primShowInt0(Pos(Zero)) 42.09/20.36 new_show16(x0) 42.09/20.36 new_show26(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_Integer) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.36 new_primModNatS02(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.36 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.36 new_div(x0, x1) 42.09/20.36 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.36 new_primIntToChar(x0, x1) 42.09/20.36 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show18(x0) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.36 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.36 new_primDivNatS2(Zero, Zero, x0) 42.09/20.36 new_show20(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.36 new_show25(x0, x1) 42.09/20.36 new_show23(x0) 42.09/20.36 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.36 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show28(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.36 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, ty_@0) 42.09/20.36 new_primDivNatS3(Zero, Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.36 42.09/20.36 We have to consider all minimal (P,Q,R)-chains. 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (95) TransformationProof (EQUIVALENT) 42.09/20.36 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.36 42.09/20.36 (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)) 42.09/20.36 (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)) 42.09/20.36 42.09/20.36 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (96) 42.09/20.36 Obligation: 42.09/20.36 Q DP problem: 42.09/20.36 The TRS P consists of the following rules: 42.09/20.36 42.09/20.36 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.36 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) 42.09/20.36 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) 42.09/20.36 42.09/20.36 The TRS R consists of the following rules: 42.09/20.36 42.09/20.36 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.36 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.36 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.36 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.36 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.36 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.36 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.36 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.36 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.36 new_primModNatS4(ww304) -> Zero 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.36 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.36 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.36 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.36 new_psPs0([], ww200) -> ww200 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.36 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.36 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.36 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.36 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.36 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.36 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.36 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.36 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.36 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.36 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.36 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.36 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.36 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.36 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.36 new_primDivNatS4(ww308) -> Zero 42.09/20.36 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.36 42.09/20.36 The set Q consists of the following terms: 42.09/20.36 42.09/20.36 new_psPs0([], x0) 42.09/20.36 new_show22(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_IOError) 42.09/20.36 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Bool) 42.09/20.36 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.36 new_show15(x0, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.36 new_psPs0(:(x0, x1), x2) 42.09/20.36 new_primShowInt0(Pos(Succ(x0))) 42.09/20.36 new_show27(x0, x1, x2) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.36 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.36 new_showsPrec(x0, x1, ty_Float) 42.09/20.36 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.36 new_primDivNatS3(Succ(x0), Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.36 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.36 new_show19(x0) 42.09/20.36 new_primModNatS3(Zero, Zero, x0) 42.09/20.36 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.36 new_primModNatS2(Zero, Succ(x0)) 42.09/20.36 new_show31(x0) 42.09/20.36 new_show29(x0) 42.09/20.36 new_show21(x0, x1, x2) 42.09/20.36 new_primModNatS2(Succ(x0), Zero) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_showsPrec(x0, x1, ty_Double) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.36 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.36 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.36 new_showsPrec(x0, x1, ty_Char) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.36 new_primDivNatS01(x0, x1) 42.09/20.36 new_primShowInt0(Neg(x0)) 42.09/20.36 new_show17(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_primModNatS2(Zero, Zero) 42.09/20.36 new_primModNatS4(x0) 42.09/20.36 new_show30(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Int) 42.09/20.36 new_show24(x0, x1, x2, x3) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.36 new_primDivNatS4(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.36 new_primShowInt0(Pos(Zero)) 42.09/20.36 new_show16(x0) 42.09/20.36 new_show26(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_Integer) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.36 new_primModNatS02(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.36 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.36 new_div(x0, x1) 42.09/20.36 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.36 new_primIntToChar(x0, x1) 42.09/20.36 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show18(x0) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.36 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.36 new_primDivNatS2(Zero, Zero, x0) 42.09/20.36 new_show20(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.36 new_show25(x0, x1) 42.09/20.36 new_show23(x0) 42.09/20.36 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.36 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show28(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.36 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, ty_@0) 42.09/20.36 new_primDivNatS3(Zero, Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.36 42.09/20.36 We have to consider all minimal (P,Q,R)-chains. 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (97) DependencyGraphProof (EQUIVALENT) 42.09/20.36 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (98) 42.09/20.36 Obligation: 42.09/20.36 Q DP problem: 42.09/20.36 The TRS P consists of the following rules: 42.09/20.36 42.09/20.36 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.36 42.09/20.36 The TRS R consists of the following rules: 42.09/20.36 42.09/20.36 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.36 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.36 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.36 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.36 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.36 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.36 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.36 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.36 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.36 new_primModNatS4(ww304) -> Zero 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.36 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.36 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.36 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.36 new_psPs0([], ww200) -> ww200 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.36 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.36 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.36 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.36 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.36 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.36 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.36 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.36 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.36 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.36 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.36 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.36 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.36 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.36 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.36 new_primDivNatS4(ww308) -> Zero 42.09/20.36 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.36 42.09/20.36 The set Q consists of the following terms: 42.09/20.36 42.09/20.36 new_psPs0([], x0) 42.09/20.36 new_show22(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_IOError) 42.09/20.36 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Bool) 42.09/20.36 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.36 new_show15(x0, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.36 new_psPs0(:(x0, x1), x2) 42.09/20.36 new_primShowInt0(Pos(Succ(x0))) 42.09/20.36 new_show27(x0, x1, x2) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.36 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.36 new_showsPrec(x0, x1, ty_Float) 42.09/20.36 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.36 new_primDivNatS3(Succ(x0), Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.36 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.36 new_show19(x0) 42.09/20.36 new_primModNatS3(Zero, Zero, x0) 42.09/20.36 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.36 new_primModNatS2(Zero, Succ(x0)) 42.09/20.36 new_show31(x0) 42.09/20.36 new_show29(x0) 42.09/20.36 new_show21(x0, x1, x2) 42.09/20.36 new_primModNatS2(Succ(x0), Zero) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_showsPrec(x0, x1, ty_Double) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.36 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.36 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.36 new_showsPrec(x0, x1, ty_Char) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.36 new_primDivNatS01(x0, x1) 42.09/20.36 new_primShowInt0(Neg(x0)) 42.09/20.36 new_show17(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_primModNatS2(Zero, Zero) 42.09/20.36 new_primModNatS4(x0) 42.09/20.36 new_show30(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Int) 42.09/20.36 new_show24(x0, x1, x2, x3) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.36 new_primDivNatS4(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.36 new_primShowInt0(Pos(Zero)) 42.09/20.36 new_show16(x0) 42.09/20.36 new_show26(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_Integer) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.36 new_primModNatS02(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.36 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.36 new_div(x0, x1) 42.09/20.36 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.36 new_primIntToChar(x0, x1) 42.09/20.36 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show18(x0) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.36 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.36 new_primDivNatS2(Zero, Zero, x0) 42.09/20.36 new_show20(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.36 new_show25(x0, x1) 42.09/20.36 new_show23(x0) 42.09/20.36 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.36 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show28(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.36 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, ty_@0) 42.09/20.36 new_primDivNatS3(Zero, Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.36 42.09/20.36 We have to consider all minimal (P,Q,R)-chains. 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (99) TransformationProof (EQUIVALENT) 42.09/20.36 By instantiating [LPAR04] the rule new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, be), app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) we obtained the following new rules [LPAR04]: 42.09/20.36 42.09/20.36 (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)) 42.09/20.36 (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)) 42.09/20.36 42.09/20.36 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (100) 42.09/20.36 Obligation: 42.09/20.36 Q DP problem: 42.09/20.36 The TRS P consists of the following rules: 42.09/20.36 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.36 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) 42.09/20.36 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) 42.09/20.36 42.09/20.36 The TRS R consists of the following rules: 42.09/20.36 42.09/20.36 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.36 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.36 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.36 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.36 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.36 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.36 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.36 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.36 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.36 new_primModNatS4(ww304) -> Zero 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.36 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.36 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.36 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.36 new_psPs0([], ww200) -> ww200 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.36 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.36 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.36 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.36 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.36 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.36 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.36 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.36 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.36 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.36 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.36 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.36 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.36 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.36 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.36 new_primDivNatS4(ww308) -> Zero 42.09/20.36 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.36 42.09/20.36 The set Q consists of the following terms: 42.09/20.36 42.09/20.36 new_psPs0([], x0) 42.09/20.36 new_show22(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_IOError) 42.09/20.36 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Bool) 42.09/20.36 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.36 new_show15(x0, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.36 new_psPs0(:(x0, x1), x2) 42.09/20.36 new_primShowInt0(Pos(Succ(x0))) 42.09/20.36 new_show27(x0, x1, x2) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.36 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.36 new_showsPrec(x0, x1, ty_Float) 42.09/20.36 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.36 new_primDivNatS3(Succ(x0), Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.36 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.36 new_show19(x0) 42.09/20.36 new_primModNatS3(Zero, Zero, x0) 42.09/20.36 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.36 new_primModNatS2(Zero, Succ(x0)) 42.09/20.36 new_show31(x0) 42.09/20.36 new_show29(x0) 42.09/20.36 new_show21(x0, x1, x2) 42.09/20.36 new_primModNatS2(Succ(x0), Zero) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_showsPrec(x0, x1, ty_Double) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.36 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.36 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.36 new_showsPrec(x0, x1, ty_Char) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.36 new_primDivNatS01(x0, x1) 42.09/20.36 new_primShowInt0(Neg(x0)) 42.09/20.36 new_show17(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_primModNatS2(Zero, Zero) 42.09/20.36 new_primModNatS4(x0) 42.09/20.36 new_show30(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Int) 42.09/20.36 new_show24(x0, x1, x2, x3) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.36 new_primDivNatS4(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.36 new_primShowInt0(Pos(Zero)) 42.09/20.36 new_show16(x0) 42.09/20.36 new_show26(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_Integer) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.36 new_primModNatS02(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.36 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.36 new_div(x0, x1) 42.09/20.36 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.36 new_primIntToChar(x0, x1) 42.09/20.36 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show18(x0) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.36 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.36 new_primDivNatS2(Zero, Zero, x0) 42.09/20.36 new_show20(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.36 new_show25(x0, x1) 42.09/20.36 new_show23(x0) 42.09/20.36 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.36 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show28(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.36 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, ty_@0) 42.09/20.36 new_primDivNatS3(Zero, Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.36 42.09/20.36 We have to consider all minimal (P,Q,R)-chains. 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (101) TransformationProof (EQUIVALENT) 42.09/20.36 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.36 42.09/20.36 (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))) 42.09/20.36 (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))) 42.09/20.36 42.09/20.36 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (102) 42.09/20.36 Obligation: 42.09/20.36 Q DP problem: 42.09/20.36 The TRS P consists of the following rules: 42.09/20.36 42.09/20.36 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.36 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) 42.09/20.36 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) 42.09/20.36 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)) 42.09/20.36 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)) 42.09/20.36 42.09/20.36 The TRS R consists of the following rules: 42.09/20.36 42.09/20.36 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.36 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.36 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.36 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.36 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.36 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.36 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.36 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.36 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.36 new_primModNatS4(ww304) -> Zero 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.36 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.36 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.36 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.36 new_psPs0([], ww200) -> ww200 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.36 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.36 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.36 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.36 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.36 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.36 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.36 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.36 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.36 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.36 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.36 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.36 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.36 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.36 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.36 new_primDivNatS4(ww308) -> Zero 42.09/20.36 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.36 42.09/20.36 The set Q consists of the following terms: 42.09/20.36 42.09/20.36 new_psPs0([], x0) 42.09/20.36 new_show22(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_IOError) 42.09/20.36 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Bool) 42.09/20.36 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.36 new_show15(x0, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.36 new_psPs0(:(x0, x1), x2) 42.09/20.36 new_primShowInt0(Pos(Succ(x0))) 42.09/20.36 new_show27(x0, x1, x2) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.36 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.36 new_showsPrec(x0, x1, ty_Float) 42.09/20.36 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.36 new_primDivNatS3(Succ(x0), Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.36 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.36 new_show19(x0) 42.09/20.36 new_primModNatS3(Zero, Zero, x0) 42.09/20.36 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.36 new_primModNatS2(Zero, Succ(x0)) 42.09/20.36 new_show31(x0) 42.09/20.36 new_show29(x0) 42.09/20.36 new_show21(x0, x1, x2) 42.09/20.36 new_primModNatS2(Succ(x0), Zero) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_showsPrec(x0, x1, ty_Double) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.36 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.36 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.36 new_showsPrec(x0, x1, ty_Char) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.36 new_primDivNatS01(x0, x1) 42.09/20.36 new_primShowInt0(Neg(x0)) 42.09/20.36 new_show17(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_primModNatS2(Zero, Zero) 42.09/20.36 new_primModNatS4(x0) 42.09/20.36 new_show30(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Int) 42.09/20.36 new_show24(x0, x1, x2, x3) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.36 new_primDivNatS4(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.36 new_primShowInt0(Pos(Zero)) 42.09/20.36 new_show16(x0) 42.09/20.36 new_show26(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_Integer) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.36 new_primModNatS02(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.36 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.36 new_div(x0, x1) 42.09/20.36 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.36 new_primIntToChar(x0, x1) 42.09/20.36 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show18(x0) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.36 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.36 new_primDivNatS2(Zero, Zero, x0) 42.09/20.36 new_show20(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.36 new_show25(x0, x1) 42.09/20.36 new_show23(x0) 42.09/20.36 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.36 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show28(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.36 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, ty_@0) 42.09/20.36 new_primDivNatS3(Zero, Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.36 42.09/20.36 We have to consider all minimal (P,Q,R)-chains. 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (103) DependencyGraphProof (EQUIVALENT) 42.09/20.36 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (104) 42.09/20.36 Obligation: 42.09/20.36 Q DP problem: 42.09/20.36 The TRS P consists of the following rules: 42.09/20.36 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.36 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) 42.09/20.36 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) 42.09/20.36 42.09/20.36 The TRS R consists of the following rules: 42.09/20.36 42.09/20.36 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.36 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.36 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.36 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.36 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.36 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.36 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.36 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.36 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.36 new_primModNatS4(ww304) -> Zero 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.36 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.36 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.36 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.36 new_psPs0([], ww200) -> ww200 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.36 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.36 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.36 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.36 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.36 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.36 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.36 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.36 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.36 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.36 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.36 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.36 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.36 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.36 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.36 new_primDivNatS4(ww308) -> Zero 42.09/20.36 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.36 42.09/20.36 The set Q consists of the following terms: 42.09/20.36 42.09/20.36 new_psPs0([], x0) 42.09/20.36 new_show22(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_IOError) 42.09/20.36 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Bool) 42.09/20.36 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.36 new_show15(x0, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.36 new_psPs0(:(x0, x1), x2) 42.09/20.36 new_primShowInt0(Pos(Succ(x0))) 42.09/20.36 new_show27(x0, x1, x2) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.36 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.36 new_showsPrec(x0, x1, ty_Float) 42.09/20.36 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.36 new_primDivNatS3(Succ(x0), Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.36 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.36 new_show19(x0) 42.09/20.36 new_primModNatS3(Zero, Zero, x0) 42.09/20.36 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.36 new_primModNatS2(Zero, Succ(x0)) 42.09/20.36 new_show31(x0) 42.09/20.36 new_show29(x0) 42.09/20.36 new_show21(x0, x1, x2) 42.09/20.36 new_primModNatS2(Succ(x0), Zero) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_showsPrec(x0, x1, ty_Double) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.36 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.36 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.36 new_showsPrec(x0, x1, ty_Char) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.36 new_primDivNatS01(x0, x1) 42.09/20.36 new_primShowInt0(Neg(x0)) 42.09/20.36 new_show17(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_primModNatS2(Zero, Zero) 42.09/20.36 new_primModNatS4(x0) 42.09/20.36 new_show30(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Int) 42.09/20.36 new_show24(x0, x1, x2, x3) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.36 new_primDivNatS4(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.36 new_primShowInt0(Pos(Zero)) 42.09/20.36 new_show16(x0) 42.09/20.36 new_show26(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_Integer) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.36 new_primModNatS02(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.36 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.36 new_div(x0, x1) 42.09/20.36 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.36 new_primIntToChar(x0, x1) 42.09/20.36 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show18(x0) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.36 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.36 new_primDivNatS2(Zero, Zero, x0) 42.09/20.36 new_show20(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.36 new_show25(x0, x1) 42.09/20.36 new_show23(x0) 42.09/20.36 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.36 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show28(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.36 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, ty_@0) 42.09/20.36 new_primDivNatS3(Zero, Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.36 42.09/20.36 We have to consider all minimal (P,Q,R)-chains. 