30.57/15.90	MAYBE
32.88/16.50	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
32.88/16.50	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
32.88/16.50	
32.88/16.50	
32.88/16.50	H-Termination with start terms of the given HASKELL could not be shown:
32.88/16.50	
32.88/16.50	(0) HASKELL
32.88/16.50	(1) IFR [EQUIVALENT, 0 ms]
32.88/16.50	(2) HASKELL
32.88/16.50	(3) BR [EQUIVALENT, 0 ms]
32.88/16.50	(4) HASKELL
32.88/16.50	(5) COR [EQUIVALENT, 0 ms]
32.88/16.50	(6) HASKELL
32.88/16.50	(7) NumRed [SOUND, 0 ms]
32.88/16.50	(8) HASKELL
32.88/16.50	(9) Narrow [SOUND, 0 ms]
32.88/16.50	(10) AND
32.88/16.50	    (11) QDP
32.88/16.50	        (12) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (13) QDP
32.88/16.50	        (14) QDPOrderProof [EQUIVALENT, 0 ms]
32.88/16.50	        (15) QDP
32.88/16.50	        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (17) QDP
32.88/16.50	        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
32.88/16.50	        (19) YES
32.88/16.50	    (20) QDP
32.88/16.50	        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
32.88/16.50	        (22) YES
32.88/16.50	    (23) QDP
32.88/16.50	        (24) TransformationProof [EQUIVALENT, 36 ms]
32.88/16.50	        (25) QDP
32.88/16.50	        (26) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (27) QDP
32.88/16.50	        (28) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (29) QDP
32.88/16.50	        (30) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (31) QDP
32.88/16.50	        (32) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (33) QDP
32.88/16.50	        (34) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (35) QDP
32.88/16.50	        (36) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (37) QDP
32.88/16.50	        (38) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (39) QDP
32.88/16.50	        (40) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (41) QDP
32.88/16.50	        (42) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (43) QDP
32.88/16.50	        (44) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (45) QDP
32.88/16.50	        (46) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (47) QDP
32.88/16.50	        (48) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (49) QDP
32.88/16.50	        (50) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (51) QDP
32.88/16.50	        (52) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (53) QDP
32.88/16.50	        (54) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (55) QDP
32.88/16.50	        (56) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (57) QDP
32.88/16.50	        (58) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (59) QDP
32.88/16.50	        (60) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (61) QDP
32.88/16.50	        (62) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (63) QDP
32.88/16.50	        (64) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (65) QDP
32.88/16.50	        (66) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (67) QDP
32.88/16.50	        (68) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (69) QDP
32.88/16.50	        (70) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (71) QDP
32.88/16.50	        (72) TransformationProof [EQUIVALENT, 3 ms]
32.88/16.50	        (73) QDP
32.88/16.50	        (74) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (75) QDP
32.88/16.50	        (76) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (77) QDP
32.88/16.50	        (78) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (79) QDP
32.88/16.50	        (80) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (81) QDP
32.88/16.50	        (82) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (83) QDP
32.88/16.50	        (84) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (85) QDP
32.88/16.50	        (86) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (87) QDP
32.88/16.50	        (88) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (89) QDP
32.88/16.50	        (90) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (91) QDP
32.88/16.50	        (92) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (93) QDP
32.88/16.50	        (94) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (95) QDP
32.88/16.50	        (96) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (97) QDP
32.88/16.50	        (98) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (99) QDP
32.88/16.50	        (100) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (101) QDP
32.88/16.50	        (102) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (103) QDP
32.88/16.50	        (104) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (105) QDP
32.88/16.50	        (106) QDPSizeChangeProof [EQUIVALENT, 0 ms]
32.88/16.50	        (107) YES
32.88/16.50	    (108) QDP
32.88/16.50	        (109) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (110) QDP
32.88/16.50	        (111) QDPOrderProof [EQUIVALENT, 0 ms]
32.88/16.50	        (112) QDP
32.88/16.50	        (113) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (114) QDP
32.88/16.50	        (115) QDPSizeChangeProof [EQUIVALENT, 0 ms]
32.88/16.50	        (116) YES
32.88/16.50	    (117) QDP
32.88/16.50	        (118) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	        (119) QDP
32.88/16.50	        (120) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (121) QDP
32.88/16.50	        (122) UsableRulesProof [EQUIVALENT, 0 ms]
32.88/16.50	        (123) QDP
32.88/16.50	        (124) QReductionProof [EQUIVALENT, 0 ms]
32.88/16.50	        (125) QDP
32.88/16.50	        (126) MNOCProof [EQUIVALENT, 0 ms]
32.88/16.50	        (127) QDP
32.88/16.50	        (128) InductionCalculusProof [EQUIVALENT, 0 ms]
32.88/16.50	        (129) QDP
32.88/16.50	        (130) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	        (131) QDP
32.88/16.50	            (132) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	            (133) QDP
32.88/16.50	            (134) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	            (135) QDP
32.88/16.50	            (136) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	            (137) QDP
32.88/16.50	            (138) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	            (139) QDP
32.88/16.50	            (140) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	            (141) QDP
32.88/16.50	            (142) TransformationProof [EQUIVALENT, 0 ms]
32.88/16.50	            (143) QDP
32.88/16.50	            (144) DependencyGraphProof [EQUIVALENT, 0 ms]
32.88/16.50	            (145) QDP
32.88/16.50	            (146) MNOCProof [EQUIVALENT, 0 ms]
32.88/16.50	            (147) QDP
32.88/16.50	            (148) InductionCalculusProof [EQUIVALENT, 0 ms]
32.88/16.50	            (149) QDP
32.88/16.50	(150) Narrow [COMPLETE, 0 ms]
32.88/16.50	(151) TRUE
32.88/16.50	
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(0)
32.88/16.50	Obligation:
32.88/16.50	mainModule Main 
32.88/16.50	module Main where {
32.88/16.50	import qualified Prelude;
32.88/16.50	}
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(1) IFR (EQUIVALENT)
32.88/16.50	If Reductions:
32.88/16.50	The following If expression
32.88/16.50	"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
32.88/16.50	is transformed to
32.88/16.50	"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
32.88/16.50	primDivNatS0 x y False = Zero;
32.88/16.50	"
32.88/16.50	The following If expression
32.88/16.50	"if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x"
32.88/16.50	is transformed to
32.88/16.50	"primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y);
32.88/16.50	primModNatS0 x y False = Succ x;
32.88/16.50	"
32.88/16.50	The following If expression
32.88/16.50	"if primGEqNatS x y then primModNatP (primMinusNatS x y) (Succ y) else primMinusNatS y x"
32.88/16.50	is transformed to
32.88/16.50	"primModNatP0 x y True = primModNatP (primMinusNatS x y) (Succ y);
32.88/16.50	primModNatP0 x y False = primMinusNatS y x;
32.88/16.50	"
32.88/16.50	The following If expression
32.88/16.50	"if b then (showChar '(') . p . showChar ')' else p"
32.88/16.50	is transformed to
32.88/16.50	"showParen0 p True = (showChar '(') . p . showChar ')';
32.88/16.50	showParen0 p False = p;
32.88/16.50	"
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(2)
32.88/16.50	Obligation:
32.88/16.50	mainModule Main 
32.88/16.50	module Main where {
32.88/16.50	import qualified Prelude;
32.88/16.50	}
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(3) BR (EQUIVALENT)
32.88/16.50	Replaced joker patterns by fresh variables and removed binding patterns.
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(4)
32.88/16.50	Obligation:
32.88/16.50	mainModule Main 
32.88/16.50	module Main where {
32.88/16.50	import qualified Prelude;
32.88/16.50	}
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(5) COR (EQUIVALENT)
32.88/16.50	Cond Reductions:
32.88/16.50	The following Function with conditions
32.88/16.50	"undefined |Falseundefined;
32.88/16.50	"
32.88/16.50	is transformed to
32.88/16.50	"undefined  = undefined1;
32.88/16.50	"
32.88/16.50	"undefined0 True = undefined;
32.88/16.50	"
32.88/16.50	"undefined1  = undefined0 False;
32.88/16.50	"
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(6)
32.88/16.50	Obligation:
32.88/16.50	mainModule Main 
32.88/16.50	module Main where {
32.88/16.50	import qualified Prelude;
32.88/16.50	}
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(7) NumRed (SOUND)
32.88/16.50	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(8)
32.88/16.50	Obligation:
32.88/16.50	mainModule Main 
32.88/16.50	module Main where {
32.88/16.50	import qualified Prelude;
32.88/16.50	}
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(9) Narrow (SOUND)
32.88/16.50	Haskell To QDPs
32.88/16.50	
32.88/16.50	digraph dp_graph {
32.88/16.50	node [outthreshold=100, inthreshold=100];1[label="shows",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
32.88/16.50	3[label="shows ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
32.88/16.50	4[label="shows ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
32.88/16.50	5[label="showsPrec (Pos Zero) ww3 ww4",fontsize=16,color="burlywood",shape="box"];1224[label="ww3/ww30 :% ww31",fontsize=10,color="white",style="solid",shape="box"];5 -> 1224[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1224 -> 6[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	6[label="showsPrec (Pos Zero) (ww30 :% ww31) ww4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
32.88/16.50	7 -> 24[label="",style="dashed", color="red", weight=0];
32.88/16.50	7[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww30) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww31) ww4",fontsize=16,color="magenta"];7 -> 25[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	7 -> 26[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	7 -> 27[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	7 -> 28[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	7 -> 29[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	7 -> 30[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	25[label="ww30",fontsize=16,color="green",shape="box"];26[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];27[label="ww4",fontsize=16,color="green",shape="box"];28[label="ww31",fontsize=16,color="green",shape="box"];29[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];30[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];24[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) ww22",fontsize=16,color="black",shape="triangle"];24 -> 37[label="",style="solid", color="black", weight=3];
32.88/16.50	37[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww22",fontsize=16,color="black",shape="box"];37 -> 38[label="",style="solid", color="black", weight=3];
32.88/16.50	38[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww22",fontsize=16,color="black",shape="box"];38 -> 39[label="",style="solid", color="black", weight=3];
32.88/16.50	39[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww22",fontsize=16,color="black",shape="box"];39 -> 40[label="",style="solid", color="black", weight=3];
32.88/16.50	40[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww22",fontsize=16,color="black",shape="box"];40 -> 41[label="",style="solid", color="black", weight=3];
32.88/16.50	41[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (LT == GT) ww22",fontsize=16,color="black",shape="box"];41 -> 42[label="",style="solid", color="black", weight=3];
32.88/16.50	42[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) False ww22",fontsize=16,color="black",shape="box"];42 -> 43[label="",style="solid", color="black", weight=3];
32.88/16.50	43[label="(shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="black",shape="box"];43 -> 44[label="",style="solid", color="black", weight=3];
32.88/16.50	44[label="shows ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];44 -> 45[label="",style="solid", color="black", weight=3];
32.88/16.50	45[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="blue",shape="box"];1225[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1225[label="",style="solid", color="blue", weight=9];
32.88/16.50	1225 -> 46[label="",style="solid", color="blue", weight=3];
32.88/16.50	1226[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1226[label="",style="solid", color="blue", weight=9];
32.88/16.50	1226 -> 47[label="",style="solid", color="blue", weight=3];
32.88/16.50	1227[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1227[label="",style="solid", color="blue", weight=9];
32.88/16.50	1227 -> 48[label="",style="solid", color="blue", weight=3];
32.88/16.50	1228[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1228[label="",style="solid", color="blue", weight=9];
32.88/16.50	1228 -> 49[label="",style="solid", color="blue", weight=3];
32.88/16.50	1229[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1229[label="",style="solid", color="blue", weight=9];
32.88/16.50	1229 -> 50[label="",style="solid", color="blue", weight=3];
32.88/16.50	1230[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1230[label="",style="solid", color="blue", weight=9];
32.88/16.50	1230 -> 51[label="",style="solid", color="blue", weight=3];
32.88/16.50	1231[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1231[label="",style="solid", color="blue", weight=9];
32.88/16.50	1231 -> 52[label="",style="solid", color="blue", weight=3];
32.88/16.50	1232[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1232[label="",style="solid", color="blue", weight=9];
32.88/16.50	1232 -> 53[label="",style="solid", color="blue", weight=3];
32.88/16.50	1233[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1233[label="",style="solid", color="blue", weight=9];
32.88/16.50	1233 -> 54[label="",style="solid", color="blue", weight=3];
32.88/16.50	1234[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1234[label="",style="solid", color="blue", weight=9];
32.88/16.50	1234 -> 55[label="",style="solid", color="blue", weight=3];
32.88/16.50	1235[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1235[label="",style="solid", color="blue", weight=9];
32.88/16.50	1235 -> 56[label="",style="solid", color="blue", weight=3];
32.88/16.50	1236[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1236[label="",style="solid", color="blue", weight=9];
32.88/16.50	1236 -> 57[label="",style="solid", color="blue", weight=3];
32.88/16.50	1237[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1237[label="",style="solid", color="blue", weight=9];
32.88/16.50	1237 -> 58[label="",style="solid", color="blue", weight=3];
32.88/16.50	1238[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1238[label="",style="solid", color="blue", weight=9];
32.88/16.50	1238 -> 59[label="",style="solid", color="blue", weight=3];
32.88/16.50	1239[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1239[label="",style="solid", color="blue", weight=9];
32.88/16.50	1239 -> 60[label="",style="solid", color="blue", weight=3];
32.88/16.50	1240[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1240[label="",style="solid", color="blue", weight=9];
32.88/16.50	1240 -> 61[label="",style="solid", color="blue", weight=3];
32.88/16.50	1241[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1241[label="",style="solid", color="blue", weight=9];
32.88/16.50	1241 -> 62[label="",style="solid", color="blue", weight=3];
32.88/16.50	1242[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1242[label="",style="solid", color="blue", weight=9];
32.88/16.50	1242 -> 63[label="",style="solid", color="blue", weight=3];
32.88/16.50	46[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];46 -> 64[label="",style="solid", color="black", weight=3];
32.88/16.50	47[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];47 -> 65[label="",style="solid", color="black", weight=3];
32.88/16.50	48[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];48 -> 66[label="",style="solid", color="black", weight=3];
32.88/16.50	49[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];49 -> 67[label="",style="solid", color="black", weight=3];
32.88/16.50	50[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];50 -> 68[label="",style="solid", color="black", weight=3];
32.88/16.50	51[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];51 -> 69[label="",style="solid", color="black", weight=3];
32.88/16.50	52[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];52 -> 70[label="",style="solid", color="black", weight=3];
32.88/16.50	53[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="burlywood",shape="box"];1243[label="ww17/ww170 :% ww171",fontsize=10,color="white",style="solid",shape="box"];53 -> 1243[label="",style="solid", color="burlywood", weight=9];
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32.88/16.50	55[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];55 -> 73[label="",style="solid", color="black", weight=3];
32.88/16.50	56[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];56 -> 74[label="",style="solid", color="black", weight=3];
32.88/16.50	57[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];57 -> 75[label="",style="solid", color="black", weight=3];
32.88/16.50	58[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];58 -> 76[label="",style="solid", color="black", weight=3];
32.88/16.50	59[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];59 -> 77[label="",style="solid", color="black", weight=3];
32.88/16.50	60[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];60 -> 78[label="",style="solid", color="black", weight=3];
32.88/16.50	61[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];61 -> 79[label="",style="solid", color="black", weight=3];
32.88/16.50	62[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];62 -> 80[label="",style="solid", color="black", weight=3];
32.88/16.50	63[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];63 -> 81[label="",style="solid", color="black", weight=3];
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32.88/16.50	64 -> 184[label="",style="dashed", color="magenta", weight=3];
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32.88/16.50	65 -> 186[label="",style="dashed", color="magenta", weight=3];
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32.88/16.50	66 -> 188[label="",style="dashed", color="magenta", weight=3];
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32.88/16.50	67 -> 190[label="",style="dashed", color="magenta", weight=3];
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32.88/16.50	68 -> 192[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	69 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	69[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];69 -> 193[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	69 -> 194[label="",style="dashed", color="magenta", weight=3];
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32.88/16.50	70 -> 196[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	71[label="showsPrec (Pos Zero) (ww170 :% ww171) ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];71 -> 89[label="",style="solid", color="black", weight=3];
32.88/16.50	72 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	72[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];72 -> 197[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	72 -> 198[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	73 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	73[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];73 -> 199[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	73 -> 200[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	74 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	74[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];74 -> 201[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	74 -> 202[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	75 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	75[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];75 -> 203[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	75 -> 204[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	76 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	76[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];76 -> 205[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	76 -> 206[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	77 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	77[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];77 -> 207[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	77 -> 208[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	78 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	78[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];78 -> 209[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	78 -> 210[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	79 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	79[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];79 -> 211[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	79 -> 212[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	80 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	80[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];80 -> 213[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	80 -> 214[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	81 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	81[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];81 -> 215[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	81 -> 216[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	183[label="show ww17",fontsize=16,color="black",shape="triangle"];183 -> 242[label="",style="solid", color="black", weight=3];
32.88/16.50	184 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.50	184[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];182[label="ww58 ++ ww56",fontsize=16,color="burlywood",shape="triangle"];1244[label="ww58/ww580 : ww581",fontsize=10,color="white",style="solid",shape="box"];182 -> 1244[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1244 -> 243[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1245[label="ww58/[]",fontsize=10,color="white",style="solid",shape="box"];182 -> 1245[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1245 -> 244[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	185[label="show ww17",fontsize=16,color="black",shape="triangle"];185 -> 245[label="",style="solid", color="black", weight=3];
32.88/16.50	186 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.50	186[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];187[label="show ww17",fontsize=16,color="black",shape="triangle"];187 -> 246[label="",style="solid", color="black", weight=3];
32.88/16.50	188 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.50	188[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];189[label="show ww17",fontsize=16,color="black",shape="triangle"];189 -> 247[label="",style="solid", color="black", weight=3];
32.88/16.50	190 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.50	190[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];191[label="show ww17",fontsize=16,color="black",shape="triangle"];191 -> 248[label="",style="solid", color="black", weight=3];
32.88/16.50	192 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.50	192[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];193[label="show ww17",fontsize=16,color="black",shape="triangle"];193 -> 249[label="",style="solid", color="black", weight=3];
32.88/16.50	194 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.50	194[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];195[label="show ww17",fontsize=16,color="black",shape="triangle"];195 -> 250[label="",style="solid", color="black", weight=3];
32.88/16.50	196 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.50	196[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];89 -> 24[label="",style="dashed", color="red", weight=0];
32.88/16.50	89[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww170) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww171) ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="magenta"];89 -> 100[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	89 -> 101[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	89 -> 102[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	89 -> 103[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	89 -> 104[label="",style="dashed", color="magenta", weight=3];
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32.88/16.50	198[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];199[label="show ww17",fontsize=16,color="black",shape="triangle"];199 -> 252[label="",style="solid", color="black", weight=3];
32.88/16.50	200 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.50	200[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];201[label="show ww17",fontsize=16,color="black",shape="triangle"];201 -> 253[label="",style="solid", color="black", weight=3];
32.88/16.50	202 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.50	202[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];203[label="show ww17",fontsize=16,color="black",shape="triangle"];203 -> 254[label="",style="solid", color="black", weight=3];
32.88/16.50	204 -> 102[label="",style="dashed", color="red", weight=0];
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32.88/16.50	206 -> 102[label="",style="dashed", color="red", weight=0];
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32.88/16.50	210 -> 102[label="",style="dashed", color="red", weight=0];
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32.88/16.50	212 -> 102[label="",style="dashed", color="red", weight=0];
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32.88/16.50	214 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.50	214[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];215[label="show ww17",fontsize=16,color="black",shape="triangle"];215 -> 260[label="",style="solid", color="black", weight=3];
32.88/16.50	216 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.50	216[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];242[label="error []",fontsize=16,color="red",shape="box"];102[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="black",shape="triangle"];102 -> 108[label="",style="solid", color="black", weight=3];
32.88/16.50	243[label="(ww580 : ww581) ++ ww56",fontsize=16,color="black",shape="box"];243 -> 262[label="",style="solid", color="black", weight=3];
32.88/16.50	244[label="[] ++ ww56",fontsize=16,color="black",shape="box"];244 -> 263[label="",style="solid", color="black", weight=3];
32.88/16.50	245[label="error []",fontsize=16,color="red",shape="box"];246[label="error []",fontsize=16,color="red",shape="box"];247[label="error []",fontsize=16,color="red",shape="box"];248[label="error []",fontsize=16,color="red",shape="box"];249[label="error []",fontsize=16,color="red",shape="box"];250[label="error []",fontsize=16,color="red",shape="box"];100[label="ww170",fontsize=16,color="green",shape="box"];101[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];103[label="ww171",fontsize=16,color="green",shape="box"];104[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];105[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];251[label="error []",fontsize=16,color="red",shape="box"];252[label="error []",fontsize=16,color="red",shape="box"];253[label="error []",fontsize=16,color="red",shape="box"];254[label="primShowInt ww17",fontsize=16,color="burlywood",shape="triangle"];1246[label="ww17/Pos ww170",fontsize=10,color="white",style="solid",shape="box"];254 -> 1246[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1246 -> 264[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1247[label="ww17/Neg ww170",fontsize=10,color="white",style="solid",shape="box"];254 -> 1247[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1247 -> 265[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	255[label="error []",fontsize=16,color="red",shape="box"];256[label="error []",fontsize=16,color="red",shape="box"];257[label="error []",fontsize=16,color="red",shape="box"];258[label="error []",fontsize=16,color="red",shape="box"];259[label="error []",fontsize=16,color="red",shape="box"];260[label="error []",fontsize=16,color="red",shape="box"];108[label="showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : []) (shows ww21 ww22)",fontsize=16,color="black",shape="box"];108 -> 112[label="",style="solid", color="black", weight=3];
32.88/16.50	262[label="ww580 : ww581 ++ ww56",fontsize=16,color="green",shape="box"];262 -> 284[label="",style="dashed", color="green", weight=3];
32.88/16.50	263[label="ww56",fontsize=16,color="green",shape="box"];264[label="primShowInt (Pos ww170)",fontsize=16,color="burlywood",shape="box"];1248[label="ww170/Succ ww1700",fontsize=10,color="white",style="solid",shape="box"];264 -> 1248[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1248 -> 285[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1249[label="ww170/Zero",fontsize=10,color="white",style="solid",shape="box"];264 -> 1249[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1249 -> 286[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	265[label="primShowInt (Neg ww170)",fontsize=16,color="black",shape="box"];265 -> 287[label="",style="solid", color="black", weight=3];
32.88/16.50	112 -> 182[label="",style="dashed", color="red", weight=0];
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32.88/16.50	112 -> 222[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	284 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	284[label="ww581 ++ ww56",fontsize=16,color="magenta"];284 -> 306[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	285[label="primShowInt (Pos (Succ ww1700))",fontsize=16,color="black",shape="box"];285 -> 307[label="",style="solid", color="black", weight=3];
32.88/16.50	286[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];286 -> 308[label="",style="solid", color="black", weight=3];
32.88/16.50	287[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))) : primShowInt (Pos ww170)",fontsize=16,color="green",shape="box"];287 -> 309[label="",style="dashed", color="green", weight=3];
32.88/16.50	221[label="Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : []",fontsize=16,color="green",shape="box"];222[label="shows ww21 ww22",fontsize=16,color="black",shape="box"];222 -> 261[label="",style="solid", color="black", weight=3];
32.88/16.50	306[label="ww581",fontsize=16,color="green",shape="box"];307 -> 182[label="",style="dashed", color="red", weight=0];
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32.88/16.50	307 -> 346[label="",style="dashed", color="magenta", weight=3];
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32.88/16.50	309[label="primShowInt (Pos ww170)",fontsize=16,color="magenta"];309 -> 347[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	261[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="blue",shape="box"];1250[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1250[label="",style="solid", color="blue", weight=9];
32.88/16.50	1250 -> 266[label="",style="solid", color="blue", weight=3];
32.88/16.50	1251[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1251[label="",style="solid", color="blue", weight=9];
32.88/16.50	1251 -> 267[label="",style="solid", color="blue", weight=3];
32.88/16.50	1252[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1252[label="",style="solid", color="blue", weight=9];
32.88/16.50	1252 -> 268[label="",style="solid", color="blue", weight=3];
32.88/16.50	1253[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1253[label="",style="solid", color="blue", weight=9];
32.88/16.50	1253 -> 269[label="",style="solid", color="blue", weight=3];
32.88/16.50	1254[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1254[label="",style="solid", color="blue", weight=9];
32.88/16.50	1254 -> 270[label="",style="solid", color="blue", weight=3];
32.88/16.50	1255[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1255[label="",style="solid", color="blue", weight=9];
32.88/16.50	1255 -> 271[label="",style="solid", color="blue", weight=3];
32.88/16.50	1256[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1256[label="",style="solid", color="blue", weight=9];
32.88/16.50	1256 -> 272[label="",style="solid", color="blue", weight=3];
32.88/16.50	1257[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1257[label="",style="solid", color="blue", weight=9];
32.88/16.50	1257 -> 273[label="",style="solid", color="blue", weight=3];
32.88/16.50	1258[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1258[label="",style="solid", color="blue", weight=9];
32.88/16.50	1258 -> 274[label="",style="solid", color="blue", weight=3];
32.88/16.50	1259[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1259[label="",style="solid", color="blue", weight=9];
32.88/16.50	1259 -> 275[label="",style="solid", color="blue", weight=3];
32.88/16.50	1260[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1260[label="",style="solid", color="blue", weight=9];
32.88/16.50	1260 -> 276[label="",style="solid", color="blue", weight=3];
32.88/16.50	1261[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1261[label="",style="solid", color="blue", weight=9];
32.88/16.50	1261 -> 277[label="",style="solid", color="blue", weight=3];
32.88/16.50	1262[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1262[label="",style="solid", color="blue", weight=9];
32.88/16.50	1262 -> 278[label="",style="solid", color="blue", weight=3];
32.88/16.50	1263[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1263[label="",style="solid", color="blue", weight=9];
32.88/16.50	1263 -> 279[label="",style="solid", color="blue", weight=3];
32.88/16.50	1264[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1264[label="",style="solid", color="blue", weight=9];
32.88/16.50	1264 -> 280[label="",style="solid", color="blue", weight=3];
32.88/16.50	1265[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1265[label="",style="solid", color="blue", weight=9];
32.88/16.50	1265 -> 281[label="",style="solid", color="blue", weight=3];
32.88/16.50	1266[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1266[label="",style="solid", color="blue", weight=9];
32.88/16.50	1266 -> 282[label="",style="solid", color="blue", weight=3];
32.88/16.50	1267[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1267[label="",style="solid", color="blue", weight=9];
32.88/16.50	1267 -> 283[label="",style="solid", color="blue", weight=3];
32.88/16.50	345 -> 254[label="",style="dashed", color="red", weight=0];
32.88/16.50	345[label="primShowInt (div Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];345 -> 370[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	346[label="toEnum (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];346 -> 371[label="",style="dashed", color="green", weight=3];
32.88/16.50	347[label="Pos ww170",fontsize=16,color="green",shape="box"];266[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];266 -> 288[label="",style="solid", color="black", weight=3];
32.88/16.50	267[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];267 -> 289[label="",style="solid", color="black", weight=3];
32.88/16.50	268[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];268 -> 290[label="",style="solid", color="black", weight=3];
32.88/16.50	269[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];269 -> 291[label="",style="solid", color="black", weight=3];
32.88/16.50	270[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];270 -> 292[label="",style="solid", color="black", weight=3];
32.88/16.50	271[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];271 -> 293[label="",style="solid", color="black", weight=3];
32.88/16.50	272[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];272 -> 294[label="",style="solid", color="black", weight=3];
32.88/16.50	273[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="burlywood",shape="box"];1268[label="ww21/ww210 :% ww211",fontsize=10,color="white",style="solid",shape="box"];273 -> 1268[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1268 -> 295[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	274[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];274 -> 296[label="",style="solid", color="black", weight=3];
32.88/16.50	275[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];275 -> 297[label="",style="solid", color="black", weight=3];
32.88/16.50	276[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];276 -> 298[label="",style="solid", color="black", weight=3];
32.88/16.50	277[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];277 -> 299[label="",style="solid", color="black", weight=3];
32.88/16.50	278[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];278 -> 300[label="",style="solid", color="black", weight=3];
32.88/16.50	279[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];279 -> 301[label="",style="solid", color="black", weight=3];
32.88/16.50	280[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];280 -> 302[label="",style="solid", color="black", weight=3];
32.88/16.50	281[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];281 -> 303[label="",style="solid", color="black", weight=3];
32.88/16.50	282[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];282 -> 304[label="",style="solid", color="black", weight=3];
32.88/16.50	283[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];283 -> 305[label="",style="solid", color="black", weight=3];
32.88/16.50	370 -> 372[label="",style="dashed", color="red", weight=0];
32.88/16.50	370[label="div Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];370 -> 373[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	370 -> 374[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	371[label="toEnum (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];371 -> 389[label="",style="solid", color="black", weight=3];
32.88/16.50	288 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	288[label="show ww21 ++ ww22",fontsize=16,color="magenta"];288 -> 310[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	288 -> 311[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	289 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	289[label="show ww21 ++ ww22",fontsize=16,color="magenta"];289 -> 312[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	289 -> 313[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	290 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	290[label="show ww21 ++ ww22",fontsize=16,color="magenta"];290 -> 314[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	290 -> 315[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	291 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	291[label="show ww21 ++ ww22",fontsize=16,color="magenta"];291 -> 316[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	291 -> 317[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	292 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	292[label="show ww21 ++ ww22",fontsize=16,color="magenta"];292 -> 318[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	292 -> 319[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	293 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	293[label="show ww21 ++ ww22",fontsize=16,color="magenta"];293 -> 320[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	293 -> 321[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	294 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	294[label="show ww21 ++ ww22",fontsize=16,color="magenta"];294 -> 322[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	294 -> 323[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	295[label="showsPrec (Pos Zero) (ww210 :% ww211) ww22",fontsize=16,color="black",shape="box"];295 -> 324[label="",style="solid", color="black", weight=3];
32.88/16.50	296 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	296[label="show ww21 ++ ww22",fontsize=16,color="magenta"];296 -> 325[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	296 -> 326[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	297 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	297[label="show ww21 ++ ww22",fontsize=16,color="magenta"];297 -> 327[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	297 -> 328[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	298 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	298[label="show ww21 ++ ww22",fontsize=16,color="magenta"];298 -> 329[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	298 -> 330[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	299 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	299[label="show ww21 ++ ww22",fontsize=16,color="magenta"];299 -> 331[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	299 -> 332[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	300 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	300[label="show ww21 ++ ww22",fontsize=16,color="magenta"];300 -> 333[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	300 -> 334[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	301 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	301[label="show ww21 ++ ww22",fontsize=16,color="magenta"];301 -> 335[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	301 -> 336[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	302 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	302[label="show ww21 ++ ww22",fontsize=16,color="magenta"];302 -> 337[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	302 -> 338[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	303 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	303[label="show ww21 ++ ww22",fontsize=16,color="magenta"];303 -> 339[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	303 -> 340[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	304 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	304[label="show ww21 ++ ww22",fontsize=16,color="magenta"];304 -> 341[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	304 -> 342[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	305 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.50	305[label="show ww21 ++ ww22",fontsize=16,color="magenta"];305 -> 343[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	305 -> 344[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	373[label="ww1700",fontsize=16,color="green",shape="box"];374[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];372[label="div Pos (Succ ww60) Pos (Succ ww61)",fontsize=16,color="black",shape="triangle"];372 -> 378[label="",style="solid", color="black", weight=3];
32.88/16.50	389 -> 400[label="",style="dashed", color="red", weight=0];
32.88/16.50	389[label="primIntToChar (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];389 -> 401[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	389 -> 402[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	310 -> 183[label="",style="dashed", color="red", weight=0];
32.88/16.50	310[label="show ww21",fontsize=16,color="magenta"];310 -> 348[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	311[label="ww22",fontsize=16,color="green",shape="box"];312 -> 185[label="",style="dashed", color="red", weight=0];
32.88/16.50	312[label="show ww21",fontsize=16,color="magenta"];312 -> 349[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	313[label="ww22",fontsize=16,color="green",shape="box"];314 -> 187[label="",style="dashed", color="red", weight=0];
32.88/16.50	314[label="show ww21",fontsize=16,color="magenta"];314 -> 350[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	315[label="ww22",fontsize=16,color="green",shape="box"];316 -> 189[label="",style="dashed", color="red", weight=0];
32.88/16.50	316[label="show ww21",fontsize=16,color="magenta"];316 -> 351[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	317[label="ww22",fontsize=16,color="green",shape="box"];318 -> 191[label="",style="dashed", color="red", weight=0];
32.88/16.50	318[label="show ww21",fontsize=16,color="magenta"];318 -> 352[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	319[label="ww22",fontsize=16,color="green",shape="box"];320 -> 193[label="",style="dashed", color="red", weight=0];
32.88/16.50	320[label="show ww21",fontsize=16,color="magenta"];320 -> 353[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	321[label="ww22",fontsize=16,color="green",shape="box"];322 -> 195[label="",style="dashed", color="red", weight=0];
32.88/16.50	322[label="show ww21",fontsize=16,color="magenta"];322 -> 354[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	323[label="ww22",fontsize=16,color="green",shape="box"];324 -> 24[label="",style="dashed", color="red", weight=0];
32.88/16.50	324[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww210) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww211) ww22",fontsize=16,color="magenta"];324 -> 355[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	324 -> 356[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	324 -> 357[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	324 -> 358[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	324 -> 359[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	325 -> 197[label="",style="dashed", color="red", weight=0];
32.88/16.50	325[label="show ww21",fontsize=16,color="magenta"];325 -> 360[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	326[label="ww22",fontsize=16,color="green",shape="box"];327 -> 199[label="",style="dashed", color="red", weight=0];
32.88/16.50	327[label="show ww21",fontsize=16,color="magenta"];327 -> 361[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	328[label="ww22",fontsize=16,color="green",shape="box"];329 -> 201[label="",style="dashed", color="red", weight=0];
32.88/16.50	329[label="show ww21",fontsize=16,color="magenta"];329 -> 362[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	330[label="ww22",fontsize=16,color="green",shape="box"];331 -> 203[label="",style="dashed", color="red", weight=0];
32.88/16.50	331[label="show ww21",fontsize=16,color="magenta"];331 -> 363[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	332[label="ww22",fontsize=16,color="green",shape="box"];333 -> 205[label="",style="dashed", color="red", weight=0];
32.88/16.50	333[label="show ww21",fontsize=16,color="magenta"];333 -> 364[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	334[label="ww22",fontsize=16,color="green",shape="box"];335 -> 207[label="",style="dashed", color="red", weight=0];
32.88/16.50	335[label="show ww21",fontsize=16,color="magenta"];335 -> 365[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	336[label="ww22",fontsize=16,color="green",shape="box"];337 -> 209[label="",style="dashed", color="red", weight=0];
32.88/16.50	337[label="show ww21",fontsize=16,color="magenta"];337 -> 366[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	338[label="ww22",fontsize=16,color="green",shape="box"];339 -> 211[label="",style="dashed", color="red", weight=0];
32.88/16.50	339[label="show ww21",fontsize=16,color="magenta"];339 -> 367[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	340[label="ww22",fontsize=16,color="green",shape="box"];341 -> 213[label="",style="dashed", color="red", weight=0];
32.88/16.50	341[label="show ww21",fontsize=16,color="magenta"];341 -> 368[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	342[label="ww22",fontsize=16,color="green",shape="box"];343 -> 215[label="",style="dashed", color="red", weight=0];
32.88/16.50	343[label="show ww21",fontsize=16,color="magenta"];343 -> 369[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	344[label="ww22",fontsize=16,color="green",shape="box"];378[label="primDivInt (Pos (Succ ww60)) (Pos (Succ ww61))",fontsize=16,color="black",shape="box"];378 -> 388[label="",style="solid", color="black", weight=3];
32.88/16.50	401[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];402[label="ww1700",fontsize=16,color="green",shape="box"];400[label="primIntToChar (mod Pos (Succ ww66) Pos (Succ ww67))",fontsize=16,color="black",shape="triangle"];400 -> 403[label="",style="solid", color="black", weight=3];
32.88/16.50	348[label="ww21",fontsize=16,color="green",shape="box"];349[label="ww21",fontsize=16,color="green",shape="box"];350[label="ww21",fontsize=16,color="green",shape="box"];351[label="ww21",fontsize=16,color="green",shape="box"];352[label="ww21",fontsize=16,color="green",shape="box"];353[label="ww21",fontsize=16,color="green",shape="box"];354[label="ww21",fontsize=16,color="green",shape="box"];355[label="ww210",fontsize=16,color="green",shape="box"];356[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];357[label="ww211",fontsize=16,color="green",shape="box"];358[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];359[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];360[label="ww21",fontsize=16,color="green",shape="box"];361[label="ww21",fontsize=16,color="green",shape="box"];362[label="ww21",fontsize=16,color="green",shape="box"];363[label="ww21",fontsize=16,color="green",shape="box"];364[label="ww21",fontsize=16,color="green",shape="box"];365[label="ww21",fontsize=16,color="green",shape="box"];366[label="ww21",fontsize=16,color="green",shape="box"];367[label="ww21",fontsize=16,color="green",shape="box"];368[label="ww21",fontsize=16,color="green",shape="box"];369[label="ww21",fontsize=16,color="green",shape="box"];388[label="Pos (primDivNatS (Succ ww60) (Succ ww61))",fontsize=16,color="green",shape="box"];388 -> 399[label="",style="dashed", color="green", weight=3];
32.88/16.50	403[label="primIntToChar (primModInt (Pos (Succ ww66)) (Pos (Succ ww67)))",fontsize=16,color="black",shape="box"];403 -> 405[label="",style="solid", color="black", weight=3];
32.88/16.50	399[label="primDivNatS (Succ ww60) (Succ ww61)",fontsize=16,color="black",shape="triangle"];399 -> 404[label="",style="solid", color="black", weight=3];
32.88/16.50	405[label="primIntToChar (Pos (primModNatS (Succ ww66) (Succ ww67)))",fontsize=16,color="black",shape="box"];405 -> 408[label="",style="solid", color="black", weight=3];
32.88/16.50	404[label="primDivNatS0 ww60 ww61 (primGEqNatS ww60 ww61)",fontsize=16,color="burlywood",shape="box"];1269[label="ww60/Succ ww600",fontsize=10,color="white",style="solid",shape="box"];404 -> 1269[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1269 -> 406[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1270[label="ww60/Zero",fontsize=10,color="white",style="solid",shape="box"];404 -> 1270[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1270 -> 407[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	408[label="Char (primModNatS (Succ ww66) (Succ ww67))",fontsize=16,color="green",shape="box"];408 -> 413[label="",style="dashed", color="green", weight=3];