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (105) TransformationProof (EQUIVALENT) 42.09/20.36 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.36 42.09/20.36 (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)) 42.09/20.36 (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)) 42.09/20.36 42.09/20.36 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (106) 42.09/20.36 Obligation: 42.09/20.36 Q DP problem: 42.09/20.36 The TRS P consists of the following rules: 42.09/20.36 42.09/20.36 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.36 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) 42.09/20.36 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) 42.09/20.36 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) 42.09/20.36 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) 42.09/20.36 42.09/20.36 The TRS R consists of the following rules: 42.09/20.36 42.09/20.36 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.36 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.36 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.36 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.36 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.36 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.36 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.36 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.36 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.36 new_primModNatS4(ww304) -> Zero 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.36 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.36 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.36 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.36 new_psPs0([], ww200) -> ww200 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.36 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.36 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.36 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.36 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.36 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.36 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.36 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.36 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.36 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.36 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.36 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.36 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.36 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.36 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.36 new_primDivNatS4(ww308) -> Zero 42.09/20.36 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.36 42.09/20.36 The set Q consists of the following terms: 42.09/20.36 42.09/20.36 new_psPs0([], x0) 42.09/20.36 new_show22(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_IOError) 42.09/20.36 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Bool) 42.09/20.36 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.36 new_show15(x0, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.36 new_psPs0(:(x0, x1), x2) 42.09/20.36 new_primShowInt0(Pos(Succ(x0))) 42.09/20.36 new_show27(x0, x1, x2) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.36 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.36 new_showsPrec(x0, x1, ty_Float) 42.09/20.36 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.36 new_primDivNatS3(Succ(x0), Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.36 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.36 new_show19(x0) 42.09/20.36 new_primModNatS3(Zero, Zero, x0) 42.09/20.36 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.36 new_primModNatS2(Zero, Succ(x0)) 42.09/20.36 new_show31(x0) 42.09/20.36 new_show29(x0) 42.09/20.36 new_show21(x0, x1, x2) 42.09/20.36 new_primModNatS2(Succ(x0), Zero) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_showsPrec(x0, x1, ty_Double) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.36 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.36 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.36 new_showsPrec(x0, x1, ty_Char) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.36 new_primDivNatS01(x0, x1) 42.09/20.36 new_primShowInt0(Neg(x0)) 42.09/20.36 new_show17(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_primModNatS2(Zero, Zero) 42.09/20.36 new_primModNatS4(x0) 42.09/20.36 new_show30(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Int) 42.09/20.36 new_show24(x0, x1, x2, x3) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.36 new_primDivNatS4(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.36 new_primShowInt0(Pos(Zero)) 42.09/20.36 new_show16(x0) 42.09/20.36 new_show26(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_Integer) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.36 new_primModNatS02(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.36 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.36 new_div(x0, x1) 42.09/20.36 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.36 new_primIntToChar(x0, x1) 42.09/20.36 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show18(x0) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.36 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.36 new_primDivNatS2(Zero, Zero, x0) 42.09/20.36 new_show20(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.36 new_show25(x0, x1) 42.09/20.36 new_show23(x0) 42.09/20.36 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.36 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show28(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.36 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, ty_@0) 42.09/20.36 new_primDivNatS3(Zero, Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.36 42.09/20.36 We have to consider all minimal (P,Q,R)-chains. 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (107) DependencyGraphProof (EQUIVALENT) 42.09/20.36 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (108) 42.09/20.36 Obligation: 42.09/20.36 Q DP problem: 42.09/20.36 The TRS P consists of the following rules: 42.09/20.36 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.36 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) 42.09/20.36 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) 42.09/20.36 42.09/20.36 The TRS R consists of the following rules: 42.09/20.36 42.09/20.36 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.36 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.36 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.36 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.36 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.36 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.36 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.36 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.36 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.36 new_primModNatS4(ww304) -> Zero 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.36 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.36 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.36 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.36 new_psPs0([], ww200) -> ww200 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.36 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.36 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.36 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.36 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.36 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.36 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.36 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.36 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.36 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.36 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.36 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.36 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.36 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.36 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.36 new_primDivNatS4(ww308) -> Zero 42.09/20.36 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.36 42.09/20.36 The set Q consists of the following terms: 42.09/20.36 42.09/20.36 new_psPs0([], x0) 42.09/20.36 new_show22(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_IOError) 42.09/20.36 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Bool) 42.09/20.36 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.36 new_show15(x0, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.36 new_psPs0(:(x0, x1), x2) 42.09/20.36 new_primShowInt0(Pos(Succ(x0))) 42.09/20.36 new_show27(x0, x1, x2) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.36 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.36 new_showsPrec(x0, x1, ty_Float) 42.09/20.36 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.36 new_primDivNatS3(Succ(x0), Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.36 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.36 new_show19(x0) 42.09/20.36 new_primModNatS3(Zero, Zero, x0) 42.09/20.36 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.36 new_primModNatS2(Zero, Succ(x0)) 42.09/20.36 new_show31(x0) 42.09/20.36 new_show29(x0) 42.09/20.36 new_show21(x0, x1, x2) 42.09/20.36 new_primModNatS2(Succ(x0), Zero) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_showsPrec(x0, x1, ty_Double) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.36 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.36 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.36 new_showsPrec(x0, x1, ty_Char) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.36 new_primDivNatS01(x0, x1) 42.09/20.36 new_primShowInt0(Neg(x0)) 42.09/20.36 new_show17(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_primModNatS2(Zero, Zero) 42.09/20.36 new_primModNatS4(x0) 42.09/20.36 new_show30(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Int) 42.09/20.36 new_show24(x0, x1, x2, x3) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.36 new_primDivNatS4(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.36 new_primShowInt0(Pos(Zero)) 42.09/20.36 new_show16(x0) 42.09/20.36 new_show26(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_Integer) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.36 new_primModNatS02(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.36 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.36 new_div(x0, x1) 42.09/20.36 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.36 new_primIntToChar(x0, x1) 42.09/20.36 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show18(x0) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.36 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.36 new_primDivNatS2(Zero, Zero, x0) 42.09/20.36 new_show20(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.36 new_show25(x0, x1) 42.09/20.36 new_show23(x0) 42.09/20.36 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.36 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.36 new_show28(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.36 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, ty_@0) 42.09/20.36 new_primDivNatS3(Zero, Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.36 42.09/20.36 We have to consider all minimal (P,Q,R)-chains. 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (109) TransformationProof (EQUIVALENT) 42.09/20.36 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.36 42.09/20.36 (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))) 42.09/20.36 (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))) 42.09/20.36 42.09/20.36 42.09/20.36 ---------------------------------------- 42.09/20.36 42.09/20.36 (110) 42.09/20.36 Obligation: 42.09/20.36 Q DP problem: 42.09/20.36 The TRS P consists of the following rules: 42.09/20.36 42.09/20.36 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.36 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.36 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) 42.09/20.36 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) 42.09/20.36 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)) 42.09/20.36 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)) 42.09/20.36 42.09/20.36 The TRS R consists of the following rules: 42.09/20.36 42.09/20.36 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.36 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.36 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.36 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.36 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.36 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.36 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.36 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.36 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.36 new_primModNatS4(ww304) -> Zero 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.36 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.36 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.36 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.36 new_psPs0([], ww200) -> ww200 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.36 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.36 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.36 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.36 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.36 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.36 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.36 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.36 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.36 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.36 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.36 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.36 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.36 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.36 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.36 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.36 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.36 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.36 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.36 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.36 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.36 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.36 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.36 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.36 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.36 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.36 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.36 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.36 new_primDivNatS4(ww308) -> Zero 42.09/20.36 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.36 42.09/20.36 The set Q consists of the following terms: 42.09/20.36 42.09/20.36 new_psPs0([], x0) 42.09/20.36 new_show22(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.36 new_showsPrec(x0, x1, ty_IOError) 42.09/20.36 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Bool) 42.09/20.36 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.36 new_show15(x0, x1) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.36 new_psPs0(:(x0, x1), x2) 42.09/20.36 new_primShowInt0(Pos(Succ(x0))) 42.09/20.36 new_show27(x0, x1, x2) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.36 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.36 new_showsPrec(x0, x1, ty_Float) 42.09/20.36 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.36 new_primDivNatS3(Succ(x0), Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.36 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.36 new_show19(x0) 42.09/20.36 new_primModNatS3(Zero, Zero, x0) 42.09/20.36 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.36 new_primModNatS2(Zero, Succ(x0)) 42.09/20.36 new_show31(x0) 42.09/20.36 new_show29(x0) 42.09/20.36 new_show21(x0, x1, x2) 42.09/20.36 new_primModNatS2(Succ(x0), Zero) 42.09/20.36 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_showsPrec(x0, x1, ty_Double) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.36 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.36 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.36 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.36 new_showsPrec(x0, x1, ty_Char) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.36 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.36 new_primDivNatS01(x0, x1) 42.09/20.36 new_primShowInt0(Neg(x0)) 42.09/20.36 new_show17(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.36 new_primModNatS2(Zero, Zero) 42.09/20.36 new_primModNatS4(x0) 42.09/20.36 new_show30(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, ty_Int) 42.09/20.36 new_show24(x0, x1, x2, x3) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.36 new_primDivNatS4(x0) 42.09/20.36 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.36 new_primShowInt0(Pos(Zero)) 42.09/20.36 new_show16(x0) 42.09/20.36 new_show26(x0) 42.09/20.36 new_showsPrec(x0, x1, ty_Integer) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.36 new_primModNatS02(x0, x1) 42.09/20.36 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.36 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.36 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.36 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.36 new_div(x0, x1) 42.09/20.37 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.37 new_primIntToChar(x0, x1) 42.09/20.37 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show18(x0) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.37 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.37 new_primDivNatS2(Zero, Zero, x0) 42.09/20.37 new_show20(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.37 new_show25(x0, x1) 42.09/20.37 new_show23(x0) 42.09/20.37 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.37 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show28(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.37 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, ty_@0) 42.09/20.37 new_primDivNatS3(Zero, Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.37 42.09/20.37 We have to consider all minimal (P,Q,R)-chains. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (111) DependencyGraphProof (EQUIVALENT) 42.09/20.37 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (112) 42.09/20.37 Obligation: 42.09/20.37 Q DP problem: 42.09/20.37 The TRS P consists of the following rules: 42.09/20.37 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 42.09/20.37 The TRS R consists of the following rules: 42.09/20.37 42.09/20.37 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.37 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.37 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.37 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.37 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.37 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.37 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.37 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.37 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.37 new_primModNatS4(ww304) -> Zero 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.37 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.37 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.37 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.37 new_psPs0([], ww200) -> ww200 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.37 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.37 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.37 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.37 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.37 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.37 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.37 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.37 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.37 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.37 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.37 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.37 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.37 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.37 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.37 new_primDivNatS4(ww308) -> Zero 42.09/20.37 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.37 42.09/20.37 The set Q consists of the following terms: 42.09/20.37 42.09/20.37 new_psPs0([], x0) 42.09/20.37 new_show22(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_IOError) 42.09/20.37 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Bool) 42.09/20.37 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.37 new_show15(x0, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.37 new_psPs0(:(x0, x1), x2) 42.09/20.37 new_primShowInt0(Pos(Succ(x0))) 42.09/20.37 new_show27(x0, x1, x2) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.37 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.37 new_showsPrec(x0, x1, ty_Float) 42.09/20.37 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.37 new_primDivNatS3(Succ(x0), Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.37 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.37 new_show19(x0) 42.09/20.37 new_primModNatS3(Zero, Zero, x0) 42.09/20.37 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.37 new_primModNatS2(Zero, Succ(x0)) 42.09/20.37 new_show31(x0) 42.09/20.37 new_show29(x0) 42.09/20.37 new_show21(x0, x1, x2) 42.09/20.37 new_primModNatS2(Succ(x0), Zero) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_showsPrec(x0, x1, ty_Double) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.37 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.37 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.37 new_showsPrec(x0, x1, ty_Char) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.37 new_primDivNatS01(x0, x1) 42.09/20.37 new_primShowInt0(Neg(x0)) 42.09/20.37 new_show17(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_primModNatS2(Zero, Zero) 42.09/20.37 new_primModNatS4(x0) 42.09/20.37 new_show30(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Int) 42.09/20.37 new_show24(x0, x1, x2, x3) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.37 new_primDivNatS4(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.37 new_primShowInt0(Pos(Zero)) 42.09/20.37 new_show16(x0) 42.09/20.37 new_show26(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_Integer) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.37 new_primModNatS02(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.37 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.37 new_div(x0, x1) 42.09/20.37 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.37 new_primIntToChar(x0, x1) 42.09/20.37 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show18(x0) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.37 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.37 new_primDivNatS2(Zero, Zero, x0) 42.09/20.37 new_show20(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.37 new_show25(x0, x1) 42.09/20.37 new_show23(x0) 42.09/20.37 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.37 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show28(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.37 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, ty_@0) 42.09/20.37 new_primDivNatS3(Zero, Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.37 42.09/20.37 We have to consider all minimal (P,Q,R)-chains. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (113) TransformationProof (EQUIVALENT) 42.09/20.37 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.37 42.09/20.37 (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))) 42.09/20.37 (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))) 42.09/20.37 42.09/20.37 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (114) 42.09/20.37 Obligation: 42.09/20.37 Q DP problem: 42.09/20.37 The TRS P consists of the following rules: 42.09/20.37 42.09/20.37 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 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)) 42.09/20.37 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)) 42.09/20.37 42.09/20.37 The TRS R consists of the following rules: 42.09/20.37 42.09/20.37 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.37 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.37 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.37 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.37 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.37 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.37 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.37 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.37 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.37 new_primModNatS4(ww304) -> Zero 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.37 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.37 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.37 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.37 new_psPs0([], ww200) -> ww200 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.37 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.37 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.37 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.37 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.37 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.37 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.37 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.37 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.37 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.37 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.37 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.37 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.37 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.37 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.37 new_primDivNatS4(ww308) -> Zero 42.09/20.37 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.37 42.09/20.37 The set Q consists of the following terms: 42.09/20.37 42.09/20.37 new_psPs0([], x0) 42.09/20.37 new_show22(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_IOError) 42.09/20.37 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Bool) 42.09/20.37 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.37 new_show15(x0, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.37 new_psPs0(:(x0, x1), x2) 42.09/20.37 new_primShowInt0(Pos(Succ(x0))) 42.09/20.37 new_show27(x0, x1, x2) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.37 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.37 new_showsPrec(x0, x1, ty_Float) 42.09/20.37 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.37 new_primDivNatS3(Succ(x0), Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.37 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.37 new_show19(x0) 42.09/20.37 new_primModNatS3(Zero, Zero, x0) 42.09/20.37 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.37 new_primModNatS2(Zero, Succ(x0)) 42.09/20.37 new_show31(x0) 42.09/20.37 new_show29(x0) 42.09/20.37 new_show21(x0, x1, x2) 42.09/20.37 new_primModNatS2(Succ(x0), Zero) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_showsPrec(x0, x1, ty_Double) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.37 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.37 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.37 new_showsPrec(x0, x1, ty_Char) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.37 new_primDivNatS01(x0, x1) 42.09/20.37 new_primShowInt0(Neg(x0)) 42.09/20.37 new_show17(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_primModNatS2(Zero, Zero) 42.09/20.37 new_primModNatS4(x0) 42.09/20.37 new_show30(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Int) 42.09/20.37 new_show24(x0, x1, x2, x3) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.37 new_primDivNatS4(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.37 new_primShowInt0(Pos(Zero)) 42.09/20.37 new_show16(x0) 42.09/20.37 new_show26(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_Integer) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.37 new_primModNatS02(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.37 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.37 new_div(x0, x1) 42.09/20.37 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.37 new_primIntToChar(x0, x1) 42.09/20.37 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show18(x0) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.37 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.37 new_primDivNatS2(Zero, Zero, x0) 42.09/20.37 new_show20(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.37 new_show25(x0, x1) 42.09/20.37 new_show23(x0) 42.09/20.37 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.37 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show28(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.37 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, ty_@0) 42.09/20.37 new_primDivNatS3(Zero, Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.37 42.09/20.37 We have to consider all minimal (P,Q,R)-chains. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (115) DependencyGraphProof (EQUIVALENT) 42.09/20.37 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (116) 42.09/20.37 Obligation: 42.09/20.37 Q DP problem: 42.09/20.37 The TRS P consists of the following rules: 42.09/20.37 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 42.09/20.37 The TRS R consists of the following rules: 42.09/20.37 42.09/20.37 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.37 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.37 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.37 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.37 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.37 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.37 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.37 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.37 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.37 new_primModNatS4(ww304) -> Zero 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.37 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.37 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.37 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.37 new_psPs0([], ww200) -> ww200 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.37 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.37 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.37 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.37 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.37 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.37 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.37 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.37 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.37 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.37 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.37 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.37 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.37 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.37 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.37 new_primDivNatS4(ww308) -> Zero 42.09/20.37 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.37 42.09/20.37 The set Q consists of the following terms: 42.09/20.37 42.09/20.37 new_psPs0([], x0) 42.09/20.37 new_show22(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_IOError) 42.09/20.37 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Bool) 42.09/20.37 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.37 new_show15(x0, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.37 new_psPs0(:(x0, x1), x2) 42.09/20.37 new_primShowInt0(Pos(Succ(x0))) 42.09/20.37 new_show27(x0, x1, x2) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.37 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.37 new_showsPrec(x0, x1, ty_Float) 42.09/20.37 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.37 new_primDivNatS3(Succ(x0), Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.37 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.37 new_show19(x0) 42.09/20.37 new_primModNatS3(Zero, Zero, x0) 42.09/20.37 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.37 new_primModNatS2(Zero, Succ(x0)) 42.09/20.37 new_show31(x0) 42.09/20.37 new_show29(x0) 42.09/20.37 new_show21(x0, x1, x2) 42.09/20.37 new_primModNatS2(Succ(x0), Zero) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_showsPrec(x0, x1, ty_Double) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.37 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.37 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.37 new_showsPrec(x0, x1, ty_Char) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.37 new_primDivNatS01(x0, x1) 42.09/20.37 new_primShowInt0(Neg(x0)) 42.09/20.37 new_show17(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_primModNatS2(Zero, Zero) 42.09/20.37 new_primModNatS4(x0) 42.09/20.37 new_show30(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Int) 42.09/20.37 new_show24(x0, x1, x2, x3) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.37 new_primDivNatS4(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.37 new_primShowInt0(Pos(Zero)) 42.09/20.37 new_show16(x0) 42.09/20.37 new_show26(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_Integer) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.37 new_primModNatS02(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.37 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.37 new_div(x0, x1) 42.09/20.37 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.37 new_primIntToChar(x0, x1) 42.09/20.37 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show18(x0) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.37 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.37 new_primDivNatS2(Zero, Zero, x0) 42.09/20.37 new_show20(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.37 new_show25(x0, x1) 42.09/20.37 new_show23(x0) 42.09/20.37 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.37 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show28(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.37 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, ty_@0) 42.09/20.37 new_primDivNatS3(Zero, Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.37 42.09/20.37 We have to consider all minimal (P,Q,R)-chains. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (117) TransformationProof (EQUIVALENT) 42.09/20.37 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.37 42.09/20.37 (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)) 42.09/20.37 (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)) 42.09/20.37 42.09/20.37 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (118) 42.09/20.37 Obligation: 42.09/20.37 Q DP problem: 42.09/20.37 The TRS P consists of the following rules: 42.09/20.37 42.09/20.37 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 42.09/20.37 The TRS R consists of the following rules: 42.09/20.37 42.09/20.37 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.37 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.37 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.37 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.37 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.37 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.37 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.37 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.37 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.37 new_primModNatS4(ww304) -> Zero 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.37 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.37 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.37 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.37 new_psPs0([], ww200) -> ww200 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.37 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.37 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.37 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.37 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.37 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.37 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.37 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.37 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.37 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.37 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.37 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.37 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.37 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.37 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.37 new_primDivNatS4(ww308) -> Zero 42.09/20.37 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.37 42.09/20.37 The set Q consists of the following terms: 42.09/20.37 42.09/20.37 new_psPs0([], x0) 42.09/20.37 new_show22(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_IOError) 42.09/20.37 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Bool) 42.09/20.37 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.37 new_show15(x0, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.37 new_psPs0(:(x0, x1), x2) 42.09/20.37 new_primShowInt0(Pos(Succ(x0))) 42.09/20.37 new_show27(x0, x1, x2) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.37 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.37 new_showsPrec(x0, x1, ty_Float) 42.09/20.37 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.37 new_primDivNatS3(Succ(x0), Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.37 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.37 new_show19(x0) 42.09/20.37 new_primModNatS3(Zero, Zero, x0) 42.09/20.37 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.37 new_primModNatS2(Zero, Succ(x0)) 42.09/20.37 new_show31(x0) 42.09/20.37 new_show29(x0) 42.09/20.37 new_show21(x0, x1, x2) 42.09/20.37 new_primModNatS2(Succ(x0), Zero) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_showsPrec(x0, x1, ty_Double) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.37 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.37 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.37 new_showsPrec(x0, x1, ty_Char) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.37 new_primDivNatS01(x0, x1) 42.09/20.37 new_primShowInt0(Neg(x0)) 42.09/20.37 new_show17(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_primModNatS2(Zero, Zero) 42.09/20.37 new_primModNatS4(x0) 42.09/20.37 new_show30(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Int) 42.09/20.37 new_show24(x0, x1, x2, x3) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.37 new_primDivNatS4(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.37 new_primShowInt0(Pos(Zero)) 42.09/20.37 new_show16(x0) 42.09/20.37 new_show26(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_Integer) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.37 new_primModNatS02(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.37 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.37 new_div(x0, x1) 42.09/20.37 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.37 new_primIntToChar(x0, x1) 42.09/20.37 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show18(x0) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.37 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.37 new_primDivNatS2(Zero, Zero, x0) 42.09/20.37 new_show20(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.37 new_show25(x0, x1) 42.09/20.37 new_show23(x0) 42.09/20.37 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.37 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show28(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.37 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, ty_@0) 42.09/20.37 new_primDivNatS3(Zero, Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.37 42.09/20.37 We have to consider all minimal (P,Q,R)-chains. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (119) DependencyGraphProof (EQUIVALENT) 42.09/20.37 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (120) 42.09/20.37 Obligation: 42.09/20.37 Q DP problem: 42.09/20.37 The TRS P consists of the following rules: 42.09/20.37 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 42.09/20.37 The TRS R consists of the following rules: 42.09/20.37 42.09/20.37 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.37 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.37 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.37 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.37 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.37 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.37 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.37 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.37 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.37 new_primModNatS4(ww304) -> Zero 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.37 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.37 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.37 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.37 new_psPs0([], ww200) -> ww200 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.37 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.37 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.37 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.37 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.37 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.37 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.37 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.37 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.37 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.37 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.37 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.37 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.37 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.37 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.37 new_primDivNatS4(ww308) -> Zero 42.09/20.37 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.37 42.09/20.37 The set Q consists of the following terms: 42.09/20.37 42.09/20.37 new_psPs0([], x0) 42.09/20.37 new_show22(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_IOError) 42.09/20.37 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Bool) 42.09/20.37 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.37 new_show15(x0, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.37 new_psPs0(:(x0, x1), x2) 42.09/20.37 new_primShowInt0(Pos(Succ(x0))) 42.09/20.37 new_show27(x0, x1, x2) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.37 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.37 new_showsPrec(x0, x1, ty_Float) 42.09/20.37 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.37 new_primDivNatS3(Succ(x0), Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.37 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.37 new_show19(x0) 42.09/20.37 new_primModNatS3(Zero, Zero, x0) 42.09/20.37 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.37 new_primModNatS2(Zero, Succ(x0)) 42.09/20.37 new_show31(x0) 42.09/20.37 new_show29(x0) 42.09/20.37 new_show21(x0, x1, x2) 42.09/20.37 new_primModNatS2(Succ(x0), Zero) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_showsPrec(x0, x1, ty_Double) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.37 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.37 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.37 new_showsPrec(x0, x1, ty_Char) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.37 new_primDivNatS01(x0, x1) 42.09/20.37 new_primShowInt0(Neg(x0)) 42.09/20.37 new_show17(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_primModNatS2(Zero, Zero) 42.09/20.37 new_primModNatS4(x0) 42.09/20.37 new_show30(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Int) 42.09/20.37 new_show24(x0, x1, x2, x3) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.37 new_primDivNatS4(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.37 new_primShowInt0(Pos(Zero)) 42.09/20.37 new_show16(x0) 42.09/20.37 new_show26(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_Integer) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.37 new_primModNatS02(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.37 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.37 new_div(x0, x1) 42.09/20.37 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.37 new_primIntToChar(x0, x1) 42.09/20.37 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show18(x0) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.37 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.37 new_primDivNatS2(Zero, Zero, x0) 42.09/20.37 new_show20(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.37 new_show25(x0, x1) 42.09/20.37 new_show23(x0) 42.09/20.37 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.37 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show28(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.37 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, ty_@0) 42.09/20.37 new_primDivNatS3(Zero, Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.37 42.09/20.37 We have to consider all minimal (P,Q,R)-chains. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (121) TransformationProof (EQUIVALENT) 42.09/20.37 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.37 42.09/20.37 (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)) 42.09/20.37 (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)) 42.09/20.37 42.09/20.37 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (122) 42.09/20.37 Obligation: 42.09/20.37 Q DP problem: 42.09/20.37 The TRS P consists of the following rules: 42.09/20.37 42.09/20.37 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 42.09/20.37 The TRS R consists of the following rules: 42.09/20.37 42.09/20.37 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.37 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.37 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.37 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.37 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.37 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.37 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.37 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.37 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.37 new_primModNatS4(ww304) -> Zero 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.37 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.37 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.37 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.37 new_psPs0([], ww200) -> ww200 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.37 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.37 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.37 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.37 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.37 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.37 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.37 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.37 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.37 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.37 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.37 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.37 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.37 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.37 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.37 new_primDivNatS4(ww308) -> Zero 42.09/20.37 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.37 42.09/20.37 The set Q consists of the following terms: 42.09/20.37 42.09/20.37 new_psPs0([], x0) 42.09/20.37 new_show22(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_IOError) 42.09/20.37 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Bool) 42.09/20.37 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.37 new_show15(x0, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.37 new_psPs0(:(x0, x1), x2) 42.09/20.37 new_primShowInt0(Pos(Succ(x0))) 42.09/20.37 new_show27(x0, x1, x2) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.37 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.37 new_showsPrec(x0, x1, ty_Float) 42.09/20.37 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.37 new_primDivNatS3(Succ(x0), Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.37 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.37 new_show19(x0) 42.09/20.37 new_primModNatS3(Zero, Zero, x0) 42.09/20.37 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.37 new_primModNatS2(Zero, Succ(x0)) 42.09/20.37 new_show31(x0) 42.09/20.37 new_show29(x0) 42.09/20.37 new_show21(x0, x1, x2) 42.09/20.37 new_primModNatS2(Succ(x0), Zero) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_showsPrec(x0, x1, ty_Double) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.37 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.37 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.37 new_showsPrec(x0, x1, ty_Char) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.37 new_primDivNatS01(x0, x1) 42.09/20.37 new_primShowInt0(Neg(x0)) 42.09/20.37 new_show17(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_primModNatS2(Zero, Zero) 42.09/20.37 new_primModNatS4(x0) 42.09/20.37 new_show30(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Int) 42.09/20.37 new_show24(x0, x1, x2, x3) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.37 new_primDivNatS4(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.37 new_primShowInt0(Pos(Zero)) 42.09/20.37 new_show16(x0) 42.09/20.37 new_show26(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_Integer) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.37 new_primModNatS02(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.37 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.37 new_div(x0, x1) 42.09/20.37 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.37 new_primIntToChar(x0, x1) 42.09/20.37 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show18(x0) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.37 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.37 new_primDivNatS2(Zero, Zero, x0) 42.09/20.37 new_show20(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.37 new_show25(x0, x1) 42.09/20.37 new_show23(x0) 42.09/20.37 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.37 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show28(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.37 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, ty_@0) 42.09/20.37 new_primDivNatS3(Zero, Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.37 42.09/20.37 We have to consider all minimal (P,Q,R)-chains. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (123) DependencyGraphProof (EQUIVALENT) 42.09/20.37 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (124) 42.09/20.37 Obligation: 42.09/20.37 Q DP problem: 42.09/20.37 The TRS P consists of the following rules: 42.09/20.37 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 42.09/20.37 The TRS R consists of the following rules: 42.09/20.37 42.09/20.37 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.37 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.37 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.37 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.37 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.37 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.37 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.37 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.37 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.37 new_primModNatS4(ww304) -> Zero 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.37 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.37 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.37 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.37 new_psPs0([], ww200) -> ww200 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.37 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.37 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.37 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.37 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.37 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.37 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.37 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.37 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.37 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.37 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.37 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.37 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.37 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.37 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.37 new_primDivNatS4(ww308) -> Zero 42.09/20.37 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.37 42.09/20.37 The set Q consists of the following terms: 42.09/20.37 42.09/20.37 new_psPs0([], x0) 42.09/20.37 new_show22(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_IOError) 42.09/20.37 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Bool) 42.09/20.37 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.37 new_show15(x0, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.37 new_psPs0(:(x0, x1), x2) 42.09/20.37 new_primShowInt0(Pos(Succ(x0))) 42.09/20.37 new_show27(x0, x1, x2) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.37 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.37 new_showsPrec(x0, x1, ty_Float) 42.09/20.37 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.37 new_primDivNatS3(Succ(x0), Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.37 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.37 new_show19(x0) 42.09/20.37 new_primModNatS3(Zero, Zero, x0) 42.09/20.37 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.37 new_primModNatS2(Zero, Succ(x0)) 42.09/20.37 new_show31(x0) 42.09/20.37 new_show29(x0) 42.09/20.37 new_show21(x0, x1, x2) 42.09/20.37 new_primModNatS2(Succ(x0), Zero) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_showsPrec(x0, x1, ty_Double) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.37 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.37 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.37 new_showsPrec(x0, x1, ty_Char) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.37 new_primDivNatS01(x0, x1) 42.09/20.37 new_primShowInt0(Neg(x0)) 42.09/20.37 new_show17(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_primModNatS2(Zero, Zero) 42.09/20.37 new_primModNatS4(x0) 42.09/20.37 new_show30(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Int) 42.09/20.37 new_show24(x0, x1, x2, x3) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.37 new_primDivNatS4(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.37 new_primShowInt0(Pos(Zero)) 42.09/20.37 new_show16(x0) 42.09/20.37 new_show26(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_Integer) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.37 new_primModNatS02(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.37 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.37 new_div(x0, x1) 42.09/20.37 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.37 new_primIntToChar(x0, x1) 42.09/20.37 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show18(x0) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.37 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.37 new_primDivNatS2(Zero, Zero, x0) 42.09/20.37 new_show20(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.37 new_show25(x0, x1) 42.09/20.37 new_show23(x0) 42.09/20.37 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.37 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show28(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.37 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, ty_@0) 42.09/20.37 new_primDivNatS3(Zero, Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.37 42.09/20.37 We have to consider all minimal (P,Q,R)-chains. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (125) TransformationProof (EQUIVALENT) 42.09/20.37 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.37 42.09/20.37 (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)) 42.09/20.37 (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)) 42.09/20.37 42.09/20.37 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (126) 42.09/20.37 Obligation: 42.09/20.37 Q DP problem: 42.09/20.37 The TRS P consists of the following rules: 42.09/20.37 42.09/20.37 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 42.09/20.37 The TRS R consists of the following rules: 42.09/20.37 42.09/20.37 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.37 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.37 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.37 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.37 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.37 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.37 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.37 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.37 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.37 new_primModNatS4(ww304) -> Zero 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.37 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.37 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.37 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.37 new_psPs0([], ww200) -> ww200 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.37 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.37 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.37 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.37 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.37 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.37 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.37 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.37 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.37 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.37 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.37 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.37 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.37 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.37 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.37 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.37 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.37 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.37 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.37 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.37 new_primDivNatS4(ww308) -> Zero 42.09/20.37 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.37 42.09/20.37 The set Q consists of the following terms: 42.09/20.37 42.09/20.37 new_psPs0([], x0) 42.09/20.37 new_show22(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_IOError) 42.09/20.37 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Bool) 42.09/20.37 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.37 new_show15(x0, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.37 new_psPs0(:(x0, x1), x2) 42.09/20.37 new_primShowInt0(Pos(Succ(x0))) 42.09/20.37 new_show27(x0, x1, x2) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.37 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.37 new_showsPrec(x0, x1, ty_Float) 42.09/20.37 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.37 new_primDivNatS3(Succ(x0), Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.37 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.37 new_show19(x0) 42.09/20.37 new_primModNatS3(Zero, Zero, x0) 42.09/20.37 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.37 new_primModNatS2(Zero, Succ(x0)) 42.09/20.37 new_show31(x0) 42.09/20.37 new_show29(x0) 42.09/20.37 new_show21(x0, x1, x2) 42.09/20.37 new_primModNatS2(Succ(x0), Zero) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_showsPrec(x0, x1, ty_Double) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.37 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.37 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.37 new_showsPrec(x0, x1, ty_Char) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.37 new_primDivNatS01(x0, x1) 42.09/20.37 new_primShowInt0(Neg(x0)) 42.09/20.37 new_show17(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.37 new_primModNatS2(Zero, Zero) 42.09/20.37 new_primModNatS4(x0) 42.09/20.37 new_show30(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, ty_Int) 42.09/20.37 new_show24(x0, x1, x2, x3) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.37 new_primDivNatS4(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.37 new_primShowInt0(Pos(Zero)) 42.09/20.37 new_show16(x0) 42.09/20.37 new_show26(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_Integer) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.37 new_primModNatS02(x0, x1) 42.09/20.37 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.37 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.37 new_div(x0, x1) 42.09/20.37 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.37 new_primIntToChar(x0, x1) 42.09/20.37 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show18(x0) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.37 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.37 new_primDivNatS2(Zero, Zero, x0) 42.09/20.37 new_show20(x0) 42.09/20.37 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.37 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.37 new_show25(x0, x1) 42.09/20.37 new_show23(x0) 42.09/20.37 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.37 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.37 new_show28(x0) 42.09/20.37 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.37 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.37 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.37 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.37 new_showsPrec(x0, x1, ty_@0) 42.09/20.37 new_primDivNatS3(Zero, Zero) 42.09/20.37 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.37 42.09/20.37 We have to consider all minimal (P,Q,R)-chains. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (127) DependencyGraphProof (EQUIVALENT) 42.09/20.37 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.37 ---------------------------------------- 42.09/20.37 42.09/20.37 (128) 42.09/20.37 Obligation: 42.09/20.37 Q DP problem: 42.09/20.37 The TRS P consists of the following rules: 42.09/20.37 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.37 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.37 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.37 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) 42.09/20.37 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) 42.09/20.37 42.09/20.37 The TRS R consists of the following rules: 42.09/20.37 42.09/20.37 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.37 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.37 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.37 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.37 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.37 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.37 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.37 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.37 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.37 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.37 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.37 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.37 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.37 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.37 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.37 new_primModNatS4(ww304) -> Zero 42.09/20.37 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.37 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.37 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.37 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.37 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.38 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.38 new_psPs0([], ww200) -> ww200 42.09/20.38 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.38 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.38 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.38 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.38 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.38 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.38 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.38 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.38 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.38 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.38 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.38 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.38 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.38 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.38 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_psPs0([], x0) 42.09/20.38 new_show22(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_showsPrec(x0, x1, ty_IOError) 42.09/20.38 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.38 new_showsPrec(x0, x1, ty_Bool) 42.09/20.38 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.38 new_show15(x0, x1) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.38 new_psPs0(:(x0, x1), x2) 42.09/20.38 new_primShowInt0(Pos(Succ(x0))) 42.09/20.38 new_show27(x0, x1, x2) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_showsPrec(x0, x1, ty_Float) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.38 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.38 new_show19(x0) 42.09/20.38 new_primModNatS3(Zero, Zero, x0) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primModNatS2(Zero, Succ(x0)) 42.09/20.38 new_show31(x0) 42.09/20.38 new_show29(x0) 42.09/20.38 new_show21(x0, x1, x2) 42.09/20.38 new_primModNatS2(Succ(x0), Zero) 42.09/20.38 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_showsPrec(x0, x1, ty_Double) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.38 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.38 new_showsPrec(x0, x1, ty_Char) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.38 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_primShowInt0(Neg(x0)) 42.09/20.38 new_show17(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primModNatS2(Zero, Zero) 42.09/20.38 new_primModNatS4(x0) 42.09/20.38 new_show30(x0, x1) 42.09/20.38 new_showsPrec(x0, x1, ty_Int) 42.09/20.38 new_show24(x0, x1, x2, x3) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.38 new_primShowInt0(Pos(Zero)) 42.09/20.38 new_show16(x0) 42.09/20.38 new_show26(x0) 42.09/20.38 new_showsPrec(x0, x1, ty_Integer) 42.09/20.38 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.38 new_primModNatS02(x0, x1) 42.09/20.38 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.38 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.38 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.38 new_div(x0, x1) 42.09/20.38 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.38 new_primIntToChar(x0, x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_show18(x0) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.38 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_show20(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.38 new_show25(x0, x1) 42.09/20.38 new_show23(x0) 42.09/20.38 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.38 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.38 new_show28(x0) 42.09/20.38 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.38 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.38 new_showsPrec(x0, x1, ty_@0) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (129) TransformationProof (EQUIVALENT) 42.09/20.38 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.38 42.09/20.38 (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))) 42.09/20.38 (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))) 42.09/20.38 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (130) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.38 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.38 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.38 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) 42.09/20.38 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) 42.09/20.38 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)) 42.09/20.38 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)) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.38 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.38 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.38 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.38 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.38 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.38 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.38 new_primModNatS4(ww304) -> Zero 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.38 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.38 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.38 new_psPs0([], ww200) -> ww200 42.09/20.38 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.38 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.38 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.38 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.38 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.38 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.38 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.38 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.38 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.38 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.38 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.38 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.38 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.38 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.38 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_psPs0([], x0) 42.09/20.38 new_show22(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_showsPrec(x0, x1, ty_IOError) 42.09/20.38 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.38 new_showsPrec(x0, x1, ty_Bool) 42.09/20.38 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.38 new_show15(x0, x1) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.38 new_psPs0(:(x0, x1), x2) 42.09/20.38 new_primShowInt0(Pos(Succ(x0))) 42.09/20.38 new_show27(x0, x1, x2) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_showsPrec(x0, x1, ty_Float) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.38 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.38 new_show19(x0) 42.09/20.38 new_primModNatS3(Zero, Zero, x0) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primModNatS2(Zero, Succ(x0)) 42.09/20.38 new_show31(x0) 42.09/20.38 new_show29(x0) 42.09/20.38 new_show21(x0, x1, x2) 42.09/20.38 new_primModNatS2(Succ(x0), Zero) 42.09/20.38 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_showsPrec(x0, x1, ty_Double) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.38 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.38 new_showsPrec(x0, x1, ty_Char) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.38 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_primShowInt0(Neg(x0)) 42.09/20.38 new_show17(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primModNatS2(Zero, Zero) 42.09/20.38 new_primModNatS4(x0) 42.09/20.38 new_show30(x0, x1) 42.09/20.38 new_showsPrec(x0, x1, ty_Int) 42.09/20.38 new_show24(x0, x1, x2, x3) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.38 new_primShowInt0(Pos(Zero)) 42.09/20.38 new_show16(x0) 42.09/20.38 new_show26(x0) 42.09/20.38 new_showsPrec(x0, x1, ty_Integer) 42.09/20.38 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.38 new_primModNatS02(x0, x1) 42.09/20.38 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.38 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.38 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.38 new_div(x0, x1) 42.09/20.38 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.38 new_primIntToChar(x0, x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_show18(x0) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.38 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_show20(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.38 new_show25(x0, x1) 42.09/20.38 new_show23(x0) 42.09/20.38 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.38 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.38 new_show28(x0) 42.09/20.38 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.38 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.38 new_showsPrec(x0, x1, ty_@0) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (131) DependencyGraphProof (EQUIVALENT) 42.09/20.38 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (132) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) 42.09/20.38 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.38 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.38 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) 42.09/20.38 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) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.38 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.38 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.38 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.38 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.38 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.38 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.38 new_primModNatS4(ww304) -> Zero 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.38 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.38 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.38 new_psPs0([], ww200) -> ww200 42.09/20.38 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.38 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.38 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.38 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.38 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.38 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.38 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.38 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.38 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.38 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.38 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.38 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.38 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.38 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.38 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_psPs0([], x0) 42.09/20.38 new_show22(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_showsPrec(x0, x1, ty_IOError) 42.09/20.38 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.38 new_showsPrec(x0, x1, ty_Bool) 42.09/20.38 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.38 new_show15(x0, x1) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.38 new_psPs0(:(x0, x1), x2) 42.09/20.38 new_primShowInt0(Pos(Succ(x0))) 42.09/20.38 new_show27(x0, x1, x2) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_showsPrec(x0, x1, ty_Float) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.38 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.38 new_show19(x0) 42.09/20.38 new_primModNatS3(Zero, Zero, x0) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primModNatS2(Zero, Succ(x0)) 42.09/20.38 new_show31(x0) 42.09/20.38 new_show29(x0) 42.09/20.38 new_show21(x0, x1, x2) 42.09/20.38 new_primModNatS2(Succ(x0), Zero) 42.09/20.38 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_showsPrec(x0, x1, ty_Double) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.38 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.38 new_showsPrec(x0, x1, ty_Char) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.38 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_primShowInt0(Neg(x0)) 42.09/20.38 new_show17(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primModNatS2(Zero, Zero) 42.09/20.38 new_primModNatS4(x0) 42.09/20.38 new_show30(x0, x1) 42.09/20.38 new_showsPrec(x0, x1, ty_Int) 42.09/20.38 new_show24(x0, x1, x2, x3) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.38 new_primShowInt0(Pos(Zero)) 42.09/20.38 new_show16(x0) 42.09/20.38 new_show26(x0) 42.09/20.38 new_showsPrec(x0, x1, ty_Integer) 42.09/20.38 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.38 new_primModNatS02(x0, x1) 42.09/20.38 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.38 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.38 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.38 new_div(x0, x1) 42.09/20.38 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.38 new_primIntToChar(x0, x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_show18(x0) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.38 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_show20(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.38 new_show25(x0, x1) 42.09/20.38 new_show23(x0) 42.09/20.38 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.38 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.38 new_show28(x0) 42.09/20.38 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.38 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.38 new_showsPrec(x0, x1, ty_@0) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (133) TransformationProof (EQUIVALENT) 42.09/20.38 By instantiating [LPAR04] the rule new_showParen(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_pt(ww195, ww196, ww197, ww198, ww199, bb) we obtained the following new rules [LPAR04]: 42.09/20.38 42.09/20.38 (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)) 42.09/20.38 (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)) 42.09/20.38 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (134) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_pt(ww195, ww196, ww197, :%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.38 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.38 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) 42.09/20.38 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) 42.09/20.38 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) 42.09/20.38 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) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.38 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.38 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.38 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.38 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.38 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.38 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.38 new_primModNatS4(ww304) -> Zero 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.38 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.38 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.38 new_psPs0([], ww200) -> ww200 42.09/20.38 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.38 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.38 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.38 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.38 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.38 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.38 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.38 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.38 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.38 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.38 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.38 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.38 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.38 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.38 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_psPs0([], x0) 42.09/20.38 new_show22(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_showsPrec(x0, x1, ty_IOError) 42.09/20.38 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.38 new_showsPrec(x0, x1, ty_Bool) 42.09/20.38 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.38 new_show15(x0, x1) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.38 new_psPs0(:(x0, x1), x2) 42.09/20.38 new_primShowInt0(Pos(Succ(x0))) 42.09/20.38 new_show27(x0, x1, x2) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_showsPrec(x0, x1, ty_Float) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.38 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.38 new_show19(x0) 42.09/20.38 new_primModNatS3(Zero, Zero, x0) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primModNatS2(Zero, Succ(x0)) 42.09/20.38 new_show31(x0) 42.09/20.38 new_show29(x0) 42.09/20.38 new_show21(x0, x1, x2) 42.09/20.38 new_primModNatS2(Succ(x0), Zero) 42.09/20.38 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_showsPrec(x0, x1, ty_Double) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.38 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.38 new_showsPrec(x0, x1, ty_Char) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.38 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_primShowInt0(Neg(x0)) 42.09/20.38 new_show17(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primModNatS2(Zero, Zero) 42.09/20.38 new_primModNatS4(x0) 42.09/20.38 new_show30(x0, x1) 42.09/20.38 new_showsPrec(x0, x1, ty_Int) 42.09/20.38 new_show24(x0, x1, x2, x3) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.38 new_primShowInt0(Pos(Zero)) 42.09/20.38 new_show16(x0) 42.09/20.38 new_show26(x0) 42.09/20.38 new_showsPrec(x0, x1, ty_Integer) 42.09/20.38 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.38 new_primModNatS02(x0, x1) 42.09/20.38 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.38 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.38 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.38 new_div(x0, x1) 42.09/20.38 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.38 new_primIntToChar(x0, x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_show18(x0) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.38 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_show20(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.38 new_show25(x0, x1) 42.09/20.38 new_show23(x0) 42.09/20.38 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.38 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.38 new_show28(x0) 42.09/20.38 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.38 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.38 new_showsPrec(x0, x1, ty_@0) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (135) DependencyGraphProof (EQUIVALENT) 42.09/20.38 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (136) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) 42.09/20.38 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) 42.09/20.38 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) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.38 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.38 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.38 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.38 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.38 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.38 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.38 new_primModNatS4(ww304) -> Zero 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.38 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.38 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.38 new_psPs0([], ww200) -> ww200 42.09/20.38 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.38 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.38 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.38 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.38 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.38 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.38 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.38 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.38 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.38 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.38 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.38 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.38 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.38 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.38 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_psPs0([], x0) 42.09/20.38 new_show22(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_showsPrec(x0, x1, ty_IOError) 42.09/20.38 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.38 new_showsPrec(x0, x1, ty_Bool) 42.09/20.38 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.38 new_show15(x0, x1) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.38 new_psPs0(:(x0, x1), x2) 42.09/20.38 new_primShowInt0(Pos(Succ(x0))) 42.09/20.38 new_show27(x0, x1, x2) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_showsPrec(x0, x1, ty_Float) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.38 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.38 new_show19(x0) 42.09/20.38 new_primModNatS3(Zero, Zero, x0) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primModNatS2(Zero, Succ(x0)) 42.09/20.38 new_show31(x0) 42.09/20.38 new_show29(x0) 42.09/20.38 new_show21(x0, x1, x2) 42.09/20.38 new_primModNatS2(Succ(x0), Zero) 42.09/20.38 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_showsPrec(x0, x1, ty_Double) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.38 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.38 new_showsPrec(x0, x1, ty_Char) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.38 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_primShowInt0(Neg(x0)) 42.09/20.38 new_show17(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primModNatS2(Zero, Zero) 42.09/20.38 new_primModNatS4(x0) 42.09/20.38 new_show30(x0, x1) 42.09/20.38 new_showsPrec(x0, x1, ty_Int) 42.09/20.38 new_show24(x0, x1, x2, x3) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.38 new_primShowInt0(Pos(Zero)) 42.09/20.38 new_show16(x0) 42.09/20.38 new_show26(x0) 42.09/20.38 new_showsPrec(x0, x1, ty_Integer) 42.09/20.38 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.38 new_primModNatS02(x0, x1) 42.09/20.38 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.38 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.38 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.38 new_div(x0, x1) 42.09/20.38 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.38 new_primIntToChar(x0, x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_show18(x0) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.38 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_show20(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.38 new_show25(x0, x1) 42.09/20.38 new_show23(x0) 42.09/20.38 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.38 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.38 new_show28(x0) 42.09/20.38 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.38 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.38 new_showsPrec(x0, x1, ty_@0) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (137) TransformationProof (EQUIVALENT) 42.09/20.38 By instantiating [LPAR04] the rule new_showParen(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, :(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), new_showsPrec(ww198, ww199, be)))), be, be) we obtained the following new rules [LPAR04]: 42.09/20.38 42.09/20.38 (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)) 42.09/20.38 (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)) 42.09/20.38 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (138) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 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) 42.09/20.38 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) 42.09/20.38 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) 42.09/20.38 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) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_show18(ww194) -> new_psPs0(new_show18(ww194), []) 42.09/20.38 new_showsPrec(ww198, ww199, ty_HugsException) -> new_psPs0(new_show22(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, ty_@0) -> new_psPs0(new_show20(ww198), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_@2, cb), cc), bb) -> new_psPs0(new_show27(ww194, cb, cc), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show20(ww194) -> new_psPs0(new_show20(ww194), []) 42.09/20.38 new_primIntToChar(ww248, ww249) -> Char(new_primModNatS2(ww248, ww249)) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(app(ty_@3, da), db), dc)) -> new_psPs0(new_show24(ww198, da, db, dc), ww199) 42.09/20.38 new_primShowInt0(Neg(ww1940)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(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(ww1940))) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 new_primModNatS3(Zero, Succ(ww3030), ww304) -> new_primModNatS4(ww304) 42.09/20.38 new_primModNatS2(Succ(ww2480), Succ(ww2490)) -> new_primModNatS01(ww2480, ww2490, ww2480, ww2490) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_show25(ww194, ca) -> new_psPs0(new_show25(ww194, ca), []) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_[], dg)) -> new_psPs0(new_show30(ww198, dg), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Integer, bb) -> new_psPs0(new_show16(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.38 new_show19(ww194) -> new_psPs0(new_show19(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Char, bb) -> new_psPs0(new_show29(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS02(ww297, ww298) -> new_primModNatS3(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.38 new_show15(ww194, ba) -> new_psPs0(new_show15(ww194, ba), []) 42.09/20.38 new_primModNatS4(ww304) -> Zero 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_psPs0(:(ww2400, ww2401), ww200) -> :(ww2400, new_psPs0(ww2401, ww200)) 42.09/20.38 new_primModNatS2(Zero, Zero) -> new_primModNatS3(Zero, Zero, Zero) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Float, bb) -> new_psPs0(new_show18(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show31(ww194) -> new_psPs0(new_show31(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_Maybe, ca), bb) -> new_psPs0(new_show25(ww194, ca), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show17(ww194) -> new_psPs0(new_show17(ww194), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(app(ty_@3, bf), bg), bh), bb) -> new_psPs0(new_show24(ww194, bf, bg, bh), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(app(ty_Either, bc), bd), bb) -> new_psPs0(new_show21(ww194, bc, bd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_HugsException, bb) -> new_psPs0(new_show22(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_show27(ww194, cb, cc) -> new_psPs0(new_show27(ww194, cb, cc), []) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOError, bb) -> new_psPs0(new_show26(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Bool, bb) -> new_psPs0(new_show31(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS3(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS3(ww3020, ww3030, ww304) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Double, bb) -> new_psPs0(new_show17(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS01(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS01(ww297, ww298, ww2990, ww3000) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Int, bb) -> new_psPs0(new_show23(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Ordering) -> new_psPs0(new_show19(ww198), ww199) 42.09/20.38 