32.88/16.50	406[label="primDivNatS0 (Succ ww600) ww61 (primGEqNatS (Succ ww600) ww61)",fontsize=16,color="burlywood",shape="box"];1271[label="ww61/Succ ww610",fontsize=10,color="white",style="solid",shape="box"];406 -> 1271[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1271 -> 409[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1272[label="ww61/Zero",fontsize=10,color="white",style="solid",shape="box"];406 -> 1272[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1272 -> 410[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	407[label="primDivNatS0 Zero ww61 (primGEqNatS Zero ww61)",fontsize=16,color="burlywood",shape="box"];1273[label="ww61/Succ ww610",fontsize=10,color="white",style="solid",shape="box"];407 -> 1273[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1273 -> 411[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1274[label="ww61/Zero",fontsize=10,color="white",style="solid",shape="box"];407 -> 1274[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1274 -> 412[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	413[label="primModNatS (Succ ww66) (Succ ww67)",fontsize=16,color="black",shape="triangle"];413 -> 418[label="",style="solid", color="black", weight=3];
32.88/16.50	409[label="primDivNatS0 (Succ ww600) (Succ ww610) (primGEqNatS (Succ ww600) (Succ ww610))",fontsize=16,color="black",shape="box"];409 -> 414[label="",style="solid", color="black", weight=3];
32.88/16.50	410[label="primDivNatS0 (Succ ww600) Zero (primGEqNatS (Succ ww600) Zero)",fontsize=16,color="black",shape="box"];410 -> 415[label="",style="solid", color="black", weight=3];
32.88/16.50	411[label="primDivNatS0 Zero (Succ ww610) (primGEqNatS Zero (Succ ww610))",fontsize=16,color="black",shape="box"];411 -> 416[label="",style="solid", color="black", weight=3];
32.88/16.50	412[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];412 -> 417[label="",style="solid", color="black", weight=3];
32.88/16.50	418[label="primModNatS0 ww66 ww67 (primGEqNatS ww66 ww67)",fontsize=16,color="burlywood",shape="box"];1275[label="ww66/Succ ww660",fontsize=10,color="white",style="solid",shape="box"];418 -> 1275[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1275 -> 424[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1276[label="ww66/Zero",fontsize=10,color="white",style="solid",shape="box"];418 -> 1276[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1276 -> 425[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	414 -> 930[label="",style="dashed", color="red", weight=0];
32.88/16.50	414[label="primDivNatS0 (Succ ww600) (Succ ww610) (primGEqNatS ww600 ww610)",fontsize=16,color="magenta"];414 -> 931[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	414 -> 932[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	414 -> 933[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	414 -> 934[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	415[label="primDivNatS0 (Succ ww600) Zero True",fontsize=16,color="black",shape="box"];415 -> 421[label="",style="solid", color="black", weight=3];
32.88/16.50	416[label="primDivNatS0 Zero (Succ ww610) False",fontsize=16,color="black",shape="box"];416 -> 422[label="",style="solid", color="black", weight=3];
32.88/16.50	417[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];417 -> 423[label="",style="solid", color="black", weight=3];
32.88/16.50	424[label="primModNatS0 (Succ ww660) ww67 (primGEqNatS (Succ ww660) ww67)",fontsize=16,color="burlywood",shape="box"];1277[label="ww67/Succ ww670",fontsize=10,color="white",style="solid",shape="box"];424 -> 1277[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1277 -> 432[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1278[label="ww67/Zero",fontsize=10,color="white",style="solid",shape="box"];424 -> 1278[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1278 -> 433[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	425[label="primModNatS0 Zero ww67 (primGEqNatS Zero ww67)",fontsize=16,color="burlywood",shape="box"];1279[label="ww67/Succ ww670",fontsize=10,color="white",style="solid",shape="box"];425 -> 1279[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1279 -> 434[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1280[label="ww67/Zero",fontsize=10,color="white",style="solid",shape="box"];425 -> 1280[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1280 -> 435[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	931[label="ww610",fontsize=16,color="green",shape="box"];932[label="ww600",fontsize=16,color="green",shape="box"];933[label="ww600",fontsize=16,color="green",shape="box"];934[label="ww610",fontsize=16,color="green",shape="box"];930[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS ww112 ww113)",fontsize=16,color="burlywood",shape="triangle"];1281[label="ww112/Succ ww1120",fontsize=10,color="white",style="solid",shape="box"];930 -> 1281[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1281 -> 971[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1282[label="ww112/Zero",fontsize=10,color="white",style="solid",shape="box"];930 -> 1282[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1282 -> 972[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	421[label="Succ (primDivNatS (primMinusNatS (Succ ww600) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];421 -> 430[label="",style="dashed", color="green", weight=3];
32.88/16.50	422[label="Zero",fontsize=16,color="green",shape="box"];423[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];423 -> 431[label="",style="dashed", color="green", weight=3];
32.88/16.50	432[label="primModNatS0 (Succ ww660) (Succ ww670) (primGEqNatS (Succ ww660) (Succ ww670))",fontsize=16,color="black",shape="box"];432 -> 442[label="",style="solid", color="black", weight=3];
32.88/16.50	433[label="primModNatS0 (Succ ww660) Zero (primGEqNatS (Succ ww660) Zero)",fontsize=16,color="black",shape="box"];433 -> 443[label="",style="solid", color="black", weight=3];
32.88/16.50	434[label="primModNatS0 Zero (Succ ww670) (primGEqNatS Zero (Succ ww670))",fontsize=16,color="black",shape="box"];434 -> 444[label="",style="solid", color="black", weight=3];
32.88/16.50	435[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];435 -> 445[label="",style="solid", color="black", weight=3];
32.88/16.50	971[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS (Succ ww1120) ww113)",fontsize=16,color="burlywood",shape="box"];1283[label="ww113/Succ ww1130",fontsize=10,color="white",style="solid",shape="box"];971 -> 1283[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1283 -> 983[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1284[label="ww113/Zero",fontsize=10,color="white",style="solid",shape="box"];971 -> 1284[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1284 -> 984[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	972[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS Zero ww113)",fontsize=16,color="burlywood",shape="box"];1285[label="ww113/Succ ww1130",fontsize=10,color="white",style="solid",shape="box"];972 -> 1285[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1285 -> 985[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1286[label="ww113/Zero",fontsize=10,color="white",style="solid",shape="box"];972 -> 1286[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1286 -> 986[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	430 -> 1184[label="",style="dashed", color="red", weight=0];
32.88/16.50	430[label="primDivNatS (primMinusNatS (Succ ww600) Zero) (Succ Zero)",fontsize=16,color="magenta"];430 -> 1185[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	430 -> 1186[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	430 -> 1187[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	431 -> 1184[label="",style="dashed", color="red", weight=0];
32.88/16.50	431[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];431 -> 1188[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	431 -> 1189[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	431 -> 1190[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	442 -> 1005[label="",style="dashed", color="red", weight=0];
32.88/16.50	442[label="primModNatS0 (Succ ww660) (Succ ww670) (primGEqNatS ww660 ww670)",fontsize=16,color="magenta"];442 -> 1006[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	442 -> 1007[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	442 -> 1008[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	442 -> 1009[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	443[label="primModNatS0 (Succ ww660) Zero True",fontsize=16,color="black",shape="box"];443 -> 456[label="",style="solid", color="black", weight=3];
32.88/16.50	444[label="primModNatS0 Zero (Succ ww670) False",fontsize=16,color="black",shape="box"];444 -> 457[label="",style="solid", color="black", weight=3];
32.88/16.50	445[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];445 -> 458[label="",style="solid", color="black", weight=3];
32.88/16.50	983[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS (Succ ww1120) (Succ ww1130))",fontsize=16,color="black",shape="box"];983 -> 997[label="",style="solid", color="black", weight=3];
32.88/16.50	984[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS (Succ ww1120) Zero)",fontsize=16,color="black",shape="box"];984 -> 998[label="",style="solid", color="black", weight=3];
32.88/16.50	985[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS Zero (Succ ww1130))",fontsize=16,color="black",shape="box"];985 -> 999[label="",style="solid", color="black", weight=3];
32.88/16.50	986[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];986 -> 1000[label="",style="solid", color="black", weight=3];
32.88/16.50	1185[label="Succ ww600",fontsize=16,color="green",shape="box"];1186[label="Zero",fontsize=16,color="green",shape="box"];1187[label="Zero",fontsize=16,color="green",shape="box"];1184[label="primDivNatS (primMinusNatS ww124 ww125) (Succ ww126)",fontsize=16,color="burlywood",shape="triangle"];1287[label="ww124/Succ ww1240",fontsize=10,color="white",style="solid",shape="box"];1184 -> 1287[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1287 -> 1209[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1288[label="ww124/Zero",fontsize=10,color="white",style="solid",shape="box"];1184 -> 1288[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1288 -> 1210[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1188[label="Zero",fontsize=16,color="green",shape="box"];1189[label="Zero",fontsize=16,color="green",shape="box"];1190[label="Zero",fontsize=16,color="green",shape="box"];1006[label="ww660",fontsize=16,color="green",shape="box"];1007[label="ww670",fontsize=16,color="green",shape="box"];1008[label="ww660",fontsize=16,color="green",shape="box"];1009[label="ww670",fontsize=16,color="green",shape="box"];1005[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS ww117 ww118)",fontsize=16,color="burlywood",shape="triangle"];1289[label="ww117/Succ ww1170",fontsize=10,color="white",style="solid",shape="box"];1005 -> 1289[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1289 -> 1046[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1290[label="ww117/Zero",fontsize=10,color="white",style="solid",shape="box"];1005 -> 1290[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1290 -> 1047[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	456 -> 1092[label="",style="dashed", color="red", weight=0];
32.88/16.50	456[label="primModNatS (primMinusNatS (Succ ww660) Zero) (Succ Zero)",fontsize=16,color="magenta"];456 -> 1093[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	456 -> 1094[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	456 -> 1095[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	457[label="Succ Zero",fontsize=16,color="green",shape="box"];458 -> 1092[label="",style="dashed", color="red", weight=0];
32.88/16.50	458[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];458 -> 1096[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	458 -> 1097[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	458 -> 1098[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	997 -> 930[label="",style="dashed", color="red", weight=0];
32.88/16.50	997[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS ww1120 ww1130)",fontsize=16,color="magenta"];997 -> 1048[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	997 -> 1049[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	998[label="primDivNatS0 (Succ ww110) (Succ ww111) True",fontsize=16,color="black",shape="triangle"];998 -> 1050[label="",style="solid", color="black", weight=3];
32.88/16.50	999[label="primDivNatS0 (Succ ww110) (Succ ww111) False",fontsize=16,color="black",shape="box"];999 -> 1051[label="",style="solid", color="black", weight=3];
32.88/16.50	1000 -> 998[label="",style="dashed", color="red", weight=0];
32.88/16.50	1000[label="primDivNatS0 (Succ ww110) (Succ ww111) True",fontsize=16,color="magenta"];1209[label="primDivNatS (primMinusNatS (Succ ww1240) ww125) (Succ ww126)",fontsize=16,color="burlywood",shape="box"];1291[label="ww125/Succ ww1250",fontsize=10,color="white",style="solid",shape="box"];1209 -> 1291[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1291 -> 1211[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1292[label="ww125/Zero",fontsize=10,color="white",style="solid",shape="box"];1209 -> 1292[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1292 -> 1212[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1210[label="primDivNatS (primMinusNatS Zero ww125) (Succ ww126)",fontsize=16,color="burlywood",shape="box"];1293[label="ww125/Succ ww1250",fontsize=10,color="white",style="solid",shape="box"];1210 -> 1293[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1293 -> 1213[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1294[label="ww125/Zero",fontsize=10,color="white",style="solid",shape="box"];1210 -> 1294[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1294 -> 1214[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1046[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS (Succ ww1170) ww118)",fontsize=16,color="burlywood",shape="box"];1295[label="ww118/Succ ww1180",fontsize=10,color="white",style="solid",shape="box"];1046 -> 1295[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1295 -> 1056[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1296[label="ww118/Zero",fontsize=10,color="white",style="solid",shape="box"];1046 -> 1296[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1296 -> 1057[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1047[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS Zero ww118)",fontsize=16,color="burlywood",shape="box"];1297[label="ww118/Succ ww1180",fontsize=10,color="white",style="solid",shape="box"];1047 -> 1297[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1297 -> 1058[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1298[label="ww118/Zero",fontsize=10,color="white",style="solid",shape="box"];1047 -> 1298[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1298 -> 1059[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1093[label="Succ ww660",fontsize=16,color="green",shape="box"];1094[label="Zero",fontsize=16,color="green",shape="box"];1095[label="Zero",fontsize=16,color="green",shape="box"];1092[label="primModNatS (primMinusNatS ww120 ww121) (Succ ww122)",fontsize=16,color="burlywood",shape="triangle"];1299[label="ww120/Succ ww1200",fontsize=10,color="white",style="solid",shape="box"];1092 -> 1299[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1299 -> 1123[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1300[label="ww120/Zero",fontsize=10,color="white",style="solid",shape="box"];1092 -> 1300[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1300 -> 1124[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1096[label="Zero",fontsize=16,color="green",shape="box"];1097[label="Zero",fontsize=16,color="green",shape="box"];1098[label="Zero",fontsize=16,color="green",shape="box"];1048[label="ww1130",fontsize=16,color="green",shape="box"];1049[label="ww1120",fontsize=16,color="green",shape="box"];1050[label="Succ (primDivNatS (primMinusNatS (Succ ww110) (Succ ww111)) (Succ (Succ ww111)))",fontsize=16,color="green",shape="box"];1050 -> 1060[label="",style="dashed", color="green", weight=3];
32.88/16.50	1051[label="Zero",fontsize=16,color="green",shape="box"];1211[label="primDivNatS (primMinusNatS (Succ ww1240) (Succ ww1250)) (Succ ww126)",fontsize=16,color="black",shape="box"];1211 -> 1215[label="",style="solid", color="black", weight=3];
32.88/16.50	1212[label="primDivNatS (primMinusNatS (Succ ww1240) Zero) (Succ ww126)",fontsize=16,color="black",shape="box"];1212 -> 1216[label="",style="solid", color="black", weight=3];
32.88/16.50	1213[label="primDivNatS (primMinusNatS Zero (Succ ww1250)) (Succ ww126)",fontsize=16,color="black",shape="box"];1213 -> 1217[label="",style="solid", color="black", weight=3];
32.88/16.50	1214[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww126)",fontsize=16,color="black",shape="box"];1214 -> 1218[label="",style="solid", color="black", weight=3];
32.88/16.50	1056[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS (Succ ww1170) (Succ ww1180))",fontsize=16,color="black",shape="box"];1056 -> 1067[label="",style="solid", color="black", weight=3];
32.88/16.50	1057[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS (Succ ww1170) Zero)",fontsize=16,color="black",shape="box"];1057 -> 1068[label="",style="solid", color="black", weight=3];
32.88/16.50	1058[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS Zero (Succ ww1180))",fontsize=16,color="black",shape="box"];1058 -> 1069[label="",style="solid", color="black", weight=3];
32.88/16.50	1059[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1059 -> 1070[label="",style="solid", color="black", weight=3];
32.88/16.50	1123[label="primModNatS (primMinusNatS (Succ ww1200) ww121) (Succ ww122)",fontsize=16,color="burlywood",shape="box"];1301[label="ww121/Succ ww1210",fontsize=10,color="white",style="solid",shape="box"];1123 -> 1301[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1301 -> 1129[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1302[label="ww121/Zero",fontsize=10,color="white",style="solid",shape="box"];1123 -> 1302[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1302 -> 1130[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1124[label="primModNatS (primMinusNatS Zero ww121) (Succ ww122)",fontsize=16,color="burlywood",shape="box"];1303[label="ww121/Succ ww1210",fontsize=10,color="white",style="solid",shape="box"];1124 -> 1303[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1303 -> 1131[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1304[label="ww121/Zero",fontsize=10,color="white",style="solid",shape="box"];1124 -> 1304[label="",style="solid", color="burlywood", weight=9];
32.88/16.50	1304 -> 1132[label="",style="solid", color="burlywood", weight=3];
32.88/16.50	1060 -> 1184[label="",style="dashed", color="red", weight=0];
32.88/16.50	1060[label="primDivNatS (primMinusNatS (Succ ww110) (Succ ww111)) (Succ (Succ ww111))",fontsize=16,color="magenta"];1060 -> 1191[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1060 -> 1192[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1060 -> 1193[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1215 -> 1184[label="",style="dashed", color="red", weight=0];
32.88/16.50	1215[label="primDivNatS (primMinusNatS ww1240 ww1250) (Succ ww126)",fontsize=16,color="magenta"];1215 -> 1219[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1215 -> 1220[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1216 -> 399[label="",style="dashed", color="red", weight=0];
32.88/16.50	1216[label="primDivNatS (Succ ww1240) (Succ ww126)",fontsize=16,color="magenta"];1216 -> 1221[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1216 -> 1222[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1217[label="primDivNatS Zero (Succ ww126)",fontsize=16,color="black",shape="triangle"];1217 -> 1223[label="",style="solid", color="black", weight=3];
32.88/16.50	1218 -> 1217[label="",style="dashed", color="red", weight=0];
32.88/16.50	1218[label="primDivNatS Zero (Succ ww126)",fontsize=16,color="magenta"];1067 -> 1005[label="",style="dashed", color="red", weight=0];
32.88/16.50	1067[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS ww1170 ww1180)",fontsize=16,color="magenta"];1067 -> 1076[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1067 -> 1077[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1068[label="primModNatS0 (Succ ww115) (Succ ww116) True",fontsize=16,color="black",shape="triangle"];1068 -> 1078[label="",style="solid", color="black", weight=3];
32.88/16.50	1069[label="primModNatS0 (Succ ww115) (Succ ww116) False",fontsize=16,color="black",shape="box"];1069 -> 1079[label="",style="solid", color="black", weight=3];
32.88/16.50	1070 -> 1068[label="",style="dashed", color="red", weight=0];
32.88/16.50	1070[label="primModNatS0 (Succ ww115) (Succ ww116) True",fontsize=16,color="magenta"];1129[label="primModNatS (primMinusNatS (Succ ww1200) (Succ ww1210)) (Succ ww122)",fontsize=16,color="black",shape="box"];1129 -> 1139[label="",style="solid", color="black", weight=3];
32.88/16.50	1130[label="primModNatS (primMinusNatS (Succ ww1200) Zero) (Succ ww122)",fontsize=16,color="black",shape="box"];1130 -> 1140[label="",style="solid", color="black", weight=3];
32.88/16.50	1131[label="primModNatS (primMinusNatS Zero (Succ ww1210)) (Succ ww122)",fontsize=16,color="black",shape="box"];1131 -> 1141[label="",style="solid", color="black", weight=3];
32.88/16.50	1132[label="primModNatS (primMinusNatS Zero Zero) (Succ ww122)",fontsize=16,color="black",shape="box"];1132 -> 1142[label="",style="solid", color="black", weight=3];
32.88/16.50	1191[label="Succ ww110",fontsize=16,color="green",shape="box"];1192[label="Succ ww111",fontsize=16,color="green",shape="box"];1193[label="Succ ww111",fontsize=16,color="green",shape="box"];1219[label="ww1240",fontsize=16,color="green",shape="box"];1220[label="ww1250",fontsize=16,color="green",shape="box"];1221[label="ww1240",fontsize=16,color="green",shape="box"];1222[label="ww126",fontsize=16,color="green",shape="box"];1223[label="Zero",fontsize=16,color="green",shape="box"];1076[label="ww1170",fontsize=16,color="green",shape="box"];1077[label="ww1180",fontsize=16,color="green",shape="box"];1078 -> 1092[label="",style="dashed", color="red", weight=0];
32.88/16.50	1078[label="primModNatS (primMinusNatS (Succ ww115) (Succ ww116)) (Succ (Succ ww116))",fontsize=16,color="magenta"];1078 -> 1105[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1078 -> 1106[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1078 -> 1107[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1079[label="Succ (Succ ww115)",fontsize=16,color="green",shape="box"];1139 -> 1092[label="",style="dashed", color="red", weight=0];
32.88/16.50	1139[label="primModNatS (primMinusNatS ww1200 ww1210) (Succ ww122)",fontsize=16,color="magenta"];1139 -> 1147[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1139 -> 1148[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1140 -> 413[label="",style="dashed", color="red", weight=0];
32.88/16.50	1140[label="primModNatS (Succ ww1200) (Succ ww122)",fontsize=16,color="magenta"];1140 -> 1149[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1140 -> 1150[label="",style="dashed", color="magenta", weight=3];
32.88/16.50	1141[label="primModNatS Zero (Succ ww122)",fontsize=16,color="black",shape="triangle"];1141 -> 1151[label="",style="solid", color="black", weight=3];
32.88/16.50	1142 -> 1141[label="",style="dashed", color="red", weight=0];
32.88/16.50	1142[label="primModNatS Zero (Succ ww122)",fontsize=16,color="magenta"];1105[label="Succ ww115",fontsize=16,color="green",shape="box"];1106[label="Succ ww116",fontsize=16,color="green",shape="box"];1107[label="Succ ww116",fontsize=16,color="green",shape="box"];1147[label="ww1200",fontsize=16,color="green",shape="box"];1148[label="ww1210",fontsize=16,color="green",shape="box"];1149[label="ww122",fontsize=16,color="green",shape="box"];1150[label="ww1200",fontsize=16,color="green",shape="box"];1151[label="Zero",fontsize=16,color="green",shape="box"];}
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(10)
32.88/16.50	Complex Obligation (AND)
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(11)
32.88/16.50	Obligation:
32.88/16.50	Q DP problem:
32.88/16.50	The TRS P consists of the following rules:
32.88/16.50	
32.88/16.50	   new_primDivNatS0(ww110, ww111, Zero, Zero) -> new_primDivNatS00(ww110, ww111)
32.88/16.50	   new_primDivNatS00(ww110, ww111) -> new_primDivNatS(Succ(ww110), Succ(ww111), Succ(ww111))
32.88/16.50	   new_primDivNatS(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS(ww1240, ww1250, ww126)
32.88/16.50	   new_primDivNatS1(Succ(ww600), Zero) -> new_primDivNatS(Succ(ww600), Zero, Zero)
32.88/16.50	   new_primDivNatS0(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS0(ww110, ww111, ww1120, ww1130)
32.88/16.50	   new_primDivNatS0(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS(Succ(ww110), Succ(ww111), Succ(ww111))
32.88/16.50	   new_primDivNatS1(Succ(ww600), Succ(ww610)) -> new_primDivNatS0(ww600, ww610, ww600, ww610)
32.88/16.50	   new_primDivNatS1(Zero, Zero) -> new_primDivNatS(Zero, Zero, Zero)
32.88/16.50	   new_primDivNatS(Succ(ww1240), Zero, ww126) -> new_primDivNatS1(ww1240, ww126)
32.88/16.50	
32.88/16.50	R is empty.