new_showParen0(:%(ww1940, ww1941), ww195, ww196, ww197, ww198, ww199, app(ty_Ratio, be), bb) -> new_showParen0(ww1940, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1941, new_pt0(ww195, ww196, ww197, ww198, ww199, be), be, be) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_IO, ce)) -> new_psPs0(new_show15(ww198, ce), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_IOErrorKind, bb) -> new_psPs0(new_show28(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_[], cd), bb) -> new_psPs0(new_show30(ww194, cd), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primModNatS3(Succ(ww3020), Zero, ww304) -> new_primModNatS2(ww3020, ww304) 42.09/20.38 new_psPs0([], ww200) -> ww200 42.09/20.38 new_primModNatS01(ww297, ww298, Zero, Succ(ww3000)) -> Succ(Succ(ww297)) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_show30(ww194, cd) -> new_psPs0(new_show30(ww194, cd), []) 42.09/20.38 new_show28(ww194) -> new_psPs0(new_show28(ww194), []) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_pt0(ww195, ww196, ww197, ww198, ww199, bb) -> new_psPs0(:(Char(Succ(ww195)), :(Char(Succ(ww196)), :(Char(Succ(ww197)), []))), new_showsPrec(ww198, ww199, bb)) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, app(ty_IO, ba), bb) -> new_psPs0(new_show15(ww194, ba), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_show22(ww194) -> new_psPs0(new_show22(ww194), []) 42.09/20.38 new_primModNatS2(Succ(ww2480), Zero) -> new_primModNatS3(Succ(ww2480), Zero, Zero) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Char) -> new_psPs0(new_show29(ww198), ww199) 42.09/20.38 new_primModNatS2(Zero, Succ(ww2490)) -> Succ(Zero) 42.09/20.38 new_show24(ww194, bf, bg, bh) -> new_psPs0(new_show24(ww194, bf, bg, bh), []) 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Double) -> new_psPs0(new_show17(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Int) -> new_psPs0(new_show23(ww198), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_@0, bb) -> new_psPs0(new_show20(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showsPrec(ww198, ww199, ty_IOError) -> new_psPs0(new_show26(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(ty_@2, de), df)) -> new_psPs0(new_show27(ww198, de, df), ww199) 42.09/20.38 new_showParen0(ww194, ww195, ww196, ww197, ww198, ww199, ty_Ordering, bb) -> new_psPs0(new_show19(ww194), new_pt0(ww195, ww196, ww197, ww198, ww199, bb)) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Bool) -> new_psPs0(new_show31(ww198), ww199) 42.09/20.38 new_primShowInt0(Pos(Succ(ww19400))) -> new_psPs0(new_primShowInt0(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), [])) 42.09/20.38 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))))))))))))))))))))))))))))))))))))))))))))))))), []) 42.09/20.38 new_show29(ww194) -> new_psPs0(new_show29(ww194), []) 42.09/20.38 new_primModNatS01(ww297, ww298, Zero, Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primModNatS01(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS02(ww297, ww298) 42.09/20.38 new_show26(ww194) -> new_psPs0(new_show26(ww194), []) 42.09/20.38 new_show23(ww194) -> new_primShowInt0(ww194) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_showsPrec(ww198, ww199, app(ty_Maybe, dd)) -> new_psPs0(new_show25(ww198, dd), ww199) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_showsPrec(:%(ww1980, ww1981), ww199, app(ty_Ratio, h)) -> new_showParen0(ww1980, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww1981, ww199, h, h) 42.09/20.38 new_showsPrec(ww198, ww199, ty_Float) -> new_psPs0(new_show18(ww198), ww199) 42.09/20.38 new_primModNatS3(Zero, Zero, ww304) -> new_primModNatS4(ww304) 42.09/20.38 new_show16(ww194) -> new_psPs0(new_show16(ww194), []) 42.09/20.38 new_showsPrec(ww198, ww199, ty_IOErrorKind) -> new_psPs0(new_show28(ww198), ww199) 42.09/20.38 new_showsPrec(ww198, ww199, app(app(ty_Either, cf), cg)) -> new_psPs0(new_show21(ww198, cf, cg), ww199) 42.09/20.38 new_show21(ww194, bc, bd) -> new_psPs0(new_show21(ww194, bc, bd), []) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_showsPrec(ww198, ww199, ty_Integer) -> new_psPs0(new_show16(ww198), ww199) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_psPs0([], x0) 42.09/20.38 new_show22(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_showsPrec(x0, x1, ty_IOError) 42.09/20.38 new_primModNatS3(Zero, Succ(x0), x1) 42.09/20.38 new_showsPrec(x0, x1, ty_Bool) 42.09/20.38 new_showsPrec(x0, x1, app(ty_[], x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6) 42.09/20.38 new_show15(x0, x1) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6) 42.09/20.38 new_psPs0(:(x0, x1), x2) 42.09/20.38 new_primShowInt0(Pos(Succ(x0))) 42.09/20.38 new_show27(x0, x1, x2) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_showsPrec(x0, x1, ty_Float) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6) 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6) 42.09/20.38 new_pt0(x0, x1, x2, x3, x4, x5) 42.09/20.38 new_show19(x0) 42.09/20.38 new_primModNatS3(Zero, Zero, x0) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primModNatS2(Zero, Succ(x0)) 42.09/20.38 new_show31(x0) 42.09/20.38 new_show29(x0) 42.09/20.38 new_show21(x0, x1, x2) 42.09/20.38 new_primModNatS2(Succ(x0), Zero) 42.09/20.38 new_primModNatS01(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_showsPrec(x0, x1, ty_Double) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8) 42.09/20.38 new_showsPrec(x0, x1, ty_HugsException) 42.09/20.38 new_showsPrec(x0, x1, ty_Char) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8) 42.09/20.38 new_primModNatS01(x0, x1, Zero, Zero) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_primShowInt0(Neg(x0)) 42.09/20.38 new_show17(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primModNatS2(Zero, Zero) 42.09/20.38 new_primModNatS4(x0) 42.09/20.38 new_show30(x0, x1) 42.09/20.38 new_showsPrec(x0, x1, ty_Int) 42.09/20.38 new_show24(x0, x1, x2, x3) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6) 42.09/20.38 new_primShowInt0(Pos(Zero)) 42.09/20.38 new_show16(x0) 42.09/20.38 new_show26(x0) 42.09/20.38 new_showsPrec(x0, x1, ty_Integer) 42.09/20.38 new_showsPrec(x0, x1, app(app(ty_Either, x2), x3)) 42.09/20.38 new_primModNatS02(x0, x1) 42.09/20.38 new_showsPrec(x0, x1, app(app(ty_@2, x2), x3)) 42.09/20.38 new_showsPrec(x0, x1, app(ty_IO, x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7) 42.09/20.38 new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6) 42.09/20.38 new_div(x0, x1) 42.09/20.38 new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3)) 42.09/20.38 new_primIntToChar(x0, x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_show18(x0) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6) 42.09/20.38 new_showsPrec(x0, x1, app(ty_Maybe, x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_show20(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primModNatS01(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7) 42.09/20.38 new_show25(x0, x1) 42.09/20.38 new_show23(x0) 42.09/20.38 new_primModNatS2(Succ(x0), Succ(x1)) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9) 42.09/20.38 new_primModNatS3(Succ(x0), Succ(x1), x2) 42.09/20.38 new_show28(x0) 42.09/20.38 new_showsPrec(x0, x1, ty_IOErrorKind) 42.09/20.38 new_primModNatS01(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primModNatS3(Succ(x0), Zero, x1) 42.09/20.38 new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7) 42.09/20.38 new_showsPrec(x0, x1, ty_@0) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 new_showsPrec(x0, x1, ty_Ordering) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (139) QDPSizeChangeProof (EQUIVALENT) 42.09/20.38 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. 42.09/20.38 42.09/20.38 From the DPs we obtained the following set of size-change graphs: 42.09/20.38 *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) 42.09/20.38 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 42.09/20.38 42.09/20.38 42.09/20.38 *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) 42.09/20.38 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 42.09/20.38 42.09/20.38 42.09/20.38 *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) 42.09/20.38 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 42.09/20.38 42.09/20.38 42.09/20.38 *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) 42.09/20.38 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 42.09/20.38 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (140) 42.09/20.38 YES 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (141) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_show7(ww194) -> new_show7(ww194) 42.09/20.38 42.09/20.38 R is empty. 42.09/20.38 Q is empty. 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (142) NonTerminationLoopProof (COMPLETE) 42.09/20.38 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 42.09/20.38 Found a loop by semiunifying a rule from P directly. 42.09/20.38 42.09/20.38 s = new_show7(ww194) evaluates to t =new_show7(ww194) 42.09/20.38 42.09/20.38 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 42.09/20.38 * Matcher: [ ] 42.09/20.38 * Semiunifier: [ ] 42.09/20.38 42.09/20.38 -------------------------------------------------------------------------------- 42.09/20.38 Rewriting sequence 42.09/20.38 42.09/20.38 The DP semiunifies directly so there is only one rewrite step from new_show7(ww194) to new_show7(ww194). 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (143) 42.09/20.38 NO 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (144) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_show12(ww194) -> new_show12(ww194) 42.09/20.38 42.09/20.38 R is empty. 42.09/20.38 Q is empty. 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (145) NonTerminationLoopProof (COMPLETE) 42.09/20.38 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 42.09/20.38 Found a loop by semiunifying a rule from P directly. 42.09/20.38 42.09/20.38 s = new_show12(ww194) evaluates to t =new_show12(ww194) 42.09/20.38 42.09/20.38 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 42.09/20.38 * Matcher: [ ] 42.09/20.38 * Semiunifier: [ ] 42.09/20.38 42.09/20.38 -------------------------------------------------------------------------------- 42.09/20.38 Rewriting sequence 42.09/20.38 42.09/20.38 The DP semiunifies directly so there is only one rewrite step from new_show12(ww194) to new_show12(ww194). 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (146) 42.09/20.38 NO 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (147) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_primShowInt(Neg(ww1940)) -> new_primShowInt(Pos(ww1940)) 42.09/20.38 new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_div(x0, x1) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (148) DependencyGraphProof (EQUIVALENT) 42.09/20.38 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (149) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_div(x0, x1) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (150) TransformationProof (EQUIVALENT) 42.09/20.38 By rewriting [LPAR04] the rule new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(new_div(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0] we obtained the following new rules [LPAR04]: 42.09/20.38 42.09/20.38 (new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(Pos(new_primDivNatS3(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))),new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(Pos(new_primDivNatS3(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 42.09/20.38 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (151) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(Pos(new_primDivNatS3(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_div(ww242, ww243) -> Pos(new_primDivNatS3(ww242, ww243)) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_div(x0, x1) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (152) UsableRulesProof (EQUIVALENT) 42.09/20.38 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. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (153) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(Pos(new_primDivNatS3(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_div(x0, x1) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (154) QReductionProof (EQUIVALENT) 42.09/20.38 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 42.09/20.38 42.09/20.38 new_div(x0, x1) 42.09/20.38 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (155) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(Pos(new_primDivNatS3(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (156) MNOCProof (EQUIVALENT) 42.09/20.38 We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (157) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(Pos(new_primDivNatS3(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 42.09/20.38 Q is empty. 42.09/20.38 We have to consider all (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (158) InductionCalculusProof (EQUIVALENT) 42.09/20.38 Note that final constraints are written in bold face. 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 For Pair new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(Pos(new_primDivNatS3(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) the following chains were created: 42.09/20.38 *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: 42.09/20.38 42.09/20.38 (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))))))))))))) 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint: 42.09/20.38 42.09/20.38 (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))))))))))))) 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 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: 42.09/20.38 42.09/20.38 (3) (new_primDivNatS02(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))))))))))))) 42.09/20.38 42.09/20.38 (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))))))))))))) 42.09/20.38 42.09/20.38 (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))))))))))))) 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint: 42.09/20.38 42.09/20.38 (6) (x4=x7 & x3=x8 & new_primDivNatS02(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))))))))))))) 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 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_primDivNatS02(x4, x3, x7, x8)=Succ(x1) which results in the following new constraints: 42.09/20.38 42.09/20.38 (7) (new_primDivNatS02(x12, x11, x10, x9)=Succ(x1) & x12=Succ(x10) & x11=Succ(x9) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x11 & (\/x13:new_primDivNatS02(x12, x11, x10, x9)=Succ(x13) & x12=x10 & x11=x9 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x11 ==> new_primShowInt(Pos(Succ(Succ(x12))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x12), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) ==> new_primShowInt(Pos(Succ(Succ(x12))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x12), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 42.09/20.38 42.09/20.38 (8) (new_primDivNatS01(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))))))))))))) 42.09/20.38 42.09/20.38 (9) (new_primDivNatS01(x18, x17)=Succ(x1) & x18=Zero & x17=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x17 ==> new_primShowInt(Pos(Succ(Succ(x18))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x18), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 We simplified constraint (7) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint: 42.09/20.38 42.09/20.38 (10) (new_primShowInt(Pos(Succ(Succ(Succ(x10)))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(Succ(x10)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 We solved constraint (8) using rules (I), (II), (III).We solved constraint (9) using rules (I), (II), (III). 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 To summarize, we get the following constraints P__>=_ for the following pairs. 42.09/20.38 42.09/20.38 *new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(Pos(new_primDivNatS3(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 42.09/20.38 42.09/20.38 *(new_primShowInt(Pos(Succ(Succ(Succ(x10)))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(Succ(x10)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))) 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 42.09/20.38 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. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (159) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(Pos(new_primDivNatS3(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (160) TransformationProof (EQUIVALENT) 42.09/20.38 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(ww19400))) -> new_primShowInt(Pos(new_primDivNatS3(ww19400, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]: 42.09/20.38 42.09/20.38 (new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(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_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) 42.09/20.38 (new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero))) 42.09/20.38 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (161) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 42.09/20.38 new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (162) DependencyGraphProof (EQUIVALENT) 42.09/20.38 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (163) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (164) TransformationProof (EQUIVALENT) 42.09/20.38 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS02(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]: 42.09/20.38 42.09/20.38 (new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(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_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) 42.09/20.38 (new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero))) 42.09/20.38 42.09/20.38 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (165) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) 42.09/20.38 new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)) 42.09/20.38 42.09/20.38 The TRS R consists of the following rules: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.38 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.38 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.38 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.38 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.38 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.38 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.38 new_primDivNatS4(ww308) -> Zero 42.09/20.38 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.38 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.38 42.09/20.38 The set Q consists of the following terms: 42.09/20.38 42.09/20.38 new_primDivNatS3(Succ(x0), Zero) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.38 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.38 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.38 new_primDivNatS4(x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.38 new_primDivNatS2(Zero, Zero, x0) 42.09/20.38 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.38 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.38 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.38 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.38 new_primDivNatS01(x0, x1) 42.09/20.38 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.38 new_primDivNatS3(Zero, Zero) 42.09/20.38 42.09/20.38 We have to consider all minimal (P,Q,R)-chains. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (166) DependencyGraphProof (EQUIVALENT) 42.09/20.38 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 42.09/20.38 ---------------------------------------- 42.09/20.38 42.09/20.38 (167) 42.09/20.38 Obligation: 42.09/20.38 Q DP problem: 42.09/20.38 The TRS P consists of the following rules: 42.09/20.38 42.09/20.38 new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) 42.09/20.39 42.09/20.39 The TRS R consists of the following rules: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.39 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.39 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.39 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS4(ww308) -> Zero 42.09/20.39 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.39 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.39 42.09/20.39 The set Q consists of the following terms: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(x0), Zero) 42.09/20.39 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.39 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.39 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.39 new_primDivNatS4(x0) 42.09/20.39 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.39 new_primDivNatS2(Zero, Zero, x0) 42.09/20.39 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.39 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.39 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.39 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.39 new_primDivNatS01(x0, x1) 42.09/20.39 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.39 new_primDivNatS3(Zero, Zero) 42.09/20.39 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (168) TransformationProof (EQUIVALENT) 42.09/20.39 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS02(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]: 42.09/20.39 42.09/20.39 (new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(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_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) 42.09/20.39 (new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero))) 42.09/20.39 42.09/20.39 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (169) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)) 42.09/20.39 42.09/20.39 The TRS R consists of the following rules: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.39 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.39 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.39 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS4(ww308) -> Zero 42.09/20.39 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.39 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.39 42.09/20.39 The set Q consists of the following terms: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(x0), Zero) 42.09/20.39 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.39 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.39 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.39 new_primDivNatS4(x0) 42.09/20.39 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.39 new_primDivNatS2(Zero, Zero, x0) 42.09/20.39 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.39 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.39 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.39 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.39 new_primDivNatS01(x0, x1) 42.09/20.39 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.39 new_primDivNatS3(Zero, Zero) 42.09/20.39 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (170) DependencyGraphProof (EQUIVALENT) 42.09/20.39 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (171) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 42.09/20.39 The TRS R consists of the following rules: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.39 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.39 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.39 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS4(ww308) -> Zero 42.09/20.39 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.39 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.39 42.09/20.39 The set Q consists of the following terms: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(x0), Zero) 42.09/20.39 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.39 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.39 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.39 new_primDivNatS4(x0) 42.09/20.39 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.39 new_primDivNatS2(Zero, Zero, x0) 42.09/20.39 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.39 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.39 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.39 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.39 new_primDivNatS01(x0, x1) 42.09/20.39 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.39 new_primDivNatS3(Zero, Zero) 42.09/20.39 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (172) TransformationProof (EQUIVALENT) 42.09/20.39 By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS02(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]: 42.09/20.39 42.09/20.39 (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(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_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero))) 42.09/20.39 42.09/20.39 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (173) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 42.09/20.39 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)) 42.09/20.39 42.09/20.39 The TRS R consists of the following rules: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.39 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.39 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.39 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS4(ww308) -> Zero 42.09/20.39 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.39 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.39 42.09/20.39 The set Q consists of the following terms: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(x0), Zero) 42.09/20.39 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.39 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.39 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.39 new_primDivNatS4(x0) 42.09/20.39 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.39 new_primDivNatS2(Zero, Zero, x0) 42.09/20.39 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.39 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.39 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.39 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.39 new_primDivNatS01(x0, x1) 42.09/20.39 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.39 new_primDivNatS3(Zero, Zero) 42.09/20.39 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (174) DependencyGraphProof (EQUIVALENT) 42.09/20.39 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (175) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 42.09/20.39 42.09/20.39 The TRS R consists of the following rules: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.39 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.39 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.39 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS4(ww308) -> Zero 42.09/20.39 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.39 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.39 42.09/20.39 The set Q consists of the following terms: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(x0), Zero) 42.09/20.39 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.39 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.39 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.39 new_primDivNatS4(x0) 42.09/20.39 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.39 new_primDivNatS2(Zero, Zero, x0) 42.09/20.39 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.39 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.39 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.39 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.39 new_primDivNatS01(x0, x1) 42.09/20.39 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.39 new_primDivNatS3(Zero, Zero) 42.09/20.39 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (176) MNOCProof (EQUIVALENT) 42.09/20.39 We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (177) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 42.09/20.39 42.09/20.39 The TRS R consists of the following rules: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.39 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.39 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.39 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS4(ww308) -> Zero 42.09/20.39 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.39 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.39 42.09/20.39 Q is empty. 42.09/20.39 We have to consider all (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (178) InductionCalculusProof (EQUIVALENT) 42.09/20.39 Note that final constraints are written in bold face. 