32.88/16.50	Q is empty.
32.88/16.50	We have to consider all minimal (P,Q,R)-chains.
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(12) DependencyGraphProof (EQUIVALENT)
32.88/16.50	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(13)
32.88/16.50	Obligation:
32.88/16.50	Q DP problem:
32.88/16.50	The TRS P consists of the following rules:
32.88/16.50	
32.88/16.50	   new_primDivNatS00(ww110, ww111) -> new_primDivNatS(Succ(ww110), Succ(ww111), Succ(ww111))
32.88/16.50	   new_primDivNatS(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS(ww1240, ww1250, ww126)
32.88/16.50	   new_primDivNatS(Succ(ww1240), Zero, ww126) -> new_primDivNatS1(ww1240, ww126)
32.88/16.50	   new_primDivNatS1(Succ(ww600), Zero) -> new_primDivNatS(Succ(ww600), Zero, Zero)
32.88/16.50	   new_primDivNatS1(Succ(ww600), Succ(ww610)) -> new_primDivNatS0(ww600, ww610, ww600, ww610)
32.88/16.50	   new_primDivNatS0(ww110, ww111, Zero, Zero) -> new_primDivNatS00(ww110, ww111)
32.88/16.50	   new_primDivNatS0(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS0(ww110, ww111, ww1120, ww1130)
32.88/16.50	   new_primDivNatS0(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS(Succ(ww110), Succ(ww111), Succ(ww111))
32.88/16.50	
32.88/16.50	R is empty.
32.88/16.50	Q is empty.
32.88/16.50	We have to consider all minimal (P,Q,R)-chains.
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(14) QDPOrderProof (EQUIVALENT)
32.88/16.50	We use the reduction pair processor [LPAR04,JAR06].
32.88/16.50	
32.88/16.50	
32.88/16.50	The following pairs can be oriented strictly and are deleted.
32.88/16.50	
32.88/16.50	   new_primDivNatS(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS(ww1240, ww1250, ww126)
32.88/16.50	   new_primDivNatS1(Succ(ww600), Zero) -> new_primDivNatS(Succ(ww600), Zero, Zero)
32.88/16.50	   new_primDivNatS1(Succ(ww600), Succ(ww610)) -> new_primDivNatS0(ww600, ww610, ww600, ww610)
32.88/16.50	The remaining pairs can at least be oriented weakly.
32.88/16.50	Used ordering:  Polynomial interpretation [POLO]:
32.88/16.50	
32.88/16.50	   POL(Succ(x_1)) = 1 + x_1
32.88/16.50	   POL(Zero) = 0
32.88/16.50	   POL(new_primDivNatS(x_1, x_2, x_3)) = x_1
32.88/16.50	   POL(new_primDivNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1
32.88/16.50	   POL(new_primDivNatS00(x_1, x_2)) = 1 + x_1
32.88/16.50	   POL(new_primDivNatS1(x_1, x_2)) = 1 + x_1
32.88/16.50	
32.88/16.50	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
32.88/16.50	none
32.88/16.50	
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(15)
32.88/16.50	Obligation:
32.88/16.50	Q DP problem:
32.88/16.50	The TRS P consists of the following rules:
32.88/16.50	
32.88/16.50	   new_primDivNatS00(ww110, ww111) -> new_primDivNatS(Succ(ww110), Succ(ww111), Succ(ww111))
32.88/16.50	   new_primDivNatS(Succ(ww1240), Zero, ww126) -> new_primDivNatS1(ww1240, ww126)
32.88/16.50	   new_primDivNatS0(ww110, ww111, Zero, Zero) -> new_primDivNatS00(ww110, ww111)
32.88/16.50	   new_primDivNatS0(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS0(ww110, ww111, ww1120, ww1130)
32.88/16.50	   new_primDivNatS0(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS(Succ(ww110), Succ(ww111), Succ(ww111))
32.88/16.50	
32.88/16.50	R is empty.
32.88/16.50	Q is empty.
32.88/16.50	We have to consider all minimal (P,Q,R)-chains.
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(16) DependencyGraphProof (EQUIVALENT)
32.88/16.50	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes.
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(17)
32.88/16.50	Obligation:
32.88/16.50	Q DP problem:
32.88/16.50	The TRS P consists of the following rules:
32.88/16.50	
32.88/16.50	   new_primDivNatS0(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS0(ww110, ww111, ww1120, ww1130)
32.88/16.50	
32.88/16.50	R is empty.
32.88/16.50	Q is empty.
32.88/16.50	We have to consider all minimal (P,Q,R)-chains.
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(18) QDPSizeChangeProof (EQUIVALENT)
32.88/16.50	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. 
32.88/16.50	
32.88/16.50	From the DPs we obtained the following set of size-change graphs:
32.88/16.50	*new_primDivNatS0(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS0(ww110, ww111, ww1120, ww1130)
32.88/16.50	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
32.88/16.50	
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(19)
32.88/16.50	YES
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(20)
32.88/16.50	Obligation:
32.88/16.50	Q DP problem:
32.88/16.50	The TRS P consists of the following rules:
32.88/16.50	
32.88/16.50	   new_psPs(:(ww580, ww581), ww56) -> new_psPs(ww581, ww56)
32.88/16.50	
32.88/16.50	R is empty.
32.88/16.50	Q is empty.
32.88/16.50	We have to consider all minimal (P,Q,R)-chains.
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(21) QDPSizeChangeProof (EQUIVALENT)
32.88/16.50	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. 
32.88/16.50	
32.88/16.50	From the DPs we obtained the following set of size-change graphs:
32.88/16.50	*new_psPs(:(ww580, ww581), ww56) -> new_psPs(ww581, ww56)
32.88/16.50	The graph contains the following edges 1 > 1, 2 >= 2
32.88/16.50	
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(22)
32.88/16.50	YES
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(23)
32.88/16.50	Obligation:
32.88/16.50	Q DP problem:
32.88/16.50	The TRS P consists of the following rules:
32.88/16.50	
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.50	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	
32.88/16.50	The TRS R consists of the following rules:
32.88/16.50	
32.88/16.50	   new_show2(ww17) -> error([])
32.88/16.50	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_show6(ww17, be) -> error([])
32.88/16.50	   new_show(ww17, bg, bh) -> error([])
32.88/16.50	   new_show7(ww17) -> error([])
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.50	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.50	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_show1(ww17) -> error([])
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.50	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.50	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.50	   new_show3(ww17, ba) -> error([])
32.88/16.50	   new_show8(ww17) -> error([])
32.88/16.50	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.50	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.50	   new_primModNatS4(ww122) -> Zero
32.88/16.50	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.50	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.50	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.50	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.50	   new_show0(ww17) -> error([])
32.88/16.50	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.50	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.50	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.50	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.50	   new_show9(ww17) -> error([])
32.88/16.50	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_show13(ww17) -> error([])
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.50	   new_psPs0([], ww56) -> ww56
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.50	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.50	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.50	   new_show5(ww17) -> error([])
32.88/16.50	   new_show12(ww17, ca) -> error([])
32.88/16.50	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.50	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.50	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.50	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.50	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.50	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.50	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.50	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.50	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.50	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.50	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.50	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.50	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.50	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.50	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.50	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.50	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.50	   new_show11(ww17) -> error([])
32.88/16.50	   new_show4(ww17, bc, bd) -> error([])
32.88/16.50	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.50	   new_show15(ww17) -> error([])
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.50	   new_primDivNatS4(ww126) -> Zero
32.88/16.50	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.50	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.50	
32.88/16.50	The set Q consists of the following terms:
32.88/16.50	
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.50	   new_primShowInt0(Neg(x0))
32.88/16.50	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.50	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.50	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.50	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.50	   new_primModNatS3(Succ(x0), Zero)
32.88/16.50	   new_show0(x0)
32.88/16.50	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.50	   new_showsPrec(x0, x1, ty_Double)
32.88/16.50	   new_showsPrec(x0, x1, ty_Float)
32.88/16.50	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.50	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.50	   new_showsPrec(x0, x1, ty_@0)
32.88/16.50	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.50	   new_show9(x0)
32.88/16.50	   new_primModNatS02(x0, x1)
32.88/16.50	   new_show15(x0)
32.88/16.50	   new_show3(x0, x1)
32.88/16.50	   new_show8(x0)
32.88/16.50	   new_show11(x0)
32.88/16.50	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.50	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.50	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.50	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.50	   new_show(x0, x1, x2)
32.88/16.50	   new_show10(x0)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.50	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.50	   new_psPs0(:(x0, x1), x2)
32.88/16.50	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.50	   new_primModNatS4(x0)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.50	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.50	   new_show1(x0)
32.88/16.50	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.50	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.50	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.50	   new_show6(x0, x1)
32.88/16.50	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.50	   new_show13(x0)
32.88/16.50	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.50	   new_primModNatS3(Zero, Zero)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.50	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.50	   new_div(x0, x1)
32.88/16.50	   new_primIntToChar(x0, x1)
32.88/16.50	   new_show14(x0, x1, x2, x3)
32.88/16.50	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.50	   new_primModNatS3(Zero, Succ(x0))
32.88/16.50	   new_showsPrec(x0, x1, ty_Int)
32.88/16.50	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.50	   new_show5(x0)
32.88/16.50	   new_primShowInt0(Pos(Zero))
32.88/16.50	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.50	   new_primDivNatS02(x0, x1)
32.88/16.50	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.50	   new_show12(x0, x1)
32.88/16.50	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.50	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.50	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.50	   new_primModNatS2(Zero, Zero, x0)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.50	   new_psPs0([], x0)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.50	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.50	   new_show2(x0)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.50	   new_show7(x0)
32.88/16.50	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.50	   new_show4(x0, x1, x2)
32.88/16.50	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.50	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.50	   new_showsPrec(x0, x1, ty_Char)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.50	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.50	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.50	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.50	   new_primDivNatS4(x0)
32.88/16.50	   new_primDivNatS3(Zero, Zero)
32.88/16.50	
32.88/16.50	We have to consider all minimal (P,Q,R)-chains.
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(24) TransformationProof (EQUIVALENT)
32.88/16.50	By rewriting [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf) at position [5] we obtained the following new rules [LPAR04]:
32.88/16.50	
32.88/16.50	   (new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bf)), bf, bf),new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bf)), bf, bf))
32.88/16.50	
32.88/16.50	
32.88/16.50	----------------------------------------
32.88/16.50	
32.88/16.50	(25)
32.88/16.50	Obligation:
32.88/16.50	Q DP problem:
32.88/16.50	The TRS P consists of the following rules:
32.88/16.50	
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.50	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.50	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bf)), bf, bf)
32.88/16.50	
32.88/16.50	The TRS R consists of the following rules:
32.88/16.50	
32.88/16.50	   new_show2(ww17) -> error([])
32.88/16.50	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_show6(ww17, be) -> error([])
32.88/16.50	   new_show(ww17, bg, bh) -> error([])
32.88/16.50	   new_show7(ww17) -> error([])
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.50	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.50	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_show1(ww17) -> error([])
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.50	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.50	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.50	   new_show3(ww17, ba) -> error([])
32.88/16.50	   new_show8(ww17) -> error([])
32.88/16.50	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.50	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.50	   new_primModNatS4(ww122) -> Zero
32.88/16.50	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.50	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.50	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.50	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.50	   new_show0(ww17) -> error([])
32.88/16.50	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.50	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.50	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.50	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.50	   new_show9(ww17) -> error([])
32.88/16.50	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_show13(ww17) -> error([])
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.50	   new_psPs0([], ww56) -> ww56
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.50	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.50	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.50	   new_show5(ww17) -> error([])
32.88/16.50	   new_show12(ww17, ca) -> error([])
32.88/16.50	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.50	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.50	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.50	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.50	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.50	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.50	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.50	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.50	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.50	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.50	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.50	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.50	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.50	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.50	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.50	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.50	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.50	   new_show11(ww17) -> error([])
32.88/16.50	   new_show4(ww17, bc, bd) -> error([])
32.88/16.50	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.50	   new_show15(ww17) -> error([])
32.88/16.50	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.50	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.50	   new_primDivNatS4(ww126) -> Zero
32.88/16.50	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.50	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.50	
32.88/16.50	The set Q consists of the following terms:
32.88/16.50	
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.50	   new_primShowInt0(Neg(x0))
32.88/16.50	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.50	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.50	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.50	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.50	   new_primModNatS3(Succ(x0), Zero)
32.88/16.50	   new_show0(x0)
32.88/16.50	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.50	   new_showsPrec(x0, x1, ty_Double)
32.88/16.50	   new_showsPrec(x0, x1, ty_Float)
32.88/16.50	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.50	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.50	   new_showsPrec(x0, x1, ty_@0)
32.88/16.50	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.50	   new_show9(x0)
32.88/16.50	   new_primModNatS02(x0, x1)
32.88/16.50	   new_show15(x0)
32.88/16.50	   new_show3(x0, x1)
32.88/16.50	   new_show8(x0)
32.88/16.50	   new_show11(x0)
32.88/16.50	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.50	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.50	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.50	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.50	   new_show(x0, x1, x2)
32.88/16.50	   new_show10(x0)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.50	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.50	   new_psPs0(:(x0, x1), x2)
32.88/16.50	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.50	   new_primModNatS4(x0)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.50	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.50	   new_show1(x0)
32.88/16.50	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.50	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.50	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.50	   new_show6(x0, x1)
32.88/16.50	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.50	   new_show13(x0)
32.88/16.50	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.50	   new_primModNatS3(Zero, Zero)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.50	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.50	   new_div(x0, x1)
32.88/16.50	   new_primIntToChar(x0, x1)
32.88/16.50	   new_show14(x0, x1, x2, x3)
32.88/16.50	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.50	   new_primModNatS3(Zero, Succ(x0))
32.88/16.50	   new_showsPrec(x0, x1, ty_Int)
32.88/16.50	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.50	   new_show5(x0)
32.88/16.50	   new_primShowInt0(Pos(Zero))
32.88/16.50	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.50	   new_primDivNatS02(x0, x1)
32.88/16.50	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.50	   new_show12(x0, x1)
32.88/16.50	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.50	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.50	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.50	   new_primModNatS2(Zero, Zero, x0)
32.88/16.50	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.51	   new_psPs0([], x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.51	   new_show2(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.51	   new_show7(x0)
32.88/16.51	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.51	   new_show4(x0, x1, x2)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.51	   new_showsPrec(x0, x1, ty_Char)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.51	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.51	   new_primDivNatS4(x0)
32.88/16.51	   new_primDivNatS3(Zero, Zero)
32.88/16.51	
32.88/16.51	We have to consider all minimal (P,Q,R)-chains.
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(26) TransformationProof (EQUIVALENT)
32.88/16.51	By rewriting [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bf)), bf, bf) at position [5] we obtained the following new rules [LPAR04]:
32.88/16.51	
32.88/16.51	   (new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), new_psPs0(:(Char(Succ(ww19)), :(Char(Succ(ww20)), [])), new_showsPrec(ww21, ww22, bf))), bf, bf),new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), new_psPs0(:(Char(Succ(ww19)), :(Char(Succ(ww20)), [])), new_showsPrec(ww21, ww22, bf))), bf, bf))
32.88/16.51	
32.88/16.51	
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(27)
32.88/16.51	Obligation:
32.88/16.51	Q DP problem:
32.88/16.51	The TRS P consists of the following rules:
32.88/16.51	
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), new_psPs0(:(Char(Succ(ww19)), :(Char(Succ(ww20)), [])), new_showsPrec(ww21, ww22, bf))), bf, bf)
32.88/16.51	
32.88/16.51	The TRS R consists of the following rules:
32.88/16.51	
32.88/16.51	   new_show2(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show6(ww17, be) -> error([])
32.88/16.51	   new_show(ww17, bg, bh) -> error([])
32.88/16.51	   new_show7(ww17) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.51	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show1(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.51	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.51	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_show3(ww17, ba) -> error([])
32.88/16.51	   new_show8(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.51	   new_primModNatS4(ww122) -> Zero
32.88/16.51	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.51	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.51	   new_show0(ww17) -> error([])
32.88/16.51	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.51	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.51	   new_show9(ww17) -> error([])
32.88/16.51	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show13(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.51	   new_psPs0([], ww56) -> ww56
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.51	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.51	   new_show5(ww17) -> error([])
32.88/16.51	   new_show12(ww17, ca) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.51	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.51	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.51	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.51	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.51	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.51	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.51	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.51	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_show11(ww17) -> error([])
32.88/16.51	   new_show4(ww17, bc, bd) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.51	   new_show15(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.51	   new_primDivNatS4(ww126) -> Zero
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.51	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.51	
32.88/16.51	The set Q consists of the following terms:
32.88/16.51	
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.51	   new_primShowInt0(Neg(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.51	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.51	   new_primModNatS3(Succ(x0), Zero)
32.88/16.51	   new_show0(x0)
32.88/16.51	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Double)
32.88/16.51	   new_showsPrec(x0, x1, ty_Float)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_@0)
32.88/16.51	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.51	   new_show9(x0)
32.88/16.51	   new_primModNatS02(x0, x1)
32.88/16.51	   new_show15(x0)
32.88/16.51	   new_show3(x0, x1)
32.88/16.51	   new_show8(x0)
32.88/16.51	   new_show11(x0)
32.88/16.51	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.51	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.51	   new_show(x0, x1, x2)
32.88/16.51	   new_show10(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.51	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.51	   new_psPs0(:(x0, x1), x2)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_primModNatS4(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.51	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_show1(x0)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.51	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.51	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_show6(x0, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.51	   new_show13(x0)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.51	   new_primModNatS3(Zero, Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.51	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.51	   new_div(x0, x1)
32.88/16.51	   new_primIntToChar(x0, x1)
32.88/16.51	   new_show14(x0, x1, x2, x3)
32.88/16.51	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.51	   new_primModNatS3(Zero, Succ(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_Int)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.51	   new_show5(x0)
32.88/16.51	   new_primShowInt0(Pos(Zero))
32.88/16.51	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.51	   new_primDivNatS02(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_show12(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.51	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_primModNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.51	   new_psPs0([], x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.51	   new_show2(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.51	   new_show7(x0)
32.88/16.51	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.51	   new_show4(x0, x1, x2)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.51	   new_showsPrec(x0, x1, ty_Char)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.51	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.51	   new_primDivNatS4(x0)
32.88/16.51	   new_primDivNatS3(Zero, Zero)
32.88/16.51	
32.88/16.51	We have to consider all minimal (P,Q,R)-chains.