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 For Pair new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(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: 42.09/20.39 *We consider the chain new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0))))))) -> new_primShowInt(Pos(new_primDivNatS02(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_primDivNatS02(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: 42.09/20.39 42.09/20.39 (1) (new_primShowInt(Pos(new_primDivNatS02(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_primDivNatS02(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint: 42.09/20.39 42.09/20.39 (2) (Succ(Succ(Succ(x0)))=x2 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x4 & new_primDivNatS02(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS02(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints: 42.09/20.39 42.09/20.39 (3) (new_primDivNatS02(x8, x7, x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x6))))=x8 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x7 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Succ(x5) & (\/x9:new_primDivNatS02(x8, x7, x6, x5)=Succ(Succ(Succ(Succ(Succ(x9))))) & Succ(Succ(Succ(x6)))=x8 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x7 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x5 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x6)))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x6))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x6, Succ(Succ(Succ(Succ(Succ(Zero))))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x6))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(x6)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x6), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 42.09/20.39 (4) (new_primDivNatS01(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_primDivNatS02(Succ(Succ(Succ(Succ(x10)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x10), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 42.09/20.39 (5) (new_primDivNatS01(x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Zero)))=x14 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x13 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Zero, Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 We simplified constraint (3) using rules (I), (II), (IV) which results in the following new constraint: 42.09/20.39 42.09/20.39 (6) (new_primDivNatS02(x8, x7, x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x6))))=x8 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x7 & Succ(Succ(Succ(Succ(Zero))))=x5 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x6))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(x6)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x6), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 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_primDivNatS02(x8, x7, x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints: 42.09/20.39 42.09/20.39 (7) (new_primDivNatS02(x21, x20, x19, x18)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x19)))))=x21 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x20 & Succ(Succ(Succ(Succ(Zero))))=Succ(x18) & (\/x22:new_primDivNatS02(x21, x20, x19, x18)=Succ(Succ(Succ(Succ(Succ(x22))))) & Succ(Succ(Succ(Succ(x19))))=x21 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x20 & Succ(Succ(Succ(Succ(Zero))))=x18 ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x19))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(x19)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x19), Succ(Succ(Succ(Succ(Succ(Zero))))))))) ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x19)))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Succ(x19))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x19)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 42.09/20.39 (8) (new_primDivNatS01(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_primDivNatS02(Succ(Succ(Succ(Succ(Succ(x23))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x23)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 42.09/20.39 (9) (new_primDivNatS01(x27, x26)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Zero))))=x27 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x26 & Succ(Succ(Succ(Succ(Zero))))=Zero ==> new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 We simplified constraint (7) using rules (I), (II), (III), (IV) which results in the following new constraint: 42.09/20.39 42.09/20.39 (10) (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x19)))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Succ(x19))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x19)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 We solved constraint (8) using rules (I), (II).We solved constraint (9) using rules (I), (II). 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 To summarize, we get the following constraints P__>=_ for the following pairs. 42.09/20.39 42.09/20.39 *new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 42.09/20.39 42.09/20.39 *(new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x19)))))))))_>=_new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(Succ(Succ(x19))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x19)), Succ(Succ(Succ(Succ(Succ(Zero))))))))) 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 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. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (179) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS02(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) 42.09/20.39 42.09/20.39 The TRS R consists of the following rules: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(ww2420), Succ(ww2430)) -> new_primDivNatS02(ww2420, ww2430, ww2420, ww2430) 42.09/20.39 new_primDivNatS3(Zero, Succ(ww2430)) -> Zero 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Succ(ww2950)) -> new_primDivNatS02(ww292, ww293, ww2940, ww2950) 42.09/20.39 new_primDivNatS02(ww292, ww293, Succ(ww2940), Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Zero) -> new_primDivNatS01(ww292, ww293) 42.09/20.39 new_primDivNatS02(ww292, ww293, Zero, Succ(ww2950)) -> Zero 42.09/20.39 new_primDivNatS01(ww292, ww293) -> Succ(new_primDivNatS2(Succ(ww292), Succ(ww293), Succ(ww293))) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Succ(ww3070), ww308) -> new_primDivNatS2(ww3060, ww3070, ww308) 42.09/20.39 new_primDivNatS2(Succ(ww3060), Zero, ww308) -> new_primDivNatS3(ww3060, ww308) 42.09/20.39 new_primDivNatS2(Zero, Zero, ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS2(Zero, Succ(ww3070), ww308) -> new_primDivNatS4(ww308) 42.09/20.39 new_primDivNatS4(ww308) -> Zero 42.09/20.39 new_primDivNatS3(Succ(ww2420), Zero) -> Succ(new_primDivNatS2(Succ(ww2420), Zero, Zero)) 42.09/20.39 new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero)) 42.09/20.39 42.09/20.39 The set Q consists of the following terms: 42.09/20.39 42.09/20.39 new_primDivNatS3(Succ(x0), Zero) 42.09/20.39 new_primDivNatS02(x0, x1, Succ(x2), Zero) 42.09/20.39 new_primDivNatS2(Zero, Succ(x0), x1) 42.09/20.39 new_primDivNatS2(Succ(x0), Succ(x1), x2) 42.09/20.39 new_primDivNatS4(x0) 42.09/20.39 new_primDivNatS02(x0, x1, Zero, Succ(x2)) 42.09/20.39 new_primDivNatS2(Zero, Zero, x0) 42.09/20.39 new_primDivNatS02(x0, x1, Zero, Zero) 42.09/20.39 new_primDivNatS2(Succ(x0), Zero, x1) 42.09/20.39 new_primDivNatS3(Zero, Succ(x0)) 42.09/20.39 new_primDivNatS3(Succ(x0), Succ(x1)) 42.09/20.39 new_primDivNatS01(x0, x1) 42.09/20.39 new_primDivNatS02(x0, x1, Succ(x2), Succ(x3)) 42.09/20.39 new_primDivNatS3(Zero, Zero) 42.09/20.39 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (180) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_show1(ww194) -> new_show1(ww194) 42.09/20.39 42.09/20.39 R is empty. 42.09/20.39 Q is empty. 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (181) NonTerminationLoopProof (COMPLETE) 42.09/20.39 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 42.09/20.39 Found a loop by semiunifying a rule from P directly. 42.09/20.39 42.09/20.39 s = new_show1(ww194) evaluates to t =new_show1(ww194) 42.09/20.39 42.09/20.39 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 42.09/20.39 * Matcher: [ ] 42.09/20.39 * Semiunifier: [ ] 42.09/20.39 42.09/20.39 -------------------------------------------------------------------------------- 42.09/20.39 Rewriting sequence 42.09/20.39 42.09/20.39 The DP semiunifies directly so there is only one rewrite step from new_show1(ww194) to new_show1(ww194). 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (182) 42.09/20.39 NO 42.09/20.39 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (183) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_primModNatS(Succ(ww3020), Zero, ww304) -> new_primModNatS1(ww3020, ww304) 42.09/20.39 new_primModNatS1(Zero, Zero) -> new_primModNatS(Zero, Zero, Zero) 42.09/20.39 new_primModNatS00(ww297, ww298) -> new_primModNatS(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.39 new_primModNatS0(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.39 new_primModNatS(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS(ww3020, ww3030, ww304) 42.09/20.39 new_primModNatS0(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS0(ww297, ww298, ww2990, ww3000) 42.09/20.39 new_primModNatS1(Succ(ww2480), Succ(ww2490)) -> new_primModNatS0(ww2480, ww2490, ww2480, ww2490) 42.09/20.39 new_primModNatS0(ww297, ww298, Zero, Zero) -> new_primModNatS00(ww297, ww298) 42.09/20.39 new_primModNatS1(Succ(ww2480), Zero) -> new_primModNatS(Succ(ww2480), Zero, Zero) 42.09/20.39 42.09/20.39 R is empty. 42.09/20.39 Q is empty. 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (184) DependencyGraphProof (EQUIVALENT) 42.09/20.39 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (185) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_primModNatS1(Succ(ww2480), Succ(ww2490)) -> new_primModNatS0(ww2480, ww2490, ww2480, ww2490) 42.09/20.39 new_primModNatS0(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.39 new_primModNatS(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS(ww3020, ww3030, ww304) 42.09/20.39 new_primModNatS(Succ(ww3020), Zero, ww304) -> new_primModNatS1(ww3020, ww304) 42.09/20.39 new_primModNatS1(Succ(ww2480), Zero) -> new_primModNatS(Succ(ww2480), Zero, Zero) 42.09/20.39 new_primModNatS0(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS0(ww297, ww298, ww2990, ww3000) 42.09/20.39 new_primModNatS0(ww297, ww298, Zero, Zero) -> new_primModNatS00(ww297, ww298) 42.09/20.39 new_primModNatS00(ww297, ww298) -> new_primModNatS(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.39 42.09/20.39 R is empty. 42.09/20.39 Q is empty. 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (186) QDPOrderProof (EQUIVALENT) 42.09/20.39 We use the reduction pair processor [LPAR04,JAR06]. 42.09/20.39 42.09/20.39 42.09/20.39 The following pairs can be oriented strictly and are deleted. 42.09/20.39 42.09/20.39 new_primModNatS1(Succ(ww2480), Succ(ww2490)) -> new_primModNatS0(ww2480, ww2490, ww2480, ww2490) 42.09/20.39 new_primModNatS(Succ(ww3020), Succ(ww3030), ww304) -> new_primModNatS(ww3020, ww3030, ww304) 42.09/20.39 new_primModNatS1(Succ(ww2480), Zero) -> new_primModNatS(Succ(ww2480), Zero, Zero) 42.09/20.39 The remaining pairs can at least be oriented weakly. 42.09/20.39 Used ordering: Polynomial interpretation [POLO]: 42.09/20.39 42.09/20.39 POL(Succ(x_1)) = 1 + x_1 42.09/20.39 POL(Zero) = 0 42.09/20.39 POL(new_primModNatS(x_1, x_2, x_3)) = x_1 42.09/20.39 POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1 42.09/20.39 POL(new_primModNatS00(x_1, x_2)) = 1 + x_1 42.09/20.39 POL(new_primModNatS1(x_1, x_2)) = 1 + x_1 42.09/20.39 42.09/20.39 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 42.09/20.39 none 42.09/20.39 42.09/20.39 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (187) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_primModNatS0(ww297, ww298, Succ(ww2990), Zero) -> new_primModNatS(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.39 new_primModNatS(Succ(ww3020), Zero, ww304) -> new_primModNatS1(ww3020, ww304) 42.09/20.39 new_primModNatS0(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS0(ww297, ww298, ww2990, ww3000) 42.09/20.39 new_primModNatS0(ww297, ww298, Zero, Zero) -> new_primModNatS00(ww297, ww298) 42.09/20.39 new_primModNatS00(ww297, ww298) -> new_primModNatS(Succ(ww297), Succ(ww298), Succ(ww298)) 42.09/20.39 42.09/20.39 R is empty. 42.09/20.39 Q is empty. 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (188) DependencyGraphProof (EQUIVALENT) 42.09/20.39 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (189) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_primModNatS0(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS0(ww297, ww298, ww2990, ww3000) 42.09/20.39 42.09/20.39 R is empty. 42.09/20.39 Q is empty. 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (190) QDPSizeChangeProof (EQUIVALENT) 42.09/20.39 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. 42.09/20.39 42.09/20.39 From the DPs we obtained the following set of size-change graphs: 42.09/20.39 *new_primModNatS0(ww297, ww298, Succ(ww2990), Succ(ww3000)) -> new_primModNatS0(ww297, ww298, ww2990, ww3000) 42.09/20.39 The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4 42.09/20.39 42.09/20.39 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (191) 42.09/20.39 YES 42.09/20.39 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (192) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_show0(ww194, h) -> new_show0(ww194, h) 42.09/20.39 42.09/20.39 R is empty. 42.09/20.39 Q is empty. 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (193) NonTerminationLoopProof (COMPLETE) 42.09/20.39 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 42.09/20.39 Found a loop by semiunifying a rule from P directly. 42.09/20.39 42.09/20.39 s = new_show0(ww194, h) evaluates to t =new_show0(ww194, h) 42.09/20.39 42.09/20.39 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 42.09/20.39 * Matcher: [ ] 42.09/20.39 * Semiunifier: [ ] 42.09/20.39 42.09/20.39 -------------------------------------------------------------------------------- 42.09/20.39 Rewriting sequence 42.09/20.39 42.09/20.39 The DP semiunifies directly so there is only one rewrite step from new_show0(ww194, h) to new_show0(ww194, h). 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (194) 42.09/20.39 NO 42.09/20.39 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (195) 42.09/20.39 Obligation: 42.09/20.39 Q DP problem: 42.09/20.39 The TRS P consists of the following rules: 42.09/20.39 42.09/20.39 new_show5(ww194, h) -> new_show5(ww194, h) 42.09/20.39 42.09/20.39 R is empty. 42.09/20.39 Q is empty. 42.09/20.39 We have to consider all minimal (P,Q,R)-chains. 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (196) NonTerminationLoopProof (COMPLETE) 42.09/20.39 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 42.09/20.39 Found a loop by semiunifying a rule from P directly. 42.09/20.39 42.09/20.39 s = new_show5(ww194, h) evaluates to t =new_show5(ww194, h) 42.09/20.39 42.09/20.39 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 42.09/20.39 * Matcher: [ ] 42.09/20.39 * Semiunifier: [ ] 42.09/20.39 42.09/20.39 -------------------------------------------------------------------------------- 42.09/20.39 Rewriting sequence 42.09/20.39 42.09/20.39 The DP semiunifies directly so there is only one rewrite step from new_show5(ww194, h) to new_show5(ww194, h). 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (197) 42.09/20.39 NO 42.09/20.39 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (198) Narrow (COMPLETE) 42.09/20.39 Haskell To QDPs 42.09/20.39 42.09/20.39 digraph dp_graph { 42.09/20.39 node [outthreshold=100, inthreshold=100];1[label="show",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3]; 42.09/20.39 3[label="show ww3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3]; 42.09/20.39 4[label="showsPrec (Pos Zero) ww3 []",fontsize=16,color="burlywood",shape="box"];2989[label="ww3/ww30 :% ww31",fontsize=10,color="white",style="solid",shape="box"];4 -> 2989[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 2989 -> 5[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 5[label="showsPrec (Pos Zero) (ww30 :% ww31) []",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3]; 42.09/20.39 6 -> 1526[label="",style="dashed", color="red", weight=0]; 42.09/20.39 6[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww30) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww31) []",fontsize=16,color="magenta"];6 -> 1527[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 6 -> 1528[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 6 -> 1529[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 6 -> 1530[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 6 -> 1531[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 6 -> 1532[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1527[label="[]",fontsize=16,color="green",shape="box"];1528[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];1529[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (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"];1530[label="ww30",fontsize=16,color="green",shape="box"];1531[label="ww31",fontsize=16,color="green",shape="box"];1532[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"];1526[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) ww199",fontsize=16,color="black",shape="triangle"];1526 -> 1539[label="",style="solid", color="black", weight=3]; 42.09/20.39 1539[label="showParen0 ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww199",fontsize=16,color="black",shape="box"];1539 -> 1540[label="",style="solid", color="black", weight=3]; 42.09/20.39 1540[label="showParen0 ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww199",fontsize=16,color="black",shape="box"];1540 -> 1541[label="",style="solid", color="black", weight=3]; 42.09/20.39 1541[label="showParen0 ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww199",fontsize=16,color="black",shape="box"];1541 -> 1542[label="",style="solid", color="black", weight=3]; 42.09/20.39 1542[label="showParen0 ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww199",fontsize=16,color="black",shape="box"];1542 -> 1543[label="",style="solid", color="black", weight=3]; 42.09/20.39 1543[label="showParen0 ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) (LT == GT) ww199",fontsize=16,color="black",shape="box"];1543 -> 1544[label="",style="solid", color="black", weight=3]; 42.09/20.39 1544[label="showParen0 ((shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198) False ww199",fontsize=16,color="black",shape="box"];1544 -> 1545[label="",style="solid", color="black", weight=3]; 42.09/20.39 1545[label="(shows ww194) . (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="black",shape="box"];1545 -> 1546[label="",style="solid", color="black", weight=3]; 42.09/20.39 1546[label="shows ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1546 -> 1547[label="",style="solid", color="black", weight=3]; 42.09/20.39 1547[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="blue",shape="box"];2990[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2990[label="",style="solid", color="blue", weight=9]; 42.09/20.39 2990 -> 1548[label="",style="solid", color="blue", weight=3]; 42.09/20.39 2991[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2991[label="",style="solid", color="blue", weight=9]; 42.09/20.39 2991 -> 1549[label="",style="solid", color="blue", weight=3]; 42.09/20.39 2992[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2992[label="",style="solid", color="blue", weight=9]; 42.09/20.39 2992 -> 1550[label="",style="solid", color="blue", weight=3]; 42.09/20.39 2993[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2993[label="",style="solid", color="blue", weight=9]; 42.09/20.39 2993 -> 1551[label="",style="solid", color="blue", weight=3]; 42.09/20.39 2994[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2994[label="",style="solid", color="blue", weight=9]; 42.09/20.39 2994 -> 1552[label="",style="solid", color="blue", weight=3]; 42.09/20.39 2995[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2995[label="",style="solid", color="blue", weight=9]; 42.09/20.39 2995 -> 1553[label="",style="solid", color="blue", weight=3]; 42.09/20.39 2996[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2996[label="",style="solid", color="blue", weight=9]; 42.09/20.39 2996 -> 1554[label="",style="solid", color="blue", weight=3]; 42.09/20.39 2997[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2997[label="",style="solid", color="blue", weight=9]; 42.09/20.39 2997 -> 1555[label="",style="solid", color="blue", weight=3]; 42.09/20.39 2998[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2998[label="",style="solid", color="blue", weight=9]; 42.09/20.39 2998 -> 1556[label="",style="solid", color="blue", weight=3]; 42.09/20.39 2999[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 2999[label="",style="solid", color="blue", weight=9]; 42.09/20.39 2999 -> 1557[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3000[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3000[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3000 -> 1558[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3001[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3001[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3001 -> 1559[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3002[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3002[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3002 -> 1560[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3003[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3003[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3003 -> 1561[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3004[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3004[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3004 -> 1562[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3005[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3005[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3005 -> 1563[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3006[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3006[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3006 -> 1564[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3007[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1547 -> 3007[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3007 -> 1565[label="",style="solid", color="blue", weight=3]; 42.09/20.39 1548[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1548 -> 1566[label="",style="solid", color="black", weight=3]; 42.09/20.39 1549[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1549 -> 1567[label="",style="solid", color="black", weight=3]; 42.09/20.39 1550[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1550 -> 1568[label="",style="solid", color="black", weight=3]; 42.09/20.39 1551[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1551 -> 1569[label="",style="solid", color="black", weight=3]; 42.09/20.39 1552[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1552 -> 1570[label="",style="solid", color="black", weight=3]; 42.09/20.39 1553[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1553 -> 1571[label="",style="solid", color="black", weight=3]; 42.09/20.39 1554[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1554 -> 1572[label="",style="solid", color="black", weight=3]; 42.09/20.39 1555[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="burlywood",shape="box"];3008[label="ww194/ww1940 :% ww1941",fontsize=10,color="white",style="solid",shape="box"];1555 -> 3008[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3008 -> 1573[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 1556[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1556 -> 1574[label="",style="solid", color="black", weight=3]; 42.09/20.39 1557[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1557 -> 1575[label="",style="solid", color="black", weight=3]; 42.09/20.39 1558[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1558 -> 1576[label="",style="solid", color="black", weight=3]; 42.09/20.39 1559[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1559 -> 1577[label="",style="solid", color="black", weight=3]; 42.09/20.39 1560[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1560 -> 1578[label="",style="solid", color="black", weight=3]; 42.09/20.39 1561[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1561 -> 1579[label="",style="solid", color="black", weight=3]; 42.09/20.39 1562[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1562 -> 1580[label="",style="solid", color="black", weight=3]; 42.09/20.39 1563[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1563 -> 1581[label="",style="solid", color="black", weight=3]; 42.09/20.39 1564[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1564 -> 1582[label="",style="solid", color="black", weight=3]; 42.09/20.39 1565[label="showsPrec (Pos Zero) ww194 ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1565 -> 1583[label="",style="solid", color="black", weight=3]; 42.09/20.39 1566 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1566[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1566 -> 1736[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1566 -> 1737[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1567 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1567[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1567 -> 1738[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1567 -> 1739[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1568 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1568[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1568 -> 1740[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1568 -> 1741[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1569 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1569[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1569 -> 1742[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1569 -> 1743[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1570 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1570[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1570 -> 1744[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1570 -> 1745[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1571 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1571[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1571 -> 1746[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1571 -> 1747[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1572 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1572[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1572 -> 1748[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1572 -> 1749[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1573[label="showsPrec (Pos Zero) (ww1940 :% ww1941) ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="black",shape="box"];1573 -> 1591[label="",style="solid", color="black", weight=3]; 42.09/20.39 1574 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1574[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1574 -> 1750[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1574 -> 1751[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1575 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1575[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1575 -> 1752[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1575 -> 1753[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1576 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1576[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1576 -> 1754[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1576 -> 1755[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1577 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1577[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1577 -> 1756[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1577 -> 1757[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1578 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1578[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1578 -> 1758[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1578 -> 1759[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1579 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1579[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1579 -> 1760[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1579 -> 1761[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1580 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1580[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1580 -> 1762[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1580 -> 1763[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1581 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1581[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1581 -> 1764[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1581 -> 1765[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1582 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1582[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1582 -> 1766[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1582 -> 1767[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1583 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1583[label="show ww194 ++ (showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1583 -> 1768[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1583 -> 1769[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1736[label="show ww194",fontsize=16,color="black",shape="triangle"];1736 -> 1959[label="",style="solid", color="black", weight=3]; 42.09/20.39 1737 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1737[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1735[label="ww240 ++ ww200",fontsize=16,color="burlywood",shape="triangle"];3009[label="ww240/ww2400 : ww2401",fontsize=10,color="white",style="solid",shape="box"];1735 -> 3009[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3009 -> 1960[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3010[label="ww240/[]",fontsize=10,color="white",style="solid",shape="box"];1735 -> 3010[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3010 -> 1961[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 1738[label="show ww194",fontsize=16,color="black",shape="triangle"];1738 -> 1962[label="",style="solid", color="black", weight=3]; 42.09/20.39 1739 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1739[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1740[label="show ww194",fontsize=16,color="black",shape="triangle"];1740 -> 1963[label="",style="solid", color="black", weight=3]; 42.09/20.39 1741 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1741[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1742[label="show ww194",fontsize=16,color="black",shape="triangle"];1742 -> 1964[label="",style="solid", color="black", weight=3]; 42.09/20.39 1743 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1743[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1744[label="show ww194",fontsize=16,color="black",shape="triangle"];1744 -> 1965[label="",style="solid", color="black", weight=3]; 42.09/20.39 1745 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1745[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1746[label="show ww194",fontsize=16,color="black",shape="triangle"];1746 -> 1966[label="",style="solid", color="black", weight=3]; 42.09/20.39 1747 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1747[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1748[label="show ww194",fontsize=16,color="black",shape="triangle"];1748 -> 1967[label="",style="solid", color="black", weight=3]; 42.09/20.39 1749 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1749[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1591 -> 