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(28) TransformationProof (EQUIVALENT)
32.88/16.51	By rewriting [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), new_psPs0(:(Char(Succ(ww19)), :(Char(Succ(ww20)), [])), new_showsPrec(ww21, ww22, bf))), bf, bf) at position [5,1] we obtained the following new rules [LPAR04]:
32.88/16.51	
32.88/16.51	   (new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), new_psPs0(:(Char(Succ(ww20)), []), new_showsPrec(ww21, ww22, bf)))), bf, bf),new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), new_psPs0(:(Char(Succ(ww20)), []), new_showsPrec(ww21, ww22, bf)))), bf, bf))
32.88/16.51	
32.88/16.51	
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(29)
32.88/16.51	Obligation:
32.88/16.51	Q DP problem:
32.88/16.51	The TRS P consists of the following rules:
32.88/16.51	
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), new_psPs0(:(Char(Succ(ww20)), []), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.51	
32.88/16.51	The TRS R consists of the following rules:
32.88/16.51	
32.88/16.51	   new_show2(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show6(ww17, be) -> error([])
32.88/16.51	   new_show(ww17, bg, bh) -> error([])
32.88/16.51	   new_show7(ww17) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.51	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show1(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.51	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.51	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_show3(ww17, ba) -> error([])
32.88/16.51	   new_show8(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.51	   new_primModNatS4(ww122) -> Zero
32.88/16.51	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.51	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.51	   new_show0(ww17) -> error([])
32.88/16.51	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.51	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.51	   new_show9(ww17) -> error([])
32.88/16.51	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show13(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.51	   new_psPs0([], ww56) -> ww56
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.51	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.51	   new_show5(ww17) -> error([])
32.88/16.51	   new_show12(ww17, ca) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.51	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.51	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.51	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.51	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.51	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.51	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.51	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.51	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_show11(ww17) -> error([])
32.88/16.51	   new_show4(ww17, bc, bd) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.51	   new_show15(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.51	   new_primDivNatS4(ww126) -> Zero
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.51	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.51	
32.88/16.51	The set Q consists of the following terms:
32.88/16.51	
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.51	   new_primShowInt0(Neg(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.51	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.51	   new_primModNatS3(Succ(x0), Zero)
32.88/16.51	   new_show0(x0)
32.88/16.51	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Double)
32.88/16.51	   new_showsPrec(x0, x1, ty_Float)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_@0)
32.88/16.51	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.51	   new_show9(x0)
32.88/16.51	   new_primModNatS02(x0, x1)
32.88/16.51	   new_show15(x0)
32.88/16.51	   new_show3(x0, x1)
32.88/16.51	   new_show8(x0)
32.88/16.51	   new_show11(x0)
32.88/16.51	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.51	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.51	   new_show(x0, x1, x2)
32.88/16.51	   new_show10(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.51	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.51	   new_psPs0(:(x0, x1), x2)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_primModNatS4(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.51	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_show1(x0)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.51	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.51	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_show6(x0, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.51	   new_show13(x0)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.51	   new_primModNatS3(Zero, Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.51	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.51	   new_div(x0, x1)
32.88/16.51	   new_primIntToChar(x0, x1)
32.88/16.51	   new_show14(x0, x1, x2, x3)
32.88/16.51	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.51	   new_primModNatS3(Zero, Succ(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_Int)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.51	   new_show5(x0)
32.88/16.51	   new_primShowInt0(Pos(Zero))
32.88/16.51	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.51	   new_primDivNatS02(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_show12(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.51	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_primModNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.51	   new_psPs0([], x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.51	   new_show2(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.51	   new_show7(x0)
32.88/16.51	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.51	   new_show4(x0, x1, x2)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.51	   new_showsPrec(x0, x1, ty_Char)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.51	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.51	   new_primDivNatS4(x0)
32.88/16.51	   new_primDivNatS3(Zero, Zero)
32.88/16.51	
32.88/16.51	We have to consider all minimal (P,Q,R)-chains.
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(30) TransformationProof (EQUIVALENT)
32.88/16.51	By rewriting [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), new_psPs0(:(Char(Succ(ww20)), []), new_showsPrec(ww21, ww22, bf)))), bf, bf) at position [5,1,1] we obtained the following new rules [LPAR04]:
32.88/16.51	
32.88/16.51	   (new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_psPs0([], new_showsPrec(ww21, ww22, bf))))), bf, bf),new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_psPs0([], new_showsPrec(ww21, ww22, bf))))), bf, bf))
32.88/16.51	
32.88/16.51	
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(31)
32.88/16.51	Obligation:
32.88/16.51	Q DP problem:
32.88/16.51	The TRS P consists of the following rules:
32.88/16.51	
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_psPs0([], new_showsPrec(ww21, ww22, bf))))), bf, bf)
32.88/16.51	
32.88/16.51	The TRS R consists of the following rules:
32.88/16.51	
32.88/16.51	   new_show2(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show6(ww17, be) -> error([])
32.88/16.51	   new_show(ww17, bg, bh) -> error([])
32.88/16.51	   new_show7(ww17) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.51	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show1(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.51	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.51	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_show3(ww17, ba) -> error([])
32.88/16.51	   new_show8(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.51	   new_primModNatS4(ww122) -> Zero
32.88/16.51	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.51	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.51	   new_show0(ww17) -> error([])
32.88/16.51	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.51	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.51	   new_show9(ww17) -> error([])
32.88/16.51	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show13(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.51	   new_psPs0([], ww56) -> ww56
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.51	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.51	   new_show5(ww17) -> error([])
32.88/16.51	   new_show12(ww17, ca) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.51	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.51	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.51	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.51	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.51	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.51	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.51	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.51	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_show11(ww17) -> error([])
32.88/16.51	   new_show4(ww17, bc, bd) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.51	   new_show15(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.51	   new_primDivNatS4(ww126) -> Zero
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.51	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.51	
32.88/16.51	The set Q consists of the following terms:
32.88/16.51	
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.51	   new_primShowInt0(Neg(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.51	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.51	   new_primModNatS3(Succ(x0), Zero)
32.88/16.51	   new_show0(x0)
32.88/16.51	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Double)
32.88/16.51	   new_showsPrec(x0, x1, ty_Float)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_@0)
32.88/16.51	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.51	   new_show9(x0)
32.88/16.51	   new_primModNatS02(x0, x1)
32.88/16.51	   new_show15(x0)
32.88/16.51	   new_show3(x0, x1)
32.88/16.51	   new_show8(x0)
32.88/16.51	   new_show11(x0)
32.88/16.51	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.51	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.51	   new_show(x0, x1, x2)
32.88/16.51	   new_show10(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.51	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.51	   new_psPs0(:(x0, x1), x2)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_primModNatS4(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.51	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_show1(x0)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.51	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.51	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_show6(x0, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.51	   new_show13(x0)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.51	   new_primModNatS3(Zero, Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.51	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.51	   new_div(x0, x1)
32.88/16.51	   new_primIntToChar(x0, x1)
32.88/16.51	   new_show14(x0, x1, x2, x3)
32.88/16.51	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.51	   new_primModNatS3(Zero, Succ(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_Int)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.51	   new_show5(x0)
32.88/16.51	   new_primShowInt0(Pos(Zero))
32.88/16.51	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.51	   new_primDivNatS02(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_show12(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.51	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_primModNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.51	   new_psPs0([], x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.51	   new_show2(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.51	   new_show7(x0)
32.88/16.51	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.51	   new_show4(x0, x1, x2)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.51	   new_showsPrec(x0, x1, ty_Char)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.51	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.51	   new_primDivNatS4(x0)
32.88/16.51	   new_primDivNatS3(Zero, Zero)
32.88/16.51	
32.88/16.51	We have to consider all minimal (P,Q,R)-chains.
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(32) TransformationProof (EQUIVALENT)
32.88/16.51	By rewriting [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_psPs0([], new_showsPrec(ww21, ww22, bf))))), bf, bf) at position [5,1,1,1] we obtained the following new rules [LPAR04]:
32.88/16.51	
32.88/16.51	   (new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf),new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf))
32.88/16.51	
32.88/16.51	
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(33)
32.88/16.51	Obligation:
32.88/16.51	Q DP problem:
32.88/16.51	The TRS P consists of the following rules:
32.88/16.51	
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.51	
32.88/16.51	The TRS R consists of the following rules:
32.88/16.51	
32.88/16.51	   new_show2(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show6(ww17, be) -> error([])
32.88/16.51	   new_show(ww17, bg, bh) -> error([])
32.88/16.51	   new_show7(ww17) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.51	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show1(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.51	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.51	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_show3(ww17, ba) -> error([])
32.88/16.51	   new_show8(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.51	   new_primModNatS4(ww122) -> Zero
32.88/16.51	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.51	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.51	   new_show0(ww17) -> error([])
32.88/16.51	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.51	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.51	   new_show9(ww17) -> error([])
32.88/16.51	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show13(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.51	   new_psPs0([], ww56) -> ww56
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.51	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.51	   new_show5(ww17) -> error([])
32.88/16.51	   new_show12(ww17, ca) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.51	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.51	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.51	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.51	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.51	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.51	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.51	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.51	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_show11(ww17) -> error([])
32.88/16.51	   new_show4(ww17, bc, bd) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.51	   new_show15(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.51	   new_primDivNatS4(ww126) -> Zero
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.51	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.51	
32.88/16.51	The set Q consists of the following terms:
32.88/16.51	
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.51	   new_primShowInt0(Neg(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.51	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.51	   new_primModNatS3(Succ(x0), Zero)
32.88/16.51	   new_show0(x0)
32.88/16.51	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Double)
32.88/16.51	   new_showsPrec(x0, x1, ty_Float)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_@0)
32.88/16.51	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.51	   new_show9(x0)
32.88/16.51	   new_primModNatS02(x0, x1)
32.88/16.51	   new_show15(x0)
32.88/16.51	   new_show3(x0, x1)
32.88/16.51	   new_show8(x0)
32.88/16.51	   new_show11(x0)
32.88/16.51	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.51	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.51	   new_show(x0, x1, x2)
32.88/16.51	   new_show10(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.51	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.51	   new_psPs0(:(x0, x1), x2)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_primModNatS4(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.51	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_show1(x0)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.51	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.51	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_show6(x0, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.51	   new_show13(x0)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.51	   new_primModNatS3(Zero, Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.51	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.51	   new_div(x0, x1)
32.88/16.51	   new_primIntToChar(x0, x1)
32.88/16.51	   new_show14(x0, x1, x2, x3)
32.88/16.51	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.51	   new_primModNatS3(Zero, Succ(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_Int)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.51	   new_show5(x0)
32.88/16.51	   new_primShowInt0(Pos(Zero))
32.88/16.51	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.51	   new_primDivNatS02(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_show12(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.51	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_primModNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.51	   new_psPs0([], x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.51	   new_show2(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.51	   new_show7(x0)
32.88/16.51	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.51	   new_show4(x0, x1, x2)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.51	   new_showsPrec(x0, x1, ty_Char)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.51	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.51	   new_primDivNatS4(x0)
32.88/16.51	   new_primDivNatS3(Zero, Zero)
32.88/16.51	
32.88/16.51	We have to consider all minimal (P,Q,R)-chains.
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(34) TransformationProof (EQUIVALENT)
32.88/16.51	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.51	
32.88/16.51	   (new_showParen(z5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, ty_IOError),new_showParen(z5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, ty_IOError))
32.88/16.51	   (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))
32.88/16.51	
32.88/16.51	
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(35)
32.88/16.51	Obligation:
32.88/16.51	Q DP problem:
32.88/16.51	The TRS P consists of the following rules:
32.88/16.51	
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.51	   new_showParen(z5, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, ty_IOError, ty_IOError) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z6, z7, ty_IOError)
32.88/16.51	   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)
32.88/16.51	
32.88/16.51	The TRS R consists of the following rules:
32.88/16.51	
32.88/16.51	   new_show2(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show6(ww17, be) -> error([])
32.88/16.51	   new_show(ww17, bg, bh) -> error([])
32.88/16.51	   new_show7(ww17) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.51	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show1(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.51	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.51	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_show3(ww17, ba) -> error([])
32.88/16.51	   new_show8(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.51	   new_primModNatS4(ww122) -> Zero
32.88/16.51	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.51	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.51	   new_show0(ww17) -> error([])
32.88/16.51	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.51	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.51	   new_show9(ww17) -> error([])
32.88/16.51	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show13(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.51	   new_psPs0([], ww56) -> ww56
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.51	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.51	   new_show5(ww17) -> error([])
32.88/16.51	   new_show12(ww17, ca) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.51	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.51	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.51	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.51	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.51	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.51	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.51	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.51	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_show11(ww17) -> error([])
32.88/16.51	   new_show4(ww17, bc, bd) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.51	   new_show15(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.51	   new_primDivNatS4(ww126) -> Zero
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.51	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.51	
32.88/16.51	The set Q consists of the following terms:
32.88/16.51	
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.51	   new_primShowInt0(Neg(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.51	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.51	   new_primModNatS3(Succ(x0), Zero)
32.88/16.51	   new_show0(x0)
32.88/16.51	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Double)
32.88/16.51	   new_showsPrec(x0, x1, ty_Float)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_@0)
32.88/16.51	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.51	   new_show9(x0)
32.88/16.51	   new_primModNatS02(x0, x1)
32.88/16.51	   new_show15(x0)
32.88/16.51	   new_show3(x0, x1)
32.88/16.51	   new_show8(x0)
32.88/16.51	   new_show11(x0)
32.88/16.51	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.51	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.51	   new_show(x0, x1, x2)
32.88/16.51	   new_show10(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.51	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.51	   new_psPs0(:(x0, x1), x2)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_primModNatS4(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.51	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_show1(x0)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.51	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.51	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_show6(x0, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.51	   new_show13(x0)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.51	   new_primModNatS3(Zero, Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.51	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.51	   new_div(x0, x1)
32.88/16.51	   new_primIntToChar(x0, x1)
32.88/16.51	   new_show14(x0, x1, x2, x3)
32.88/16.51	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.51	   new_primModNatS3(Zero, Succ(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_Int)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.51	   new_show5(x0)
32.88/16.51	   new_primShowInt0(Pos(Zero))
32.88/16.51	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.51	   new_primDivNatS02(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_show12(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.51	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_primModNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.51	   new_psPs0([], x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.51	   new_show2(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.51	   new_show7(x0)
32.88/16.51	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.51	   new_show4(x0, x1, x2)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.51	   new_showsPrec(x0, x1, ty_Char)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.51	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.51	   new_primDivNatS4(x0)
32.88/16.51	   new_primDivNatS3(Zero, Zero)
32.88/16.51	
32.88/16.51	We have to consider all minimal (P,Q,R)-chains.
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(36) DependencyGraphProof (EQUIVALENT)
32.88/16.51	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(37)
32.88/16.51	Obligation:
32.88/16.51	Q DP problem:
32.88/16.51	The TRS P consists of the following rules:
32.88/16.51	
32.88/16.51	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.51	
32.88/16.51	The TRS R consists of the following rules:
32.88/16.51	
32.88/16.51	   new_show2(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show6(ww17, be) -> error([])
32.88/16.51	   new_show(ww17, bg, bh) -> error([])
32.88/16.51	   new_show7(ww17) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.51	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show1(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.51	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.51	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_show3(ww17, ba) -> error([])
32.88/16.51	   new_show8(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.51	   new_primModNatS4(ww122) -> Zero
32.88/16.51	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.51	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.51	   new_show0(ww17) -> error([])
32.88/16.51	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.51	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.51	   new_show9(ww17) -> error([])
32.88/16.51	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show13(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.51	   new_psPs0([], ww56) -> ww56
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.51	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.51	   new_show5(ww17) -> error([])
32.88/16.51	   new_show12(ww17, ca) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.51	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.51	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.51	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.51	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.51	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.51	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.51	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.51	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_show11(ww17) -> error([])
32.88/16.51	   new_show4(ww17, bc, bd) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.51	   new_show15(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.51	   new_primDivNatS4(ww126) -> Zero
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.51	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.51	
32.88/16.51	The set Q consists of the following terms:
32.88/16.51	
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.51	   new_primShowInt0(Neg(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.51	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.51	   new_primModNatS3(Succ(x0), Zero)
32.88/16.51	   new_show0(x0)
32.88/16.51	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Double)
32.88/16.51	   new_showsPrec(x0, x1, ty_Float)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_@0)
32.88/16.51	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.51	   new_show9(x0)
32.88/16.51	   new_primModNatS02(x0, x1)
32.88/16.51	   new_show15(x0)
32.88/16.51	   new_show3(x0, x1)
32.88/16.51	   new_show8(x0)
32.88/16.51	   new_show11(x0)
32.88/16.51	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.51	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.51	   new_show(x0, x1, x2)
32.88/16.51	   new_show10(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.51	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.51	   new_psPs0(:(x0, x1), x2)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_primModNatS4(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.51	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_show1(x0)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.51	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.51	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_show6(x0, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.51	   new_show13(x0)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.51	   new_primModNatS3(Zero, Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.51	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.51	   new_div(x0, x1)
32.88/16.51	   new_primIntToChar(x0, x1)
32.88/16.51	   new_show14(x0, x1, x2, x3)
32.88/16.51	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.51	   new_primModNatS3(Zero, Succ(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_Int)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.51	   new_show5(x0)
32.88/16.51	   new_primShowInt0(Pos(Zero))
32.88/16.51	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.51	   new_primDivNatS02(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_show12(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.51	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_primModNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.51	   new_psPs0([], x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.51	   new_show2(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.51	   new_show7(x0)
32.88/16.51	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.51	   new_show4(x0, x1, x2)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.51	   new_showsPrec(x0, x1, ty_Char)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.51	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.51	   new_primDivNatS4(x0)
32.88/16.51	   new_primDivNatS3(Zero, Zero)
32.88/16.51	
32.88/16.51	We have to consider all minimal (P,Q,R)-chains.
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(38) TransformationProof (EQUIVALENT)
32.88/16.51	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.51	
32.88/16.51	   (new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6)),new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6)))
32.88/16.51	   (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)))
32.88/16.51	
32.88/16.51	
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(39)
32.88/16.51	Obligation:
32.88/16.51	Q DP problem:
32.88/16.51	The TRS P consists of the following rules:
32.88/16.51	
32.88/16.51	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.51	   new_showParen(z3, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6), app(ty_IO, x6)) -> new_pt(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), z4, z5, app(ty_IO, x6))
32.88/16.51	   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))
32.88/16.51	
32.88/16.51	The TRS R consists of the following rules:
32.88/16.51	
32.88/16.51	   new_show2(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show6(ww17, be) -> error([])
32.88/16.51	   new_show(ww17, bg, bh) -> error([])
32.88/16.51	   new_show7(ww17) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.51	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show1(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.51	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.51	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_show3(ww17, ba) -> error([])
32.88/16.51	   new_show8(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.51	   new_primModNatS4(ww122) -> Zero
32.88/16.51	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.51	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.51	   new_show0(ww17) -> error([])
32.88/16.51	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.51	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.51	   new_show9(ww17) -> error([])
32.88/16.51	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show13(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.51	   new_psPs0([], ww56) -> ww56
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.51	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.51	   new_show5(ww17) -> error([])
32.88/16.51	   new_show12(ww17, ca) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.51	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.51	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.51	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.51	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.51	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.51	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.51	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.51	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_show11(ww17) -> error([])
32.88/16.51	   new_show4(ww17, bc, bd) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.51	   new_show15(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.51	   new_primDivNatS4(ww126) -> Zero
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.51	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.51	
32.88/16.51	The set Q consists of the following terms:
32.88/16.51	
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.51	   new_primShowInt0(Neg(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.51	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.51	   new_primModNatS3(Succ(x0), Zero)
32.88/16.51	   new_show0(x0)
32.88/16.51	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Double)
32.88/16.51	   new_showsPrec(x0, x1, ty_Float)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_@0)
32.88/16.51	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.51	   new_show9(x0)
32.88/16.51	   new_primModNatS02(x0, x1)
32.88/16.51	   new_show15(x0)
32.88/16.51	   new_show3(x0, x1)
32.88/16.51	   new_show8(x0)
32.88/16.51	   new_show11(x0)
32.88/16.51	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.51	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.51	   new_show(x0, x1, x2)
32.88/16.51	   new_show10(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.51	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.51	   new_psPs0(:(x0, x1), x2)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_primModNatS4(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.51	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_show1(x0)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.51	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.51	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_show6(x0, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.51	   new_show13(x0)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.51	   new_primModNatS3(Zero, Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.51	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.51	   new_div(x0, x1)
32.88/16.51	   new_primIntToChar(x0, x1)
32.88/16.51	   new_show14(x0, x1, x2, x3)
32.88/16.51	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.51	   new_primModNatS3(Zero, Succ(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_Int)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.51	   new_show5(x0)
32.88/16.51	   new_primShowInt0(Pos(Zero))
32.88/16.51	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.51	   new_primDivNatS02(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_show12(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.51	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_primModNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.51	   new_psPs0([], x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.51	   new_show2(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.51	   new_show7(x0)
32.88/16.51	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.51	   new_show4(x0, x1, x2)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.51	   new_showsPrec(x0, x1, ty_Char)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.51	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.51	   new_primDivNatS4(x0)
32.88/16.51	   new_primDivNatS3(Zero, Zero)
32.88/16.51	
32.88/16.51	We have to consider all minimal (P,Q,R)-chains.
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(40) DependencyGraphProof (EQUIVALENT)
32.88/16.51	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(41)
32.88/16.51	Obligation:
32.88/16.51	Q DP problem:
32.88/16.51	The TRS P consists of the following rules:
32.88/16.51	
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.51	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.51	
32.88/16.51	The TRS R consists of the following rules:
32.88/16.51	
32.88/16.51	   new_show2(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show6(ww17, be) -> error([])
32.88/16.51	   new_show(ww17, bg, bh) -> error([])
32.88/16.51	   new_show7(ww17) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.51	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show1(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.51	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.51	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.51	   new_show3(ww17, ba) -> error([])
32.88/16.51	   new_show8(ww17) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.51	   new_primModNatS4(ww122) -> Zero
32.88/16.51	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.51	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.51	   new_show0(ww17) -> error([])
32.88/16.51	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.51	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.51	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.51	   new_show9(ww17) -> error([])
32.88/16.51	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show13(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.51	   new_psPs0([], ww56) -> ww56
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.51	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.51	   new_show5(ww17) -> error([])
32.88/16.51	   new_show12(ww17, ca) -> error([])
32.88/16.51	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.51	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.51	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.51	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.51	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.51	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.51	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.51	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.51	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.51	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.51	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.51	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.51	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.51	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.51	   new_show11(ww17) -> error([])
32.88/16.51	   new_show4(ww17, bc, bd) -> error([])
32.88/16.51	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.51	   new_show15(ww17) -> error([])
32.88/16.51	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.51	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.51	   new_primDivNatS4(ww126) -> Zero
32.88/16.51	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.51	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.51	
32.88/16.51	The set Q consists of the following terms:
32.88/16.51	
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.51	   new_primShowInt0(Neg(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.51	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.51	   new_primModNatS3(Succ(x0), Zero)
32.88/16.51	   new_show0(x0)
32.88/16.51	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Double)
32.88/16.51	   new_showsPrec(x0, x1, ty_Float)
32.88/16.51	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_@0)
32.88/16.51	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.51	   new_show9(x0)
32.88/16.51	   new_primModNatS02(x0, x1)
32.88/16.51	   new_show15(x0)
32.88/16.51	   new_show3(x0, x1)
32.88/16.51	   new_show8(x0)
32.88/16.51	   new_show11(x0)
32.88/16.51	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.51	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.51	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.51	   new_show(x0, x1, x2)
32.88/16.51	   new_show10(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.51	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.51	   new_psPs0(:(x0, x1), x2)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_primModNatS4(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.51	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.51	   new_show1(x0)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.51	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.51	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_show6(x0, x1)
32.88/16.51	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.51	   new_show13(x0)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.51	   new_primModNatS3(Zero, Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.51	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.51	   new_div(x0, x1)
32.88/16.51	   new_primIntToChar(x0, x1)
32.88/16.51	   new_show14(x0, x1, x2, x3)
32.88/16.51	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.51	   new_primModNatS3(Zero, Succ(x0))
32.88/16.51	   new_showsPrec(x0, x1, ty_Int)
32.88/16.51	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.51	   new_show5(x0)
32.88/16.51	   new_primShowInt0(Pos(Zero))
32.88/16.51	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.51	   new_primDivNatS02(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.51	   new_show12(x0, x1)
32.88/16.51	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.51	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.51	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.51	   new_primModNatS2(Zero, Zero, x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.51	   new_psPs0([], x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.51	   new_show2(x0)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.51	   new_show7(x0)
32.88/16.51	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.51	   new_show4(x0, x1, x2)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.51	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.51	   new_showsPrec(x0, x1, ty_Char)
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.51	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.51	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.51	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.51	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.51	   new_primDivNatS4(x0)
32.88/16.51	   new_primDivNatS3(Zero, Zero)
32.88/16.51	
32.88/16.51	We have to consider all minimal (P,Q,R)-chains.
32.88/16.51	----------------------------------------
32.88/16.51	
32.88/16.51	(42) TransformationProof (EQUIVALENT)
32.88/16.51	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.51	
32.88/16.51	   (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))
32.88/16.51	   (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))
32.88/16.52	
32.88/16.52	
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(43)
32.88/16.52	Obligation:
32.88/16.52	Q DP problem:
32.88/16.52	The TRS P consists of the following rules:
32.88/16.52	
32.88/16.52	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.52	   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)
32.88/16.52	   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)
32.88/16.52	
32.88/16.52	The TRS R consists of the following rules:
32.88/16.52	
32.88/16.52	   new_show2(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show6(ww17, be) -> error([])
32.88/16.52	   new_show(ww17, bg, bh) -> error([])
32.88/16.52	   new_show7(ww17) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.52	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show1(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.52	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.52	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_show3(ww17, ba) -> error([])
32.88/16.52	   new_show8(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.52	   new_primModNatS4(ww122) -> Zero
32.88/16.52	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.52	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.52	   new_show0(ww17) -> error([])
32.88/16.52	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.52	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.52	   new_show9(ww17) -> error([])
32.88/16.52	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show13(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.52	   new_psPs0([], ww56) -> ww56
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.52	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.52	   new_show5(ww17) -> error([])
32.88/16.52	   new_show12(ww17, ca) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.52	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.52	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.52	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.52	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.52	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.52	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.52	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.52	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_show11(ww17) -> error([])
32.88/16.52	   new_show4(ww17, bc, bd) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.52	   new_show15(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.52	   new_primDivNatS4(ww126) -> Zero
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.52	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.52	
32.88/16.52	The set Q consists of the following terms:
32.88/16.52	
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.52	   new_primShowInt0(Neg(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.52	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.52	   new_primModNatS3(Succ(x0), Zero)
32.88/16.52	   new_show0(x0)
32.88/16.52	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Double)
32.88/16.52	   new_showsPrec(x0, x1, ty_Float)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_@0)
32.88/16.52	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.52	   new_show9(x0)
32.88/16.52	   new_primModNatS02(x0, x1)
32.88/16.52	   new_show15(x0)
32.88/16.52	   new_show3(x0, x1)
32.88/16.52	   new_show8(x0)
32.88/16.52	   new_show11(x0)
32.88/16.52	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.52	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.52	   new_show(x0, x1, x2)
32.88/16.52	   new_show10(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.52	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.52	   new_psPs0(:(x0, x1), x2)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_primModNatS4(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.52	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_show1(x0)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.52	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.52	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_show6(x0, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.52	   new_show13(x0)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.52	   new_primModNatS3(Zero, Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.52	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.52	   new_div(x0, x1)
32.88/16.52	   new_primIntToChar(x0, x1)
32.88/16.52	   new_show14(x0, x1, x2, x3)
32.88/16.52	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.52	   new_primModNatS3(Zero, Succ(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_Int)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.52	   new_show5(x0)
32.88/16.52	   new_primShowInt0(Pos(Zero))
32.88/16.52	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.52	   new_primDivNatS02(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_show12(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.52	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_primModNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.52	   new_psPs0([], x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.52	   new_show2(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.52	   new_show7(x0)
32.88/16.52	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.52	   new_show4(x0, x1, x2)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.52	   new_showsPrec(x0, x1, ty_Char)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.52	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.52	   new_primDivNatS4(x0)
32.88/16.52	   new_primDivNatS3(Zero, Zero)
32.88/16.52	
32.88/16.52	We have to consider all minimal (P,Q,R)-chains.
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(44) DependencyGraphProof (EQUIVALENT)
32.88/16.52	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(45)
32.88/16.52	Obligation:
32.88/16.52	Q DP problem:
32.88/16.52	The TRS P consists of the following rules:
32.88/16.52	
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.52	
32.88/16.52	The TRS R consists of the following rules:
32.88/16.52	
32.88/16.52	   new_show2(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show6(ww17, be) -> error([])
32.88/16.52	   new_show(ww17, bg, bh) -> error([])
32.88/16.52	   new_show7(ww17) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.52	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show1(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.52	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.52	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_show3(ww17, ba) -> error([])
32.88/16.52	   new_show8(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.52	   new_primModNatS4(ww122) -> Zero
32.88/16.52	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.52	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.52	   new_show0(ww17) -> error([])
32.88/16.52	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.52	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.52	   new_show9(ww17) -> error([])
32.88/16.52	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show13(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.52	   new_psPs0([], ww56) -> ww56
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.52	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.52	   new_show5(ww17) -> error([])
32.88/16.52	   new_show12(ww17, ca) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.52	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.52	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.52	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.52	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.52	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.52	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.52	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.52	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_show11(ww17) -> error([])
32.88/16.52	   new_show4(ww17, bc, bd) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.52	   new_show15(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.52	   new_primDivNatS4(ww126) -> Zero
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.52	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.52	
32.88/16.52	The set Q consists of the following terms:
32.88/16.52	
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.52	   new_primShowInt0(Neg(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.52	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.52	   new_primModNatS3(Succ(x0), Zero)
32.88/16.52	   new_show0(x0)
32.88/16.52	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Double)
32.88/16.52	   new_showsPrec(x0, x1, ty_Float)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_@0)
32.88/16.52	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.52	   new_show9(x0)
32.88/16.52	   new_primModNatS02(x0, x1)
32.88/16.52	   new_show15(x0)
32.88/16.52	   new_show3(x0, x1)
32.88/16.52	   new_show8(x0)
32.88/16.52	   new_show11(x0)
32.88/16.52	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.52	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.52	   new_show(x0, x1, x2)
32.88/16.52	   new_show10(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.52	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.52	   new_psPs0(:(x0, x1), x2)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_primModNatS4(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.52	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_show1(x0)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.52	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.52	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_show6(x0, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.52	   new_show13(x0)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.52	   new_primModNatS3(Zero, Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.52	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.52	   new_div(x0, x1)
32.88/16.52	   new_primIntToChar(x0, x1)
32.88/16.52	   new_show14(x0, x1, x2, x3)
32.88/16.52	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.52	   new_primModNatS3(Zero, Succ(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_Int)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.52	   new_show5(x0)
32.88/16.52	   new_primShowInt0(Pos(Zero))
32.88/16.52	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.52	   new_primDivNatS02(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_show12(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.52	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_primModNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.52	   new_psPs0([], x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.52	   new_show2(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.52	   new_show7(x0)
32.88/16.52	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.52	   new_show4(x0, x1, x2)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.52	   new_showsPrec(x0, x1, ty_Char)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.52	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.52	   new_primDivNatS4(x0)
32.88/16.52	   new_primDivNatS3(Zero, Zero)
32.88/16.52	
32.88/16.52	We have to consider all minimal (P,Q,R)-chains.
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(46) TransformationProof (EQUIVALENT)
32.88/16.52	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.52	
32.88/16.52	   (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))
32.88/16.52	   (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))
32.88/16.52	
32.88/16.52	
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(47)
32.88/16.52	Obligation:
32.88/16.52	Q DP problem:
32.88/16.52	The TRS P consists of the following rules:
32.88/16.52	
32.88/16.52	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.52	   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)
32.88/16.52	   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)
32.88/16.52	
32.88/16.52	The TRS R consists of the following rules:
32.88/16.52	
32.88/16.52	   new_show2(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show6(ww17, be) -> error([])
32.88/16.52	   new_show(ww17, bg, bh) -> error([])
32.88/16.52	   new_show7(ww17) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.52	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show1(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.52	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.52	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_show3(ww17, ba) -> error([])
32.88/16.52	   new_show8(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.52	   new_primModNatS4(ww122) -> Zero
32.88/16.52	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.52	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.52	   new_show0(ww17) -> error([])
32.88/16.52	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.52	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.52	   new_show9(ww17) -> error([])
32.88/16.52	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show13(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.52	   new_psPs0([], ww56) -> ww56
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.52	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.52	   new_show5(ww17) -> error([])
32.88/16.52	   new_show12(ww17, ca) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.52	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.52	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.52	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.52	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.52	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.52	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.52	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.52	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_show11(ww17) -> error([])
32.88/16.52	   new_show4(ww17, bc, bd) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.52	   new_show15(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.52	   new_primDivNatS4(ww126) -> Zero
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.52	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.52	
32.88/16.52	The set Q consists of the following terms:
32.88/16.52	
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.52	   new_primShowInt0(Neg(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.52	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.52	   new_primModNatS3(Succ(x0), Zero)
32.88/16.52	   new_show0(x0)
32.88/16.52	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Double)
32.88/16.52	   new_showsPrec(x0, x1, ty_Float)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_@0)
32.88/16.52	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.52	   new_show9(x0)
32.88/16.52	   new_primModNatS02(x0, x1)
32.88/16.52	   new_show15(x0)
32.88/16.52	   new_show3(x0, x1)
32.88/16.52	   new_show8(x0)
32.88/16.52	   new_show11(x0)
32.88/16.52	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.52	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.52	   new_show(x0, x1, x2)
32.88/16.52	   new_show10(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.52	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.52	   new_psPs0(:(x0, x1), x2)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_primModNatS4(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.52	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_show1(x0)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.52	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.52	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_show6(x0, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.52	   new_show13(x0)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.52	   new_primModNatS3(Zero, Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.52	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.52	   new_div(x0, x1)
32.88/16.52	   new_primIntToChar(x0, x1)
32.88/16.52	   new_show14(x0, x1, x2, x3)
32.88/16.52	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.52	   new_primModNatS3(Zero, Succ(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_Int)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.52	   new_show5(x0)
32.88/16.52	   new_primShowInt0(Pos(Zero))
32.88/16.52	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.52	   new_primDivNatS02(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_show12(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.52	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_primModNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.52	   new_psPs0([], x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.52	   new_show2(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.52	   new_show7(x0)
32.88/16.52	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.52	   new_show4(x0, x1, x2)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.52	   new_showsPrec(x0, x1, ty_Char)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.52	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.52	   new_primDivNatS4(x0)
32.88/16.52	   new_primDivNatS3(Zero, Zero)
32.88/16.52	
32.88/16.52	We have to consider all minimal (P,Q,R)-chains.
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(48) DependencyGraphProof (EQUIVALENT)
32.88/16.52	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(49)
32.88/16.52	Obligation:
32.88/16.52	Q DP problem:
32.88/16.52	The TRS P consists of the following rules:
32.88/16.52	
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.52	
32.88/16.52	The TRS R consists of the following rules:
32.88/16.52	
32.88/16.52	   new_show2(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show6(ww17, be) -> error([])
32.88/16.52	   new_show(ww17, bg, bh) -> error([])
32.88/16.52	   new_show7(ww17) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.52	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show1(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.52	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.52	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_show3(ww17, ba) -> error([])
32.88/16.52	   new_show8(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.52	   new_primModNatS4(ww122) -> Zero
32.88/16.52	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.52	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.52	   new_show0(ww17) -> error([])
32.88/16.52	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.52	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.52	   new_show9(ww17) -> error([])
32.88/16.52	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show13(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.52	   new_psPs0([], ww56) -> ww56
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.52	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.52	   new_show5(ww17) -> error([])
32.88/16.52	   new_show12(ww17, ca) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.52	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.52	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.52	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.52	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.52	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.52	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.52	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.52	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_show11(ww17) -> error([])
32.88/16.52	   new_show4(ww17, bc, bd) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.52	   new_show15(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.52	   new_primDivNatS4(ww126) -> Zero
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.52	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.52	
32.88/16.52	The set Q consists of the following terms:
32.88/16.52	
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.52	   new_primShowInt0(Neg(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.52	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.52	   new_primModNatS3(Succ(x0), Zero)
32.88/16.52	   new_show0(x0)
32.88/16.52	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Double)
32.88/16.52	   new_showsPrec(x0, x1, ty_Float)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_@0)
32.88/16.52	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.52	   new_show9(x0)
32.88/16.52	   new_primModNatS02(x0, x1)
32.88/16.52	   new_show15(x0)
32.88/16.52	   new_show3(x0, x1)
32.88/16.52	   new_show8(x0)
32.88/16.52	   new_show11(x0)
32.88/16.52	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.52	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.52	   new_show(x0, x1, x2)
32.88/16.52	   new_show10(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.52	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.52	   new_psPs0(:(x0, x1), x2)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_primModNatS4(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.52	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_show1(x0)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.52	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.52	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_show6(x0, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.52	   new_show13(x0)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.52	   new_primModNatS3(Zero, Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.52	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.52	   new_div(x0, x1)
32.88/16.52	   new_primIntToChar(x0, x1)
32.88/16.52	   new_show14(x0, x1, x2, x3)
32.88/16.52	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.52	   new_primModNatS3(Zero, Succ(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_Int)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.52	   new_show5(x0)
32.88/16.52	   new_primShowInt0(Pos(Zero))
32.88/16.52	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.52	   new_primDivNatS02(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_show12(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.52	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_primModNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.52	   new_psPs0([], x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.52	   new_show2(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.52	   new_show7(x0)
32.88/16.52	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.52	   new_show4(x0, x1, x2)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.52	   new_showsPrec(x0, x1, ty_Char)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.52	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.52	   new_primDivNatS4(x0)
32.88/16.52	   new_primDivNatS3(Zero, Zero)
32.88/16.52	
32.88/16.52	We have to consider all minimal (P,Q,R)-chains.