1526[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1591[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1940) . (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 ww1941) ((showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198)",fontsize=16,color="magenta"];1591 -> 1609[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1591 -> 1610[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1591 -> 1611[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1591 -> 1612[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1591 -> 1613[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1591 -> 1614[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1750[label="show ww194",fontsize=16,color="black",shape="triangle"];1750 -> 1968[label="",style="solid", color="black", weight=3]; 42.09/20.39 1751 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1751[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1752[label="show ww194",fontsize=16,color="black",shape="triangle"];1752 -> 1969[label="",style="solid", color="black", weight=3]; 42.09/20.39 1753 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1753[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1754[label="show ww194",fontsize=16,color="black",shape="triangle"];1754 -> 1970[label="",style="solid", color="black", weight=3]; 42.09/20.39 1755 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1755[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1756[label="show ww194",fontsize=16,color="black",shape="triangle"];1756 -> 1971[label="",style="solid", color="black", weight=3]; 42.09/20.39 1757 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1757[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1758[label="show ww194",fontsize=16,color="black",shape="triangle"];1758 -> 1972[label="",style="solid", color="black", weight=3]; 42.09/20.39 1759 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1759[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1760[label="show ww194",fontsize=16,color="black",shape="triangle"];1760 -> 1973[label="",style="solid", color="black", weight=3]; 42.09/20.39 1761 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1761[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1762[label="show ww194",fontsize=16,color="black",shape="triangle"];1762 -> 1974[label="",style="solid", color="black", weight=3]; 42.09/20.39 1763 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1763[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1764[label="show ww194",fontsize=16,color="black",shape="triangle"];1764 -> 1975[label="",style="solid", color="black", weight=3]; 42.09/20.39 1765 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1765[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1766[label="show ww194",fontsize=16,color="black",shape="triangle"];1766 -> 1976[label="",style="solid", color="black", weight=3]; 42.09/20.39 1767 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1767[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1768[label="show ww194",fontsize=16,color="black",shape="triangle"];1768 -> 1977[label="",style="solid", color="black", weight=3]; 42.09/20.39 1769 -> 1609[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1769[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="magenta"];1959[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1959 -> 1979[label="",style="solid", color="black", weight=3]; 42.09/20.39 1609[label="(showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : [])) . shows ww198",fontsize=16,color="black",shape="triangle"];1609 -> 1633[label="",style="solid", color="black", weight=3]; 42.09/20.39 1960[label="(ww2400 : ww2401) ++ ww200",fontsize=16,color="black",shape="box"];1960 -> 1980[label="",style="solid", color="black", weight=3]; 42.09/20.39 1961[label="[] ++ ww200",fontsize=16,color="black",shape="box"];1961 -> 1981[label="",style="solid", color="black", weight=3]; 42.09/20.39 1962[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1962 -> 1982[label="",style="solid", color="black", weight=3]; 42.09/20.39 1963[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1963 -> 1983[label="",style="solid", color="black", weight=3]; 42.09/20.39 1964[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1964 -> 1984[label="",style="solid", color="black", weight=3]; 42.09/20.39 1965[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1965 -> 1985[label="",style="solid", color="black", weight=3]; 42.09/20.39 1966[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1966 -> 1986[label="",style="solid", color="black", weight=3]; 42.09/20.39 1967[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1967 -> 1987[label="",style="solid", color="black", weight=3]; 42.09/20.39 1610[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"];1611[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"];1612[label="ww1940",fontsize=16,color="green",shape="box"];1613[label="ww1941",fontsize=16,color="green",shape="box"];1614[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"];1968[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1968 -> 1988[label="",style="solid", color="black", weight=3]; 42.09/20.39 1969[label="primShowInt ww194",fontsize=16,color="burlywood",shape="triangle"];3011[label="ww194/Pos ww1940",fontsize=10,color="white",style="solid",shape="box"];1969 -> 3011[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3011 -> 1989[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3012[label="ww194/Neg ww1940",fontsize=10,color="white",style="solid",shape="box"];1969 -> 3012[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3012 -> 1990[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 1970[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1970 -> 1991[label="",style="solid", color="black", weight=3]; 42.09/20.39 1971[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1971 -> 1992[label="",style="solid", color="black", weight=3]; 42.09/20.39 1972[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1972 -> 1993[label="",style="solid", color="black", weight=3]; 42.09/20.39 1973[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1973 -> 1994[label="",style="solid", color="black", weight=3]; 42.09/20.39 1974[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1974 -> 1995[label="",style="solid", color="black", weight=3]; 42.09/20.39 1975[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1975 -> 1996[label="",style="solid", color="black", weight=3]; 42.09/20.39 1976[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1976 -> 1997[label="",style="solid", color="black", weight=3]; 42.09/20.39 1977[label="showsPrec (Pos Zero) ww194 []",fontsize=16,color="black",shape="box"];1977 -> 1998[label="",style="solid", color="black", weight=3]; 42.09/20.39 1979 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1979[label="show ww194 ++ []",fontsize=16,color="magenta"];1979 -> 2017[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1979 -> 2018[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1633[label="showString (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : []) (shows ww198 ww199)",fontsize=16,color="black",shape="box"];1633 -> 1669[label="",style="solid", color="black", weight=3]; 42.09/20.39 1980[label="ww2400 : ww2401 ++ ww200",fontsize=16,color="green",shape="box"];1980 -> 2019[label="",style="dashed", color="green", weight=3]; 42.09/20.39 1981[label="ww200",fontsize=16,color="green",shape="box"];1982 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1982[label="show ww194 ++ []",fontsize=16,color="magenta"];1982 -> 2020[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1982 -> 2021[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1983 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1983[label="show ww194 ++ []",fontsize=16,color="magenta"];1983 -> 2022[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1983 -> 2023[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1984 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1984[label="show ww194 ++ []",fontsize=16,color="magenta"];1984 -> 2024[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1984 -> 2025[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1985 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1985[label="show ww194 ++ []",fontsize=16,color="magenta"];1985 -> 2026[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1985 -> 2027[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1986 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1986[label="show ww194 ++ []",fontsize=16,color="magenta"];1986 -> 2028[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1986 -> 2029[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1987 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1987[label="show ww194 ++ []",fontsize=16,color="magenta"];1987 -> 2030[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1987 -> 2031[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1988 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1988[label="show ww194 ++ []",fontsize=16,color="magenta"];1988 -> 2032[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1988 -> 2033[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1989[label="primShowInt (Pos ww1940)",fontsize=16,color="burlywood",shape="box"];3013[label="ww1940/Succ ww19400",fontsize=10,color="white",style="solid",shape="box"];1989 -> 3013[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3013 -> 2034[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3014[label="ww1940/Zero",fontsize=10,color="white",style="solid",shape="box"];1989 -> 3014[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3014 -> 2035[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 1990[label="primShowInt (Neg ww1940)",fontsize=16,color="black",shape="box"];1990 -> 2036[label="",style="solid", color="black", weight=3]; 42.09/20.39 1991 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1991[label="show ww194 ++ []",fontsize=16,color="magenta"];1991 -> 2037[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1991 -> 2038[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1992 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1992[label="show ww194 ++ []",fontsize=16,color="magenta"];1992 -> 2039[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1992 -> 2040[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1993 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1993[label="show ww194 ++ []",fontsize=16,color="magenta"];1993 -> 2041[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1993 -> 2042[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1994 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1994[label="show ww194 ++ []",fontsize=16,color="magenta"];1994 -> 2043[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1994 -> 2044[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1995 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1995[label="show ww194 ++ []",fontsize=16,color="magenta"];1995 -> 2045[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1995 -> 2046[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1996 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1996[label="show ww194 ++ []",fontsize=16,color="magenta"];1996 -> 2047[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1996 -> 2048[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1997 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1997[label="show ww194 ++ []",fontsize=16,color="magenta"];1997 -> 2049[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1997 -> 2050[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1998 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1998[label="show ww194 ++ []",fontsize=16,color="magenta"];1998 -> 2051[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1998 -> 2052[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2017 -> 1736[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2017[label="show ww194",fontsize=16,color="magenta"];2018[label="[]",fontsize=16,color="green",shape="box"];1669 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 1669[label="(++) (Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : []) shows ww198 ww199",fontsize=16,color="magenta"];1669 -> 1883[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1669 -> 1884[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2019 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2019[label="ww2401 ++ ww200",fontsize=16,color="magenta"];2019 -> 2071[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2020 -> 1738[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2020[label="show ww194",fontsize=16,color="magenta"];2021[label="[]",fontsize=16,color="green",shape="box"];2022 -> 1740[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2022[label="show ww194",fontsize=16,color="magenta"];2023[label="[]",fontsize=16,color="green",shape="box"];2024 -> 1742[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2024[label="show ww194",fontsize=16,color="magenta"];2025[label="[]",fontsize=16,color="green",shape="box"];2026 -> 1744[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2026[label="show ww194",fontsize=16,color="magenta"];2027[label="[]",fontsize=16,color="green",shape="box"];2028 -> 1746[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2028[label="show ww194",fontsize=16,color="magenta"];2029[label="[]",fontsize=16,color="green",shape="box"];2030 -> 1748[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2030[label="show ww194",fontsize=16,color="magenta"];2031[label="[]",fontsize=16,color="green",shape="box"];2032 -> 1750[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2032[label="show ww194",fontsize=16,color="magenta"];2033[label="[]",fontsize=16,color="green",shape="box"];2034[label="primShowInt (Pos (Succ ww19400))",fontsize=16,color="black",shape="box"];2034 -> 2072[label="",style="solid", color="black", weight=3]; 42.09/20.39 2035[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];2035 -> 2073[label="",style="solid", color="black", weight=3]; 42.09/20.39 2036[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 ww1940)",fontsize=16,color="green",shape="box"];2036 -> 2074[label="",style="dashed", color="green", weight=3]; 42.09/20.39 2037 -> 1754[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2037[label="show ww194",fontsize=16,color="magenta"];2038[label="[]",fontsize=16,color="green",shape="box"];2039 -> 1756[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2039[label="show ww194",fontsize=16,color="magenta"];2040[label="[]",fontsize=16,color="green",shape="box"];2041 -> 1758[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2041[label="show ww194",fontsize=16,color="magenta"];2042[label="[]",fontsize=16,color="green",shape="box"];2043 -> 1760[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2043[label="show ww194",fontsize=16,color="magenta"];2044[label="[]",fontsize=16,color="green",shape="box"];2045 -> 1762[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2045[label="show ww194",fontsize=16,color="magenta"];2046[label="[]",fontsize=16,color="green",shape="box"];2047 -> 1764[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2047[label="show ww194",fontsize=16,color="magenta"];2048[label="[]",fontsize=16,color="green",shape="box"];2049 -> 1766[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2049[label="show ww194",fontsize=16,color="magenta"];2050[label="[]",fontsize=16,color="green",shape="box"];2051 -> 1768[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2051[label="show ww194",fontsize=16,color="magenta"];2052[label="[]",fontsize=16,color="green",shape="box"];1883[label="Char (Succ ww195) : Char (Succ ww196) : Char (Succ ww197) : []",fontsize=16,color="green",shape="box"];1884[label="shows ww198 ww199",fontsize=16,color="black",shape="box"];1884 -> 1978[label="",style="solid", color="black", weight=3]; 42.09/20.39 2071[label="ww2401",fontsize=16,color="green",shape="box"];2072 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2072[label="primShowInt (div Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];2072 -> 2110[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2072 -> 2111[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2073[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"];2074 -> 1969[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2074[label="primShowInt (Pos ww1940)",fontsize=16,color="magenta"];2074 -> 2112[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 1978[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="blue",shape="box"];3015[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3015[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3015 -> 1999[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3016[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3016[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3016 -> 2000[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3017[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3017[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3017 -> 2001[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3018[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3018[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3018 -> 2002[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3019[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3019[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3019 -> 2003[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3020[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3020[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3020 -> 2004[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3021[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3021[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3021 -> 2005[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3022[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3022[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3022 -> 2006[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3023[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3023[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3023 -> 2007[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3024[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3024[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3024 -> 2008[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3025[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3025[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3025 -> 2009[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3026[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3026[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3026 -> 2010[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3027[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3027[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3027 -> 2011[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3028[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3028[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3028 -> 2012[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3029[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3029[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3029 -> 2013[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3030[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3030[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3030 -> 2014[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3031[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3031[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3031 -> 2015[label="",style="solid", color="blue", weight=3]; 42.09/20.39 3032[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];1978 -> 3032[label="",style="solid", color="blue", weight=9]; 42.09/20.39 3032 -> 2016[label="",style="solid", color="blue", weight=3]; 42.09/20.39 2110 -> 1969[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2110[label="primShowInt (div Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];2110 -> 2135[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2111[label="toEnum (mod Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];2111 -> 2136[label="",style="dashed", color="green", weight=3]; 42.09/20.39 2112[label="Pos ww1940",fontsize=16,color="green",shape="box"];1999[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];1999 -> 2053[label="",style="solid", color="black", weight=3]; 42.09/20.39 2000[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2000 -> 2054[label="",style="solid", color="black", weight=3]; 42.09/20.39 2001[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2001 -> 2055[label="",style="solid", color="black", weight=3]; 42.09/20.39 2002[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2002 -> 2056[label="",style="solid", color="black", weight=3]; 42.09/20.39 2003[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2003 -> 2057[label="",style="solid", color="black", weight=3]; 42.09/20.39 2004[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2004 -> 2058[label="",style="solid", color="black", weight=3]; 42.09/20.39 2005[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2005 -> 2059[label="",style="solid", color="black", weight=3]; 42.09/20.39 2006[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="burlywood",shape="box"];3033[label="ww198/ww1980 :% ww1981",fontsize=10,color="white",style="solid",shape="box"];2006 -> 3033[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3033 -> 2060[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2007[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2007 -> 2061[label="",style="solid", color="black", weight=3]; 42.09/20.39 2008[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2008 -> 2062[label="",style="solid", color="black", weight=3]; 42.09/20.39 2009[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2009 -> 2063[label="",style="solid", color="black", weight=3]; 42.09/20.39 2010[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2010 -> 2064[label="",style="solid", color="black", weight=3]; 42.09/20.39 2011[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2011 -> 2065[label="",style="solid", color="black", weight=3]; 42.09/20.39 2012[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2012 -> 2066[label="",style="solid", color="black", weight=3]; 42.09/20.39 2013[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2013 -> 2067[label="",style="solid", color="black", weight=3]; 42.09/20.39 2014[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2014 -> 2068[label="",style="solid", color="black", weight=3]; 42.09/20.39 2015[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2015 -> 2069[label="",style="solid", color="black", weight=3]; 42.09/20.39 2016[label="showsPrec (Pos Zero) ww198 ww199",fontsize=16,color="black",shape="box"];2016 -> 2070[label="",style="solid", color="black", weight=3]; 42.09/20.39 2135 -> 2137[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2135[label="div Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];2135 -> 2138[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2135 -> 2139[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2136[label="toEnum (mod Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];2136 -> 2154[label="",style="solid", color="black", weight=3]; 42.09/20.39 2053 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2053[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2053 -> 2075[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2053 -> 2076[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2054 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2054[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2054 -> 2077[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2054 -> 2078[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2055 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2055[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2055 -> 2079[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2055 -> 2080[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2056 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2056[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2056 -> 2081[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2056 -> 2082[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2057 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2057[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2057 -> 2083[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2057 -> 2084[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2058 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2058[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2058 -> 2085[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2058 -> 2086[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2059 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2059[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2059 -> 2087[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2059 -> 2088[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2060[label="showsPrec (Pos Zero) (ww1980 :% ww1981) ww199",fontsize=16,color="black",shape="box"];2060 -> 2089[label="",style="solid", color="black", weight=3]; 42.09/20.39 2061 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2061[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2061 -> 2090[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2061 -> 2091[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2062 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2062[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2062 -> 2092[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2062 -> 2093[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2063 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2063[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2063 -> 2094[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2063 -> 2095[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2064 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2064[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2064 -> 2096[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2064 -> 2097[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2065 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2065[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2065 -> 2098[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2065 -> 2099[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2066 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2066[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2066 -> 2100[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2066 -> 2101[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2067 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2067[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2067 -> 2102[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2067 -> 2103[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2068 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2068[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2068 -> 2104[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2068 -> 2105[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2069 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2069[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2069 -> 2106[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2069 -> 2107[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2070 -> 1735[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2070[label="show ww198 ++ ww199",fontsize=16,color="magenta"];2070 -> 2108[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2070 -> 2109[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2138[label="ww19400",fontsize=16,color="green",shape="box"];2139[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];2137[label="div Pos (Succ ww242) Pos (Succ ww243)",fontsize=16,color="black",shape="triangle"];2137 -> 2143[label="",style="solid", color="black", weight=3]; 42.09/20.39 2154 -> 2165[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2154[label="primIntToChar (mod Pos (Succ ww19400) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];2154 -> 2166[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2154 -> 2167[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2075 -> 1736[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2075[label="show ww198",fontsize=16,color="magenta"];2075 -> 2113[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2076[label="ww199",fontsize=16,color="green",shape="box"];2077 -> 1738[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2077[label="show ww198",fontsize=16,color="magenta"];2077 -> 2114[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2078[label="ww199",fontsize=16,color="green",shape="box"];2079 -> 1740[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2079[label="show ww198",fontsize=16,color="magenta"];2079 -> 2115[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2080[label="ww199",fontsize=16,color="green",shape="box"];2081 -> 1742[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2081[label="show ww198",fontsize=16,color="magenta"];2081 -> 2116[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2082[label="ww199",fontsize=16,color="green",shape="box"];2083 -> 1744[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2083[label="show ww198",fontsize=16,color="magenta"];2083 -> 2117[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2084[label="ww199",fontsize=16,color="green",shape="box"];2085 -> 1746[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2085[label="show ww198",fontsize=16,color="magenta"];2085 -> 2118[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2086[label="ww199",fontsize=16,color="green",shape="box"];2087 -> 1748[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2087[label="show ww198",fontsize=16,color="magenta"];2087 -> 2119[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2088[label="ww199",fontsize=16,color="green",shape="box"];2089 -> 1526[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2089[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww1980) . (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 ww1981) ww199",fontsize=16,color="magenta"];2089 -> 2120[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2089 -> 2121[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2089 -> 2122[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2089 -> 2123[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2089 -> 2124[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2090 -> 1750[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2090[label="show ww198",fontsize=16,color="magenta"];2090 -> 2125[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2091[label="ww199",fontsize=16,color="green",shape="box"];2092 -> 1752[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2092[label="show ww198",fontsize=16,color="magenta"];2092 -> 2126[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2093[label="ww199",fontsize=16,color="green",shape="box"];2094 -> 1754[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2094[label="show ww198",fontsize=16,color="magenta"];2094 -> 2127[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2095[label="ww199",fontsize=16,color="green",shape="box"];2096 -> 1756[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2096[label="show ww198",fontsize=16,color="magenta"];2096 -> 2128[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2097[label="ww199",fontsize=16,color="green",shape="box"];2098 -> 1758[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2098[label="show ww198",fontsize=16,color="magenta"];2098 -> 2129[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2099[label="ww199",fontsize=16,color="green",shape="box"];2100 -> 1760[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2100[label="show ww198",fontsize=16,color="magenta"];2100 -> 2130[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2101[label="ww199",fontsize=16,color="green",shape="box"];2102 -> 1762[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2102[label="show ww198",fontsize=16,color="magenta"];2102 -> 2131[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2103[label="ww199",fontsize=16,color="green",shape="box"];2104 -> 1764[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2104[label="show ww198",fontsize=16,color="magenta"];2104 -> 2132[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2105[label="ww199",fontsize=16,color="green",shape="box"];2106 -> 1766[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2106[label="show ww198",fontsize=16,color="magenta"];2106 -> 2133[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2107[label="ww199",fontsize=16,color="green",shape="box"];2108 -> 1768[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2108[label="show ww198",fontsize=16,color="magenta"];2108 -> 2134[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2109[label="ww199",fontsize=16,color="green",shape="box"];2143[label="primDivInt (Pos (Succ ww242)) (Pos (Succ ww243))",fontsize=16,color="black",shape="box"];2143 -> 2153[label="",style="solid", color="black", weight=3]; 42.09/20.39 2166[label="ww19400",fontsize=16,color="green",shape="box"];2167[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];2165[label="primIntToChar (mod Pos (Succ ww248) Pos (Succ ww249))",fontsize=16,color="black",shape="triangle"];2165 -> 2168[label="",style="solid", color="black", weight=3]; 42.09/20.39 2113[label="ww198",fontsize=16,color="green",shape="box"];2114[label="ww198",fontsize=16,color="green",shape="box"];2115[label="ww198",fontsize=16,color="green",shape="box"];2116[label="ww198",fontsize=16,color="green",shape="box"];2117[label="ww198",fontsize=16,color="green",shape="box"];2118[label="ww198",fontsize=16,color="green",shape="box"];2119[label="ww198",fontsize=16,color="green",shape="box"];2120[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"];2121[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"];2122[label="ww1980",fontsize=16,color="green",shape="box"];2123[label="ww1981",fontsize=16,color="green",shape="box"];2124[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"];2125[label="ww198",fontsize=16,color="green",shape="box"];2126[label="ww198",fontsize=16,color="green",shape="box"];2127[label="ww198",fontsize=16,color="green",shape="box"];2128[label="ww198",fontsize=16,color="green",shape="box"];2129[label="ww198",fontsize=16,color="green",shape="box"];2130[label="ww198",fontsize=16,color="green",shape="box"];2131[label="ww198",fontsize=16,color="green",shape="box"];2132[label="ww198",fontsize=16,color="green",shape="box"];2133[label="ww198",fontsize=16,color="green",shape="box"];2134[label="ww198",fontsize=16,color="green",shape="box"];2153[label="Pos (primDivNatS (Succ ww242) (Succ ww243))",fontsize=16,color="green",shape="box"];2153 -> 2164[label="",style="dashed", color="green", weight=3]; 42.09/20.39 2168[label="primIntToChar (primModInt (Pos (Succ ww248)) (Pos (Succ ww249)))",fontsize=16,color="black",shape="box"];2168 -> 2170[label="",style="solid", color="black", weight=3]; 42.09/20.39 2164[label="primDivNatS (Succ ww242) (Succ ww243)",fontsize=16,color="black",shape="triangle"];2164 -> 2169[label="",style="solid", color="black", weight=3]; 42.09/20.39 2170[label="primIntToChar (Pos (primModNatS (Succ ww248) (Succ ww249)))",fontsize=16,color="black",shape="box"];2170 -> 2173[label="",style="solid", color="black", weight=3]; 42.09/20.39 2169[label="primDivNatS0 ww242 ww243 (primGEqNatS ww242 ww243)",fontsize=16,color="burlywood",shape="box"];3034[label="ww242/Succ ww2420",fontsize=10,color="white",style="solid",shape="box"];2169 -> 3034[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3034 -> 2171[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3035[label="ww242/Zero",fontsize=10,color="white",style="solid",shape="box"];2169 -> 3035[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3035 -> 2172[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2173[label="Char (primModNatS (Succ ww248) (Succ ww249))",fontsize=16,color="green",shape="box"];2173 -> 2178[label="",style="dashed", color="green", weight=3]; 42.09/20.39 2171[label="primDivNatS0 (Succ ww2420) ww243 (primGEqNatS (Succ ww2420) ww243)",fontsize=16,color="burlywood",shape="box"];3036[label="ww243/Succ ww2430",fontsize=10,color="white",style="solid",shape="box"];2171 -> 3036[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3036 -> 2174[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3037[label="ww243/Zero",fontsize=10,color="white",style="solid",shape="box"];2171 -> 3037[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3037 -> 2175[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2172[label="primDivNatS0 Zero ww243 (primGEqNatS Zero ww243)",fontsize=16,color="burlywood",shape="box"];3038[label="ww243/Succ ww2430",fontsize=10,color="white",style="solid",shape="box"];2172 -> 3038[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3038 -> 2176[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3039[label="ww243/Zero",fontsize=10,color="white",style="solid",shape="box"];2172 -> 3039[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3039 -> 2177[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2178[label="primModNatS (Succ ww248) (Succ ww249)",fontsize=16,color="black",shape="triangle"];2178 -> 2183[label="",style="solid", color="black", weight=3]; 42.09/20.39 2174[label="primDivNatS0 (Succ ww2420) (Succ ww2430) (primGEqNatS (Succ ww2420) (Succ ww2430))",fontsize=16,color="black",shape="box"];2174 -> 2179[label="",style="solid", color="black", weight=3]; 42.09/20.39 2175[label="primDivNatS0 (Succ ww2420) Zero (primGEqNatS (Succ ww2420) Zero)",fontsize=16,color="black",shape="box"];2175 -> 2180[label="",style="solid", color="black", weight=3]; 42.09/20.39 2176[label="primDivNatS0 Zero (Succ ww2430) (primGEqNatS Zero (Succ ww2430))",fontsize=16,color="black",shape="box"];2176 -> 2181[label="",style="solid", color="black", weight=3]; 42.09/20.39 2177[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2177 -> 2182[label="",style="solid", color="black", weight=3]; 42.09/20.39 2183[label="primModNatS0 ww248 ww249 (primGEqNatS ww248 ww249)",fontsize=16,color="burlywood",shape="box"];3040[label="ww248/Succ ww2480",fontsize=10,color="white",style="solid",shape="box"];2183 -> 3040[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3040 -> 2189[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3041[label="ww248/Zero",fontsize=10,color="white",style="solid",shape="box"];2183 -> 3041[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3041 -> 2190[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2179 -> 2695[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2179[label="primDivNatS0 (Succ ww2420) (Succ ww2430) (primGEqNatS ww2420 ww2430)",fontsize=16,color="magenta"];2179 -> 2696[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2179 -> 2697[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2179 -> 2698[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2179 -> 2699[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2180[label="primDivNatS0 (Succ ww2420) Zero True",fontsize=16,color="black",shape="box"];2180 -> 2186[label="",style="solid", color="black", weight=3]; 42.09/20.39 2181[label="primDivNatS0 Zero (Succ ww2430) False",fontsize=16,color="black",shape="box"];2181 -> 2187[label="",style="solid", color="black", weight=3]; 42.09/20.39 2182[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2182 -> 2188[label="",style="solid", color="black", weight=3]; 42.09/20.39 2189[label="primModNatS0 (Succ ww2480) ww249 (primGEqNatS (Succ ww2480) ww249)",fontsize=16,color="burlywood",shape="box"];3042[label="ww249/Succ ww2490",fontsize=10,color="white",style="solid",shape="box"];2189 -> 3042[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3042 -> 2197[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3043[label="ww249/Zero",fontsize=10,color="white",style="solid",shape="box"];2189 -> 3043[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3043 -> 2198[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2190[label="primModNatS0 Zero ww249 (primGEqNatS Zero ww249)",fontsize=16,color="burlywood",shape="box"];3044[label="ww249/Succ ww2490",fontsize=10,color="white",style="solid",shape="box"];2190 -> 3044[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3044 -> 2199[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3045[label="ww249/Zero",fontsize=10,color="white",style="solid",shape="box"];2190 -> 3045[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3045 -> 2200[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2696[label="ww2420",fontsize=16,color="green",shape="box"];2697[label="ww2430",fontsize=16,color="green",shape="box"];2698[label="ww2420",fontsize=16,color="green",shape="box"];2699[label="ww2430",fontsize=16,color="green",shape="box"];2695[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS ww294 ww295)",fontsize=16,color="burlywood",shape="triangle"];3046[label="ww294/Succ ww2940",fontsize=10,color="white",style="solid",shape="box"];2695 -> 3046[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3046 -> 2736[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3047[label="ww294/Zero",fontsize=10,color="white",style="solid",shape="box"];2695 -> 3047[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3047 -> 2737[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2186[label="Succ (primDivNatS (primMinusNatS (Succ ww2420) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2186 -> 2195[label="",style="dashed", color="green", weight=3]; 42.09/20.39 2187[label="Zero",fontsize=16,color="green",shape="box"];2188[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];2188 -> 2196[label="",style="dashed", color="green", weight=3]; 42.09/20.39 2197[label="primModNatS0 (Succ ww2480) (Succ ww2490) (primGEqNatS (Succ ww2480) (Succ ww2490))",fontsize=16,color="black",shape="box"];2197 -> 2207[label="",style="solid", color="black", weight=3]; 42.09/20.39 2198[label="primModNatS0 (Succ ww2480) Zero (primGEqNatS (Succ ww2480) Zero)",fontsize=16,color="black",shape="box"];2198 -> 2208[label="",style="solid", color="black", weight=3]; 42.09/20.39 2199[label="primModNatS0 Zero (Succ ww2490) (primGEqNatS Zero (Succ ww2490))",fontsize=16,color="black",shape="box"];2199 -> 2209[label="",style="solid", color="black", weight=3]; 42.09/20.39 2200[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2200 -> 2210[label="",style="solid", color="black", weight=3]; 42.09/20.39 2736[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS (Succ ww2940) ww295)",fontsize=16,color="burlywood",shape="box"];3048[label="ww295/Succ ww2950",fontsize=10,color="white",style="solid",shape="box"];2736 -> 3048[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3048 -> 2748[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3049[label="ww295/Zero",fontsize=10,color="white",style="solid",shape="box"];2736 -> 3049[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3049 -> 2749[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2737[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS Zero ww295)",fontsize=16,color="burlywood",shape="box"];3050[label="ww295/Succ ww2950",fontsize=10,color="white",style="solid",shape="box"];2737 -> 3050[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3050 -> 2750[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3051[label="ww295/Zero",fontsize=10,color="white",style="solid",shape="box"];2737 -> 3051[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3051 -> 2751[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2195 -> 2949[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2195[label="primDivNatS (primMinusNatS (Succ ww2420) Zero) (Succ Zero)",fontsize=16,color="magenta"];2195 -> 2950[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2195 -> 2951[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2195 -> 2952[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2196 -> 2949[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2196[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2196 -> 2953[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2196 -> 2954[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2196 -> 2955[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2207 -> 2770[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2207[label="primModNatS0 (Succ ww2480) (Succ ww2490) (primGEqNatS ww2480 ww2490)",fontsize=16,color="magenta"];2207 -> 2771[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2207 -> 2772[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2207 -> 2773[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2207 -> 2774[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2208[label="primModNatS0 (Succ ww2480) Zero True",fontsize=16,color="black",shape="box"];2208 -> 2221[label="",style="solid", color="black", weight=3]; 42.09/20.39 2209[label="primModNatS0 Zero (Succ ww2490) False",fontsize=16,color="black",shape="box"];2209 -> 2222[label="",style="solid", color="black", weight=3]; 42.09/20.39 2210[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];2210 -> 2223[label="",style="solid", color="black", weight=3]; 42.09/20.39 2748[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS (Succ ww2940) (Succ ww2950))",fontsize=16,color="black",shape="box"];2748 -> 2762[label="",style="solid", color="black", weight=3]; 42.09/20.39 2749[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS (Succ ww2940) Zero)",fontsize=16,color="black",shape="box"];2749 -> 2763[label="",style="solid", color="black", weight=3]; 42.09/20.39 2750[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS Zero (Succ ww2950))",fontsize=16,color="black",shape="box"];2750 -> 2764[label="",style="solid", color="black", weight=3]; 42.09/20.39 2751[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2751 -> 2765[label="",style="solid", color="black", weight=3]; 42.09/20.39 2950[label="Succ ww2420",fontsize=16,color="green",shape="box"];2951[label="Zero",fontsize=16,color="green",shape="box"];2952[label="Zero",fontsize=16,color="green",shape="box"];2949[label="primDivNatS (primMinusNatS ww306 ww307) (Succ ww308)",fontsize=16,color="burlywood",shape="triangle"];3052[label="ww306/Succ ww3060",fontsize=10,color="white",style="solid",shape="box"];2949 -> 3052[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3052 -> 2974[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3053[label="ww306/Zero",fontsize=10,color="white",style="solid",shape="box"];2949 -> 3053[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3053 -> 2975[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2953[label="Zero",fontsize=16,color="green",shape="box"];2954[label="Zero",fontsize=16,color="green",shape="box"];2955[label="Zero",fontsize=16,color="green",shape="box"];2771[label="ww2480",fontsize=16,color="green",shape="box"];2772[label="ww2490",fontsize=16,color="green",shape="box"];2773[label="ww2490",fontsize=16,color="green",shape="box"];2774[label="ww2480",fontsize=16,color="green",shape="box"];2770[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS ww299 ww300)",fontsize=16,color="burlywood",shape="triangle"];3054[label="ww299/Succ ww2990",fontsize=10,color="white",style="solid",shape="box"];2770 -> 3054[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3054 -> 2811[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3055[label="ww299/Zero",fontsize=10,color="white",style="solid",shape="box"];2770 -> 3055[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3055 -> 2812[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2221 -> 2857[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2221[label="primModNatS (primMinusNatS (Succ ww2480) Zero) (Succ Zero)",fontsize=16,color="magenta"];2221 -> 2858[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2221 -> 2859[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2221 -> 2860[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2222[label="Succ Zero",fontsize=16,color="green",shape="box"];2223 -> 2857[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2223[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];2223 -> 2861[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2223 -> 2862[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2223 -> 2863[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2762 -> 2695[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2762[label="primDivNatS0 (Succ ww292) (Succ ww293) (primGEqNatS ww2940 ww2950)",fontsize=16,color="magenta"];2762 -> 2813[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2762 -> 2814[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2763[label="primDivNatS0 (Succ ww292) (Succ ww293) True",fontsize=16,color="black",shape="triangle"];2763 -> 2815[label="",style="solid", color="black", weight=3]; 42.09/20.39 2764[label="primDivNatS0 (Succ ww292) (Succ ww293) False",fontsize=16,color="black",shape="box"];2764 -> 2816[label="",style="solid", color="black", weight=3]; 42.09/20.39 2765 -> 2763[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2765[label="primDivNatS0 (Succ ww292) (Succ ww293) True",fontsize=16,color="magenta"];2974[label="primDivNatS (primMinusNatS (Succ ww3060) ww307) (Succ ww308)",fontsize=16,color="burlywood",shape="box"];3056[label="ww307/Succ ww3070",fontsize=10,color="white",style="solid",shape="box"];2974 -> 3056[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3056 -> 2976[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3057[label="ww307/Zero",fontsize=10,color="white",style="solid",shape="box"];2974 -> 3057[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3057 -> 2977[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2975[label="primDivNatS (primMinusNatS Zero ww307) (Succ ww308)",fontsize=16,color="burlywood",shape="box"];3058[label="ww307/Succ ww3070",fontsize=10,color="white",style="solid",shape="box"];2975 -> 3058[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3058 -> 2978[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3059[label="ww307/Zero",fontsize=10,color="white",style="solid",shape="box"];2975 -> 3059[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3059 -> 2979[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2811[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS (Succ ww2990) ww300)",fontsize=16,color="burlywood",shape="box"];3060[label="ww300/Succ ww3000",fontsize=10,color="white",style="solid",shape="box"];2811 -> 3060[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3060 -> 2821[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3061[label="ww300/Zero",fontsize=10,color="white",style="solid",shape="box"];2811 -> 3061[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3061 -> 2822[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2812[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS Zero ww300)",fontsize=16,color="burlywood",shape="box"];3062[label="ww300/Succ ww3000",fontsize=10,color="white",style="solid",shape="box"];2812 -> 3062[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3062 -> 2823[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3063[label="ww300/Zero",fontsize=10,color="white",style="solid",shape="box"];2812 -> 3063[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3063 -> 2824[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2858[label="Zero",fontsize=16,color="green",shape="box"];2859[label="Succ ww2480",fontsize=16,color="green",shape="box"];2860[label="Zero",fontsize=16,color="green",shape="box"];2857[label="primModNatS (primMinusNatS ww302 ww303) (Succ ww304)",fontsize=16,color="burlywood",shape="triangle"];3064[label="ww302/Succ ww3020",fontsize=10,color="white",style="solid",shape="box"];2857 -> 3064[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3064 -> 2888[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3065[label="ww302/Zero",fontsize=10,color="white",style="solid",shape="box"];2857 -> 3065[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3065 -> 2889[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2861[label="Zero",fontsize=16,color="green",shape="box"];2862[label="Zero",fontsize=16,color="green",shape="box"];2863[label="Zero",fontsize=16,color="green",shape="box"];2813[label="ww2940",fontsize=16,color="green",shape="box"];2814[label="ww2950",fontsize=16,color="green",shape="box"];2815[label="Succ (primDivNatS (primMinusNatS (Succ ww292) (Succ ww293)) (Succ (Succ ww293)))",fontsize=16,color="green",shape="box"];2815 -> 2825[label="",style="dashed", color="green", weight=3]; 42.09/20.39 2816[label="Zero",fontsize=16,color="green",shape="box"];2976[label="primDivNatS (primMinusNatS (Succ ww3060) (Succ ww3070)) (Succ ww308)",fontsize=16,color="black",shape="box"];2976 -> 2980[label="",style="solid", color="black", weight=3]; 42.09/20.39 2977[label="primDivNatS (primMinusNatS (Succ ww3060) Zero) (Succ ww308)",fontsize=16,color="black",shape="box"];2977 -> 2981[label="",style="solid", color="black", weight=3]; 42.09/20.39 2978[label="primDivNatS (primMinusNatS Zero (Succ ww3070)) (Succ ww308)",fontsize=16,color="black",shape="box"];2978 -> 2982[label="",style="solid", color="black", weight=3]; 42.09/20.39 2979[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww308)",fontsize=16,color="black",shape="box"];2979 -> 2983[label="",style="solid", color="black", weight=3]; 42.09/20.39 2821[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS (Succ ww2990) (Succ ww3000))",fontsize=16,color="black",shape="box"];2821 -> 2832[label="",style="solid", color="black", weight=3]; 42.09/20.39 2822[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS (Succ ww2990) Zero)",fontsize=16,color="black",shape="box"];2822 -> 2833[label="",style="solid", color="black", weight=3]; 42.09/20.39 2823[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS Zero (Succ ww3000))",fontsize=16,color="black",shape="box"];2823 -> 2834[label="",style="solid", color="black", weight=3]; 42.09/20.39 2824[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];2824 -> 2835[label="",style="solid", color="black", weight=3]; 42.09/20.39 2888[label="primModNatS (primMinusNatS (Succ ww3020) ww303) (Succ ww304)",fontsize=16,color="burlywood",shape="box"];3066[label="ww303/Succ ww3030",fontsize=10,color="white",style="solid",shape="box"];2888 -> 3066[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3066 -> 2894[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3067[label="ww303/Zero",fontsize=10,color="white",style="solid",shape="box"];2888 -> 3067[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3067 -> 2895[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2889[label="primModNatS (primMinusNatS Zero ww303) (Succ ww304)",fontsize=16,color="burlywood",shape="box"];3068[label="ww303/Succ ww3030",fontsize=10,color="white",style="solid",shape="box"];2889 -> 3068[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3068 -> 2896[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 3069[label="ww303/Zero",fontsize=10,color="white",style="solid",shape="box"];2889 -> 3069[label="",style="solid", color="burlywood", weight=9]; 42.09/20.39 3069 -> 2897[label="",style="solid", color="burlywood", weight=3]; 42.09/20.39 2825 -> 2949[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2825[label="primDivNatS (primMinusNatS (Succ ww292) (Succ ww293)) (Succ (Succ ww293))",fontsize=16,color="magenta"];2825 -> 2956[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2825 -> 2957[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2825 -> 2958[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2980 -> 2949[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2980[label="primDivNatS (primMinusNatS ww3060 ww3070) (Succ ww308)",fontsize=16,color="magenta"];2980 -> 2984[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2980 -> 2985[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2981 -> 2164[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2981[label="primDivNatS (Succ ww3060) (Succ ww308)",fontsize=16,color="magenta"];2981 -> 2986[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2981 -> 2987[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2982[label="primDivNatS Zero (Succ ww308)",fontsize=16,color="black",shape="triangle"];2982 -> 2988[label="",style="solid", color="black", weight=3]; 42.09/20.39 2983 -> 2982[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2983[label="primDivNatS Zero (Succ ww308)",fontsize=16,color="magenta"];2832 -> 2770[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2832[label="primModNatS0 (Succ ww297) (Succ ww298) (primGEqNatS ww2990 ww3000)",fontsize=16,color="magenta"];2832 -> 2841[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2832 -> 2842[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2833[label="primModNatS0 (Succ ww297) (Succ ww298) True",fontsize=16,color="black",shape="triangle"];2833 -> 2843[label="",style="solid", color="black", weight=3]; 42.09/20.39 2834[label="primModNatS0 (Succ ww297) (Succ ww298) False",fontsize=16,color="black",shape="box"];2834 -> 2844[label="",style="solid", color="black", weight=3]; 42.09/20.39 2835 -> 2833[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2835[label="primModNatS0 (Succ ww297) (Succ ww298) True",fontsize=16,color="magenta"];2894[label="primModNatS (primMinusNatS (Succ ww3020) (Succ ww3030)) (Succ ww304)",fontsize=16,color="black",shape="box"];2894 -> 2904[label="",style="solid", color="black", weight=3]; 42.09/20.39 2895[label="primModNatS (primMinusNatS (Succ ww3020) Zero) (Succ ww304)",fontsize=16,color="black",shape="box"];2895 -> 2905[label="",style="solid", color="black", weight=3]; 42.09/20.39 2896[label="primModNatS (primMinusNatS Zero (Succ ww3030)) (Succ ww304)",fontsize=16,color="black",shape="box"];2896 -> 2906[label="",style="solid", color="black", weight=3]; 42.09/20.39 2897[label="primModNatS (primMinusNatS Zero Zero) (Succ ww304)",fontsize=16,color="black",shape="box"];2897 -> 2907[label="",style="solid", color="black", weight=3]; 42.09/20.39 2956[label="Succ ww292",fontsize=16,color="green",shape="box"];2957[label="Succ ww293",fontsize=16,color="green",shape="box"];2958[label="Succ ww293",fontsize=16,color="green",shape="box"];2984[label="ww3060",fontsize=16,color="green",shape="box"];2985[label="ww3070",fontsize=16,color="green",shape="box"];2986[label="ww3060",fontsize=16,color="green",shape="box"];2987[label="ww308",fontsize=16,color="green",shape="box"];2988[label="Zero",fontsize=16,color="green",shape="box"];2841[label="ww2990",fontsize=16,color="green",shape="box"];2842[label="ww3000",fontsize=16,color="green",shape="box"];2843 -> 2857[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2843[label="primModNatS (primMinusNatS (Succ ww297) (Succ ww298)) (Succ (Succ ww298))",fontsize=16,color="magenta"];2843 -> 2870[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2843 -> 2871[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2843 -> 2872[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2844[label="Succ (Succ ww297)",fontsize=16,color="green",shape="box"];2904 -> 2857[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2904[label="primModNatS (primMinusNatS ww3020 ww3030) (Succ ww304)",fontsize=16,color="magenta"];2904 -> 2912[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2904 -> 2913[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2905 -> 2178[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2905[label="primModNatS (Succ ww3020) (Succ ww304)",fontsize=16,color="magenta"];2905 -> 2914[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2905 -> 2915[label="",style="dashed", color="magenta", weight=3]; 42.09/20.39 2906[label="primModNatS Zero (Succ ww304)",fontsize=16,color="black",shape="triangle"];2906 -> 2916[label="",style="solid", color="black", weight=3]; 42.09/20.39 2907 -> 2906[label="",style="dashed", color="red", weight=0]; 42.09/20.39 2907[label="primModNatS Zero (Succ ww304)",fontsize=16,color="magenta"];2870[label="Succ ww298",fontsize=16,color="green",shape="box"];2871[label="Succ ww297",fontsize=16,color="green",shape="box"];2872[label="Succ ww298",fontsize=16,color="green",shape="box"];2912[label="ww3030",fontsize=16,color="green",shape="box"];2913[label="ww3020",fontsize=16,color="green",shape="box"];2914[label="ww3020",fontsize=16,color="green",shape="box"];2915[label="ww304",fontsize=16,color="green",shape="box"];2916[label="Zero",fontsize=16,color="green",shape="box"];} 42.09/20.39 42.09/20.39 ---------------------------------------- 42.09/20.39 42.09/20.39 (199) 42.09/20.39 TRUE 42.20/20.43 EOF