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(50) TransformationProof (EQUIVALENT)
32.88/16.52	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.52	
32.88/16.52	   (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)))
32.88/16.52	   (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)))
32.88/16.52	
32.88/16.52	
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(51)
32.88/16.52	Obligation:
32.88/16.52	Q DP problem:
32.88/16.52	The TRS P consists of the following rules:
32.88/16.52	
32.88/16.52	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.52	   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))
32.88/16.52	   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))
32.88/16.52	
32.88/16.52	The TRS R consists of the following rules:
32.88/16.52	
32.88/16.52	   new_show2(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show6(ww17, be) -> error([])
32.88/16.52	   new_show(ww17, bg, bh) -> error([])
32.88/16.52	   new_show7(ww17) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.52	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show1(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.52	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.52	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_show3(ww17, ba) -> error([])
32.88/16.52	   new_show8(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.52	   new_primModNatS4(ww122) -> Zero
32.88/16.52	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.52	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.52	   new_show0(ww17) -> error([])
32.88/16.52	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.52	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.52	   new_show9(ww17) -> error([])
32.88/16.52	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show13(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.52	   new_psPs0([], ww56) -> ww56
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.52	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.52	   new_show5(ww17) -> error([])
32.88/16.52	   new_show12(ww17, ca) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.52	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.52	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.52	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.52	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.52	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.52	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.52	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.52	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_show11(ww17) -> error([])
32.88/16.52	   new_show4(ww17, bc, bd) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.52	   new_show15(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.52	   new_primDivNatS4(ww126) -> Zero
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.52	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.52	
32.88/16.52	The set Q consists of the following terms:
32.88/16.52	
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.52	   new_primShowInt0(Neg(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.52	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.52	   new_primModNatS3(Succ(x0), Zero)
32.88/16.52	   new_show0(x0)
32.88/16.52	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Double)
32.88/16.52	   new_showsPrec(x0, x1, ty_Float)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_@0)
32.88/16.52	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.52	   new_show9(x0)
32.88/16.52	   new_primModNatS02(x0, x1)
32.88/16.52	   new_show15(x0)
32.88/16.52	   new_show3(x0, x1)
32.88/16.52	   new_show8(x0)
32.88/16.52	   new_show11(x0)
32.88/16.52	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.52	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.52	   new_show(x0, x1, x2)
32.88/16.52	   new_show10(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.52	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.52	   new_psPs0(:(x0, x1), x2)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_primModNatS4(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.52	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_show1(x0)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.52	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.52	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_show6(x0, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.52	   new_show13(x0)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.52	   new_primModNatS3(Zero, Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.52	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.52	   new_div(x0, x1)
32.88/16.52	   new_primIntToChar(x0, x1)
32.88/16.52	   new_show14(x0, x1, x2, x3)
32.88/16.52	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.52	   new_primModNatS3(Zero, Succ(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_Int)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.52	   new_show5(x0)
32.88/16.52	   new_primShowInt0(Pos(Zero))
32.88/16.52	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.52	   new_primDivNatS02(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_show12(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.52	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_primModNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.52	   new_psPs0([], x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.52	   new_show2(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.52	   new_show7(x0)
32.88/16.52	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.52	   new_show4(x0, x1, x2)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.52	   new_showsPrec(x0, x1, ty_Char)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.52	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.52	   new_primDivNatS4(x0)
32.88/16.52	   new_primDivNatS3(Zero, Zero)
32.88/16.52	
32.88/16.52	We have to consider all minimal (P,Q,R)-chains.
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(52) DependencyGraphProof (EQUIVALENT)
32.88/16.52	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(53)
32.88/16.52	Obligation:
32.88/16.52	Q DP problem:
32.88/16.52	The TRS P consists of the following rules:
32.88/16.52	
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.52	
32.88/16.52	The TRS R consists of the following rules:
32.88/16.52	
32.88/16.52	   new_show2(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show6(ww17, be) -> error([])
32.88/16.52	   new_show(ww17, bg, bh) -> error([])
32.88/16.52	   new_show7(ww17) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.52	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show1(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.52	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.52	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_show3(ww17, ba) -> error([])
32.88/16.52	   new_show8(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.52	   new_primModNatS4(ww122) -> Zero
32.88/16.52	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.52	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.52	   new_show0(ww17) -> error([])
32.88/16.52	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.52	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.52	   new_show9(ww17) -> error([])
32.88/16.52	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show13(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.52	   new_psPs0([], ww56) -> ww56
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.52	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.52	   new_show5(ww17) -> error([])
32.88/16.52	   new_show12(ww17, ca) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.52	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.52	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.52	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.52	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.52	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.52	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.52	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.52	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_show11(ww17) -> error([])
32.88/16.52	   new_show4(ww17, bc, bd) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.52	   new_show15(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.52	   new_primDivNatS4(ww126) -> Zero
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.52	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.52	
32.88/16.52	The set Q consists of the following terms:
32.88/16.52	
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.52	   new_primShowInt0(Neg(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.52	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.52	   new_primModNatS3(Succ(x0), Zero)
32.88/16.52	   new_show0(x0)
32.88/16.52	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Double)
32.88/16.52	   new_showsPrec(x0, x1, ty_Float)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_@0)
32.88/16.52	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.52	   new_show9(x0)
32.88/16.52	   new_primModNatS02(x0, x1)
32.88/16.52	   new_show15(x0)
32.88/16.52	   new_show3(x0, x1)
32.88/16.52	   new_show8(x0)
32.88/16.52	   new_show11(x0)
32.88/16.52	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.52	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.52	   new_show(x0, x1, x2)
32.88/16.52	   new_show10(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.52	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.52	   new_psPs0(:(x0, x1), x2)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_primModNatS4(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.52	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_show1(x0)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.52	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.52	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_show6(x0, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.52	   new_show13(x0)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.52	   new_primModNatS3(Zero, Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.52	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.52	   new_div(x0, x1)
32.88/16.52	   new_primIntToChar(x0, x1)
32.88/16.52	   new_show14(x0, x1, x2, x3)
32.88/16.52	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.52	   new_primModNatS3(Zero, Succ(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_Int)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.52	   new_show5(x0)
32.88/16.52	   new_primShowInt0(Pos(Zero))
32.88/16.52	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.52	   new_primDivNatS02(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_show12(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.52	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_primModNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.52	   new_psPs0([], x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.52	   new_show2(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.52	   new_show7(x0)
32.88/16.52	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.52	   new_show4(x0, x1, x2)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.52	   new_showsPrec(x0, x1, ty_Char)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.52	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.52	   new_primDivNatS4(x0)
32.88/16.52	   new_primDivNatS3(Zero, Zero)
32.88/16.52	
32.88/16.52	We have to consider all minimal (P,Q,R)-chains.
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(54) TransformationProof (EQUIVALENT)
32.88/16.52	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.52	
32.88/16.52	   (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))
32.88/16.52	   (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))
32.88/16.52	
32.88/16.52	
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(55)
32.88/16.52	Obligation:
32.88/16.52	Q DP problem:
32.88/16.52	The TRS P consists of the following rules:
32.88/16.52	
32.88/16.52	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.52	   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)
32.88/16.52	   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)
32.88/16.52	
32.88/16.52	The TRS R consists of the following rules:
32.88/16.52	
32.88/16.52	   new_show2(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show6(ww17, be) -> error([])
32.88/16.52	   new_show(ww17, bg, bh) -> error([])
32.88/16.52	   new_show7(ww17) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.52	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show1(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.52	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.52	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_show3(ww17, ba) -> error([])
32.88/16.52	   new_show8(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.52	   new_primModNatS4(ww122) -> Zero
32.88/16.52	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.52	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.52	   new_show0(ww17) -> error([])
32.88/16.52	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.52	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.52	   new_show9(ww17) -> error([])
32.88/16.52	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show13(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.52	   new_psPs0([], ww56) -> ww56
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.52	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.52	   new_show5(ww17) -> error([])
32.88/16.52	   new_show12(ww17, ca) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.52	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.52	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.52	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.52	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.52	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.52	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.52	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.52	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_show11(ww17) -> error([])
32.88/16.52	   new_show4(ww17, bc, bd) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.52	   new_show15(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.52	   new_primDivNatS4(ww126) -> Zero
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.52	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.52	
32.88/16.52	The set Q consists of the following terms:
32.88/16.52	
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.52	   new_primShowInt0(Neg(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.52	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.52	   new_primModNatS3(Succ(x0), Zero)
32.88/16.52	   new_show0(x0)
32.88/16.52	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Double)
32.88/16.52	   new_showsPrec(x0, x1, ty_Float)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_@0)
32.88/16.52	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.52	   new_show9(x0)
32.88/16.52	   new_primModNatS02(x0, x1)
32.88/16.52	   new_show15(x0)
32.88/16.52	   new_show3(x0, x1)
32.88/16.52	   new_show8(x0)
32.88/16.52	   new_show11(x0)
32.88/16.52	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.52	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.52	   new_show(x0, x1, x2)
32.88/16.52	   new_show10(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.52	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.52	   new_psPs0(:(x0, x1), x2)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_primModNatS4(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.52	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_show1(x0)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.52	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.52	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_show6(x0, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.52	   new_show13(x0)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.52	   new_primModNatS3(Zero, Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.52	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.52	   new_div(x0, x1)
32.88/16.52	   new_primIntToChar(x0, x1)
32.88/16.52	   new_show14(x0, x1, x2, x3)
32.88/16.52	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.52	   new_primModNatS3(Zero, Succ(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_Int)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.52	   new_show5(x0)
32.88/16.52	   new_primShowInt0(Pos(Zero))
32.88/16.52	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.52	   new_primDivNatS02(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_show12(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.52	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_primModNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.52	   new_psPs0([], x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.52	   new_show2(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.52	   new_show7(x0)
32.88/16.52	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.52	   new_show4(x0, x1, x2)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.52	   new_showsPrec(x0, x1, ty_Char)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.52	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.52	   new_primDivNatS4(x0)
32.88/16.52	   new_primDivNatS3(Zero, Zero)
32.88/16.52	
32.88/16.52	We have to consider all minimal (P,Q,R)-chains.
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(56) DependencyGraphProof (EQUIVALENT)
32.88/16.52	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(57)
32.88/16.52	Obligation:
32.88/16.52	Q DP problem:
32.88/16.52	The TRS P consists of the following rules:
32.88/16.52	
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.52	
32.88/16.52	The TRS R consists of the following rules:
32.88/16.52	
32.88/16.52	   new_show2(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show6(ww17, be) -> error([])
32.88/16.52	   new_show(ww17, bg, bh) -> error([])
32.88/16.52	   new_show7(ww17) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.52	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show1(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.52	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.52	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_show3(ww17, ba) -> error([])
32.88/16.52	   new_show8(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.52	   new_primModNatS4(ww122) -> Zero
32.88/16.52	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.52	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.52	   new_show0(ww17) -> error([])
32.88/16.52	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.52	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.52	   new_show9(ww17) -> error([])
32.88/16.52	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show13(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.52	   new_psPs0([], ww56) -> ww56
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.52	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.52	   new_show5(ww17) -> error([])
32.88/16.52	   new_show12(ww17, ca) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.52	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.52	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.52	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.52	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.52	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.52	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.52	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.52	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.52	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.52	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.52	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_show11(ww17) -> error([])
32.88/16.52	   new_show4(ww17, bc, bd) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.52	   new_show15(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.52	   new_primDivNatS4(ww126) -> Zero
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.52	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.52	
32.88/16.52	The set Q consists of the following terms:
32.88/16.52	
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.52	   new_primShowInt0(Neg(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.52	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.52	   new_primModNatS3(Succ(x0), Zero)
32.88/16.52	   new_show0(x0)
32.88/16.52	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Double)
32.88/16.52	   new_showsPrec(x0, x1, ty_Float)
32.88/16.52	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_@0)
32.88/16.52	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.52	   new_show9(x0)
32.88/16.52	   new_primModNatS02(x0, x1)
32.88/16.52	   new_show15(x0)
32.88/16.52	   new_show3(x0, x1)
32.88/16.52	   new_show8(x0)
32.88/16.52	   new_show11(x0)
32.88/16.52	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.52	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.52	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.52	   new_show(x0, x1, x2)
32.88/16.52	   new_show10(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.52	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.52	   new_psPs0(:(x0, x1), x2)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_primModNatS4(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.52	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.52	   new_show1(x0)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.52	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.52	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_show6(x0, x1)
32.88/16.52	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.52	   new_show13(x0)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.52	   new_primModNatS3(Zero, Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.52	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.52	   new_div(x0, x1)
32.88/16.52	   new_primIntToChar(x0, x1)
32.88/16.52	   new_show14(x0, x1, x2, x3)
32.88/16.52	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.52	   new_primModNatS3(Zero, Succ(x0))
32.88/16.52	   new_showsPrec(x0, x1, ty_Int)
32.88/16.52	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.52	   new_show5(x0)
32.88/16.52	   new_primShowInt0(Pos(Zero))
32.88/16.52	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.52	   new_primDivNatS02(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.52	   new_show12(x0, x1)
32.88/16.52	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.52	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.52	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.52	   new_primModNatS2(Zero, Zero, x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.52	   new_psPs0([], x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.52	   new_show2(x0)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.52	   new_show7(x0)
32.88/16.52	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.52	   new_show4(x0, x1, x2)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.52	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.52	   new_showsPrec(x0, x1, ty_Char)
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.52	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.52	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.52	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.52	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.52	   new_primDivNatS4(x0)
32.88/16.52	   new_primDivNatS3(Zero, Zero)
32.88/16.52	
32.88/16.52	We have to consider all minimal (P,Q,R)-chains.
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(58) TransformationProof (EQUIVALENT)
32.88/16.52	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.52	
32.88/16.52	   (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))
32.88/16.52	   (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))
32.88/16.52	
32.88/16.52	
32.88/16.52	----------------------------------------
32.88/16.52	
32.88/16.52	(59)
32.88/16.52	Obligation:
32.88/16.52	Q DP problem:
32.88/16.52	The TRS P consists of the following rules:
32.88/16.52	
32.88/16.52	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.52	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.52	   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)
32.88/16.52	   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)
32.88/16.52	
32.88/16.52	The TRS R consists of the following rules:
32.88/16.52	
32.88/16.52	   new_show2(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show6(ww17, be) -> error([])
32.88/16.52	   new_show(ww17, bg, bh) -> error([])
32.88/16.52	   new_show7(ww17) -> error([])
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.52	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.52	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_show1(ww17) -> error([])
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.52	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.52	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.52	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.52	   new_show3(ww17, ba) -> error([])
32.88/16.52	   new_show8(ww17) -> error([])
32.88/16.52	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.52	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.52	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.52	   new_primModNatS4(ww122) -> Zero
32.88/16.52	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.52	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.52	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.53	   new_show0(ww17) -> error([])
32.88/16.53	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.53	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.53	   new_show9(ww17) -> error([])
32.88/16.53	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show13(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.53	   new_psPs0([], ww56) -> ww56
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.53	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.53	   new_show5(ww17) -> error([])
32.88/16.53	   new_show12(ww17, ca) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.53	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.53	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.53	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.53	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.53	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.53	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.53	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.53	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_show11(ww17) -> error([])
32.88/16.53	   new_show4(ww17, bc, bd) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.53	   new_show15(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.53	   new_primDivNatS4(ww126) -> Zero
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.53	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.53	
32.88/16.53	The set Q consists of the following terms:
32.88/16.53	
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.53	   new_primShowInt0(Neg(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.53	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.53	   new_primModNatS3(Succ(x0), Zero)
32.88/16.53	   new_show0(x0)
32.88/16.53	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Double)
32.88/16.53	   new_showsPrec(x0, x1, ty_Float)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_@0)
32.88/16.53	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.53	   new_show9(x0)
32.88/16.53	   new_primModNatS02(x0, x1)
32.88/16.53	   new_show15(x0)
32.88/16.53	   new_show3(x0, x1)
32.88/16.53	   new_show8(x0)
32.88/16.53	   new_show11(x0)
32.88/16.53	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.53	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.53	   new_show(x0, x1, x2)
32.88/16.53	   new_show10(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.53	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.53	   new_psPs0(:(x0, x1), x2)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_primModNatS4(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.53	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_show1(x0)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.53	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.53	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_show6(x0, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.53	   new_show13(x0)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.53	   new_primModNatS3(Zero, Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.53	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.53	   new_div(x0, x1)
32.88/16.53	   new_primIntToChar(x0, x1)
32.88/16.53	   new_show14(x0, x1, x2, x3)
32.88/16.53	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.53	   new_primModNatS3(Zero, Succ(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_Int)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.53	   new_show5(x0)
32.88/16.53	   new_primShowInt0(Pos(Zero))
32.88/16.53	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.53	   new_primDivNatS02(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_show12(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.53	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_primModNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.53	   new_psPs0([], x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.53	   new_show2(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.53	   new_show7(x0)
32.88/16.53	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.53	   new_show4(x0, x1, x2)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.53	   new_showsPrec(x0, x1, ty_Char)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.53	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.53	   new_primDivNatS4(x0)
32.88/16.53	   new_primDivNatS3(Zero, Zero)
32.88/16.53	
32.88/16.53	We have to consider all minimal (P,Q,R)-chains.
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(60) DependencyGraphProof (EQUIVALENT)
32.88/16.53	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(61)
32.88/16.53	Obligation:
32.88/16.53	Q DP problem:
32.88/16.53	The TRS P consists of the following rules:
32.88/16.53	
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.53	
32.88/16.53	The TRS R consists of the following rules:
32.88/16.53	
32.88/16.53	   new_show2(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show6(ww17, be) -> error([])
32.88/16.53	   new_show(ww17, bg, bh) -> error([])
32.88/16.53	   new_show7(ww17) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.53	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show1(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.53	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.53	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_show3(ww17, ba) -> error([])
32.88/16.53	   new_show8(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.53	   new_primModNatS4(ww122) -> Zero
32.88/16.53	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.53	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.53	   new_show0(ww17) -> error([])
32.88/16.53	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.53	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.53	   new_show9(ww17) -> error([])
32.88/16.53	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show13(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.53	   new_psPs0([], ww56) -> ww56
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.53	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.53	   new_show5(ww17) -> error([])
32.88/16.53	   new_show12(ww17, ca) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.53	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.53	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.53	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.53	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.53	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.53	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.53	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.53	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_show11(ww17) -> error([])
32.88/16.53	   new_show4(ww17, bc, bd) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.53	   new_show15(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.53	   new_primDivNatS4(ww126) -> Zero
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.53	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.53	
32.88/16.53	The set Q consists of the following terms:
32.88/16.53	
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.53	   new_primShowInt0(Neg(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.53	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.53	   new_primModNatS3(Succ(x0), Zero)
32.88/16.53	   new_show0(x0)
32.88/16.53	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Double)
32.88/16.53	   new_showsPrec(x0, x1, ty_Float)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_@0)
32.88/16.53	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.53	   new_show9(x0)
32.88/16.53	   new_primModNatS02(x0, x1)
32.88/16.53	   new_show15(x0)
32.88/16.53	   new_show3(x0, x1)
32.88/16.53	   new_show8(x0)
32.88/16.53	   new_show11(x0)
32.88/16.53	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.53	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.53	   new_show(x0, x1, x2)
32.88/16.53	   new_show10(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.53	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.53	   new_psPs0(:(x0, x1), x2)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_primModNatS4(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.53	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_show1(x0)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.53	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.53	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_show6(x0, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.53	   new_show13(x0)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.53	   new_primModNatS3(Zero, Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.53	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.53	   new_div(x0, x1)
32.88/16.53	   new_primIntToChar(x0, x1)
32.88/16.53	   new_show14(x0, x1, x2, x3)
32.88/16.53	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.53	   new_primModNatS3(Zero, Succ(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_Int)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.53	   new_show5(x0)
32.88/16.53	   new_primShowInt0(Pos(Zero))
32.88/16.53	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.53	   new_primDivNatS02(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_show12(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.53	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_primModNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.53	   new_psPs0([], x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.53	   new_show2(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.53	   new_show7(x0)
32.88/16.53	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.53	   new_show4(x0, x1, x2)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.53	   new_showsPrec(x0, x1, ty_Char)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.53	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.53	   new_primDivNatS4(x0)
32.88/16.53	   new_primDivNatS3(Zero, Zero)
32.88/16.53	
32.88/16.53	We have to consider all minimal (P,Q,R)-chains.
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(62) TransformationProof (EQUIVALENT)
32.88/16.53	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.53	
32.88/16.53	   (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))
32.88/16.53	   (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))
32.88/16.53	
32.88/16.53	
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(63)
32.88/16.53	Obligation:
32.88/16.53	Q DP problem:
32.88/16.53	The TRS P consists of the following rules:
32.88/16.53	
32.88/16.53	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.53	   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)
32.88/16.53	   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)
32.88/16.53	
32.88/16.53	The TRS R consists of the following rules:
32.88/16.53	
32.88/16.53	   new_show2(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show6(ww17, be) -> error([])
32.88/16.53	   new_show(ww17, bg, bh) -> error([])
32.88/16.53	   new_show7(ww17) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.53	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show1(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.53	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.53	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_show3(ww17, ba) -> error([])
32.88/16.53	   new_show8(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.53	   new_primModNatS4(ww122) -> Zero
32.88/16.53	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.53	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.53	   new_show0(ww17) -> error([])
32.88/16.53	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.53	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.53	   new_show9(ww17) -> error([])
32.88/16.53	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show13(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.53	   new_psPs0([], ww56) -> ww56
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.53	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.53	   new_show5(ww17) -> error([])
32.88/16.53	   new_show12(ww17, ca) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.53	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.53	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.53	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.53	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.53	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.53	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.53	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.53	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_show11(ww17) -> error([])
32.88/16.53	   new_show4(ww17, bc, bd) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.53	   new_show15(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.53	   new_primDivNatS4(ww126) -> Zero
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.53	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.53	
32.88/16.53	The set Q consists of the following terms:
32.88/16.53	
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.53	   new_primShowInt0(Neg(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.53	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.53	   new_primModNatS3(Succ(x0), Zero)
32.88/16.53	   new_show0(x0)
32.88/16.53	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Double)
32.88/16.53	   new_showsPrec(x0, x1, ty_Float)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_@0)
32.88/16.53	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.53	   new_show9(x0)
32.88/16.53	   new_primModNatS02(x0, x1)
32.88/16.53	   new_show15(x0)
32.88/16.53	   new_show3(x0, x1)
32.88/16.53	   new_show8(x0)
32.88/16.53	   new_show11(x0)
32.88/16.53	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.53	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.53	   new_show(x0, x1, x2)
32.88/16.53	   new_show10(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.53	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.53	   new_psPs0(:(x0, x1), x2)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_primModNatS4(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.53	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_show1(x0)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.53	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.53	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_show6(x0, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.53	   new_show13(x0)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.53	   new_primModNatS3(Zero, Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.53	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.53	   new_div(x0, x1)
32.88/16.53	   new_primIntToChar(x0, x1)
32.88/16.53	   new_show14(x0, x1, x2, x3)
32.88/16.53	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.53	   new_primModNatS3(Zero, Succ(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_Int)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.53	   new_show5(x0)
32.88/16.53	   new_primShowInt0(Pos(Zero))
32.88/16.53	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.53	   new_primDivNatS02(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_show12(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.53	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_primModNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.53	   new_psPs0([], x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.53	   new_show2(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.53	   new_show7(x0)
32.88/16.53	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.53	   new_show4(x0, x1, x2)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.53	   new_showsPrec(x0, x1, ty_Char)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.53	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.53	   new_primDivNatS4(x0)
32.88/16.53	   new_primDivNatS3(Zero, Zero)
32.88/16.53	
32.88/16.53	We have to consider all minimal (P,Q,R)-chains.
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(64) DependencyGraphProof (EQUIVALENT)
32.88/16.53	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(65)
32.88/16.53	Obligation:
32.88/16.53	Q DP problem:
32.88/16.53	The TRS P consists of the following rules:
32.88/16.53	
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.53	
32.88/16.53	The TRS R consists of the following rules:
32.88/16.53	
32.88/16.53	   new_show2(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show6(ww17, be) -> error([])
32.88/16.53	   new_show(ww17, bg, bh) -> error([])
32.88/16.53	   new_show7(ww17) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.53	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show1(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.53	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.53	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_show3(ww17, ba) -> error([])
32.88/16.53	   new_show8(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.53	   new_primModNatS4(ww122) -> Zero
32.88/16.53	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.53	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.53	   new_show0(ww17) -> error([])
32.88/16.53	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.53	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.53	   new_show9(ww17) -> error([])
32.88/16.53	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show13(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.53	   new_psPs0([], ww56) -> ww56
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.53	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.53	   new_show5(ww17) -> error([])
32.88/16.53	   new_show12(ww17, ca) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.53	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.53	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.53	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.53	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.53	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.53	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.53	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.53	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_show11(ww17) -> error([])
32.88/16.53	   new_show4(ww17, bc, bd) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.53	   new_show15(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.53	   new_primDivNatS4(ww126) -> Zero
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.53	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.53	
32.88/16.53	The set Q consists of the following terms:
32.88/16.53	
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.53	   new_primShowInt0(Neg(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.53	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.53	   new_primModNatS3(Succ(x0), Zero)
32.88/16.53	   new_show0(x0)
32.88/16.53	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Double)
32.88/16.53	   new_showsPrec(x0, x1, ty_Float)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_@0)
32.88/16.53	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.53	   new_show9(x0)
32.88/16.53	   new_primModNatS02(x0, x1)
32.88/16.53	   new_show15(x0)
32.88/16.53	   new_show3(x0, x1)
32.88/16.53	   new_show8(x0)
32.88/16.53	   new_show11(x0)
32.88/16.53	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.53	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.53	   new_show(x0, x1, x2)
32.88/16.53	   new_show10(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.53	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.53	   new_psPs0(:(x0, x1), x2)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_primModNatS4(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.53	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_show1(x0)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.53	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.53	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_show6(x0, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.53	   new_show13(x0)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.53	   new_primModNatS3(Zero, Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.53	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.53	   new_div(x0, x1)
32.88/16.53	   new_primIntToChar(x0, x1)
32.88/16.53	   new_show14(x0, x1, x2, x3)
32.88/16.53	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.53	   new_primModNatS3(Zero, Succ(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_Int)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.53	   new_show5(x0)
32.88/16.53	   new_primShowInt0(Pos(Zero))
32.88/16.53	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.53	   new_primDivNatS02(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_show12(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.53	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_primModNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.53	   new_psPs0([], x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.53	   new_show2(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.53	   new_show7(x0)
32.88/16.53	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.53	   new_show4(x0, x1, x2)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.53	   new_showsPrec(x0, x1, ty_Char)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.53	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.53	   new_primDivNatS4(x0)
32.88/16.53	   new_primDivNatS3(Zero, Zero)
32.88/16.53	
32.88/16.53	We have to consider all minimal (P,Q,R)-chains.
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(66) TransformationProof (EQUIVALENT)
32.88/16.53	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.53	
32.88/16.53	   (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)))
32.88/16.53	   (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)))
32.88/16.53	
32.88/16.53	
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(67)
32.88/16.53	Obligation:
32.88/16.53	Q DP problem:
32.88/16.53	The TRS P consists of the following rules:
32.88/16.53	
32.88/16.53	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.53	   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))
32.88/16.53	   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))
32.88/16.53	
32.88/16.53	The TRS R consists of the following rules:
32.88/16.53	
32.88/16.53	   new_show2(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show6(ww17, be) -> error([])
32.88/16.53	   new_show(ww17, bg, bh) -> error([])
32.88/16.53	   new_show7(ww17) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.53	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show1(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.53	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.53	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_show3(ww17, ba) -> error([])
32.88/16.53	   new_show8(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.53	   new_primModNatS4(ww122) -> Zero
32.88/16.53	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.53	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.53	   new_show0(ww17) -> error([])
32.88/16.53	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.53	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.53	   new_show9(ww17) -> error([])
32.88/16.53	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show13(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.53	   new_psPs0([], ww56) -> ww56
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.53	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.53	   new_show5(ww17) -> error([])
32.88/16.53	   new_show12(ww17, ca) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.53	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.53	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.53	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.53	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.53	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.53	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.53	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.53	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_show11(ww17) -> error([])
32.88/16.53	   new_show4(ww17, bc, bd) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.53	   new_show15(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.53	   new_primDivNatS4(ww126) -> Zero
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.53	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.53	
32.88/16.53	The set Q consists of the following terms:
32.88/16.53	
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.53	   new_primShowInt0(Neg(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.53	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.53	   new_primModNatS3(Succ(x0), Zero)
32.88/16.53	   new_show0(x0)
32.88/16.53	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Double)
32.88/16.53	   new_showsPrec(x0, x1, ty_Float)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_@0)
32.88/16.53	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.53	   new_show9(x0)
32.88/16.53	   new_primModNatS02(x0, x1)
32.88/16.53	   new_show15(x0)
32.88/16.53	   new_show3(x0, x1)
32.88/16.53	   new_show8(x0)
32.88/16.53	   new_show11(x0)
32.88/16.53	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.53	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.53	   new_show(x0, x1, x2)
32.88/16.53	   new_show10(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.53	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.53	   new_psPs0(:(x0, x1), x2)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_primModNatS4(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.53	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_show1(x0)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.53	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.53	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_show6(x0, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.53	   new_show13(x0)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.53	   new_primModNatS3(Zero, Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.53	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.53	   new_div(x0, x1)
32.88/16.53	   new_primIntToChar(x0, x1)
32.88/16.53	   new_show14(x0, x1, x2, x3)
32.88/16.53	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.53	   new_primModNatS3(Zero, Succ(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_Int)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.53	   new_show5(x0)
32.88/16.53	   new_primShowInt0(Pos(Zero))
32.88/16.53	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.53	   new_primDivNatS02(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_show12(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.53	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_primModNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.53	   new_psPs0([], x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.53	   new_show2(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.53	   new_show7(x0)
32.88/16.53	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.53	   new_show4(x0, x1, x2)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.53	   new_showsPrec(x0, x1, ty_Char)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.53	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.53	   new_primDivNatS4(x0)
32.88/16.53	   new_primDivNatS3(Zero, Zero)
32.88/16.53	
32.88/16.53	We have to consider all minimal (P,Q,R)-chains.
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(68) DependencyGraphProof (EQUIVALENT)
32.88/16.53	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(69)
32.88/16.53	Obligation:
32.88/16.53	Q DP problem:
32.88/16.53	The TRS P consists of the following rules:
32.88/16.53	
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.53	
32.88/16.53	The TRS R consists of the following rules:
32.88/16.53	
32.88/16.53	   new_show2(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show6(ww17, be) -> error([])
32.88/16.53	   new_show(ww17, bg, bh) -> error([])
32.88/16.53	   new_show7(ww17) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.53	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show1(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.53	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.53	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_show3(ww17, ba) -> error([])
32.88/16.53	   new_show8(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.53	   new_primModNatS4(ww122) -> Zero
32.88/16.53	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.53	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.53	   new_show0(ww17) -> error([])
32.88/16.53	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.53	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.53	   new_show9(ww17) -> error([])
32.88/16.53	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show13(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.53	   new_psPs0([], ww56) -> ww56
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.53	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.53	   new_show5(ww17) -> error([])
32.88/16.53	   new_show12(ww17, ca) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.53	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.53	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.53	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.53	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.53	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.53	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.53	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.53	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_show11(ww17) -> error([])
32.88/16.53	   new_show4(ww17, bc, bd) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.53	   new_show15(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.53	   new_primDivNatS4(ww126) -> Zero
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.53	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.53	
32.88/16.53	The set Q consists of the following terms:
32.88/16.53	
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.53	   new_primShowInt0(Neg(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.53	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.53	   new_primModNatS3(Succ(x0), Zero)
32.88/16.53	   new_show0(x0)
32.88/16.53	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Double)
32.88/16.53	   new_showsPrec(x0, x1, ty_Float)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_@0)
32.88/16.53	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.53	   new_show9(x0)
32.88/16.53	   new_primModNatS02(x0, x1)
32.88/16.53	   new_show15(x0)
32.88/16.53	   new_show3(x0, x1)
32.88/16.53	   new_show8(x0)
32.88/16.53	   new_show11(x0)
32.88/16.53	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.53	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.53	   new_show(x0, x1, x2)
32.88/16.53	   new_show10(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.53	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.53	   new_psPs0(:(x0, x1), x2)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_primModNatS4(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.53	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_show1(x0)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.53	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.53	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_show6(x0, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.53	   new_show13(x0)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.53	   new_primModNatS3(Zero, Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.53	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.53	   new_div(x0, x1)
32.88/16.53	   new_primIntToChar(x0, x1)
32.88/16.53	   new_show14(x0, x1, x2, x3)
32.88/16.53	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.53	   new_primModNatS3(Zero, Succ(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_Int)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.53	   new_show5(x0)
32.88/16.53	   new_primShowInt0(Pos(Zero))
32.88/16.53	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.53	   new_primDivNatS02(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_show12(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.53	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_primModNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.53	   new_psPs0([], x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.53	   new_show2(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.53	   new_show7(x0)
32.88/16.53	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.53	   new_show4(x0, x1, x2)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.53	   new_showsPrec(x0, x1, ty_Char)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.53	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.53	   new_primDivNatS4(x0)
32.88/16.53	   new_primDivNatS3(Zero, Zero)
32.88/16.53	
32.88/16.53	We have to consider all minimal (P,Q,R)-chains.
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(70) TransformationProof (EQUIVALENT)
32.88/16.53	By instantiating [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, bf), app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h) we obtained the following new rules [LPAR04]:
32.88/16.53	
32.88/16.53	   (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))
32.88/16.53	   (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))
32.88/16.53	
32.88/16.53	
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(71)
32.88/16.53	Obligation:
32.88/16.53	Q DP problem:
32.88/16.53	The TRS P consists of the following rules:
32.88/16.53	
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.53	   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)
32.88/16.53	   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)
32.88/16.53	
32.88/16.53	The TRS R consists of the following rules:
32.88/16.53	
32.88/16.53	   new_show2(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show6(ww17, be) -> error([])
32.88/16.53	   new_show(ww17, bg, bh) -> error([])
32.88/16.53	   new_show7(ww17) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.53	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show1(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.53	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.53	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_show3(ww17, ba) -> error([])
32.88/16.53	   new_show8(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.53	   new_primModNatS4(ww122) -> Zero
32.88/16.53	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.53	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.53	   new_show0(ww17) -> error([])
32.88/16.53	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.53	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.53	   new_show9(ww17) -> error([])
32.88/16.53	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show13(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.53	   new_psPs0([], ww56) -> ww56
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.53	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.53	   new_show5(ww17) -> error([])
32.88/16.53	   new_show12(ww17, ca) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.53	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.53	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.53	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.53	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.53	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.53	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.53	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.53	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_show11(ww17) -> error([])
32.88/16.53	   new_show4(ww17, bc, bd) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.53	   new_show15(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.53	   new_primDivNatS4(ww126) -> Zero
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.53	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.53	
32.88/16.53	The set Q consists of the following terms:
32.88/16.53	
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.53	   new_primShowInt0(Neg(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.53	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.53	   new_primModNatS3(Succ(x0), Zero)
32.88/16.53	   new_show0(x0)
32.88/16.53	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Double)
32.88/16.53	   new_showsPrec(x0, x1, ty_Float)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_@0)
32.88/16.53	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.53	   new_show9(x0)
32.88/16.53	   new_primModNatS02(x0, x1)
32.88/16.53	   new_show15(x0)
32.88/16.53	   new_show3(x0, x1)
32.88/16.53	   new_show8(x0)
32.88/16.53	   new_show11(x0)
32.88/16.53	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.53	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.53	   new_show(x0, x1, x2)
32.88/16.53	   new_show10(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.53	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.53	   new_psPs0(:(x0, x1), x2)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_primModNatS4(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.53	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_show1(x0)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.53	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.53	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_show6(x0, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.53	   new_show13(x0)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.53	   new_primModNatS3(Zero, Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.53	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.53	   new_div(x0, x1)
32.88/16.53	   new_primIntToChar(x0, x1)
32.88/16.53	   new_show14(x0, x1, x2, x3)
32.88/16.53	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.53	   new_primModNatS3(Zero, Succ(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_Int)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.53	   new_show5(x0)
32.88/16.53	   new_primShowInt0(Pos(Zero))
32.88/16.53	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.53	   new_primDivNatS02(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_show12(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.53	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_primModNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.53	   new_psPs0([], x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.53	   new_show2(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.53	   new_show7(x0)
32.88/16.53	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.53	   new_show4(x0, x1, x2)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.53	   new_showsPrec(x0, x1, ty_Char)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.53	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.53	   new_primDivNatS4(x0)
32.88/16.53	   new_primDivNatS3(Zero, Zero)
32.88/16.53	
32.88/16.53	We have to consider all minimal (P,Q,R)-chains.
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(72) TransformationProof (EQUIVALENT)
32.88/16.53	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.53	
32.88/16.53	   (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)))
32.88/16.53	   (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)))
32.88/16.53	
32.88/16.53	
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(73)
32.88/16.53	Obligation:
32.88/16.53	Q DP problem:
32.88/16.53	The TRS P consists of the following rules:
32.88/16.53	
32.88/16.53	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.53	   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)
32.88/16.53	   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)
32.88/16.53	   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))
32.88/16.53	   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))
32.88/16.53	
32.88/16.53	The TRS R consists of the following rules:
32.88/16.53	
32.88/16.53	   new_show2(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show6(ww17, be) -> error([])
32.88/16.53	   new_show(ww17, bg, bh) -> error([])
32.88/16.53	   new_show7(ww17) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.53	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show1(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.53	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.53	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_show3(ww17, ba) -> error([])
32.88/16.53	   new_show8(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.53	   new_primModNatS4(ww122) -> Zero
32.88/16.53	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.53	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.53	   new_show0(ww17) -> error([])
32.88/16.53	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.53	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.53	   new_show9(ww17) -> error([])
32.88/16.53	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show13(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.53	   new_psPs0([], ww56) -> ww56
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.53	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.53	   new_show5(ww17) -> error([])
32.88/16.53	   new_show12(ww17, ca) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.53	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.53	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.53	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.53	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.53	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.53	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.53	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.53	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_show11(ww17) -> error([])
32.88/16.53	   new_show4(ww17, bc, bd) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.53	   new_show15(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.53	   new_primDivNatS4(ww126) -> Zero
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.53	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.53	
32.88/16.53	The set Q consists of the following terms:
32.88/16.53	
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.53	   new_primShowInt0(Neg(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.53	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.53	   new_primModNatS3(Succ(x0), Zero)
32.88/16.53	   new_show0(x0)
32.88/16.53	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Double)
32.88/16.53	   new_showsPrec(x0, x1, ty_Float)
32.88/16.53	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_@0)
32.88/16.53	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.53	   new_show9(x0)
32.88/16.53	   new_primModNatS02(x0, x1)
32.88/16.53	   new_show15(x0)
32.88/16.53	   new_show3(x0, x1)
32.88/16.53	   new_show8(x0)
32.88/16.53	   new_show11(x0)
32.88/16.53	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.53	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.53	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.53	   new_show(x0, x1, x2)
32.88/16.53	   new_show10(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.53	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.53	   new_psPs0(:(x0, x1), x2)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_primModNatS4(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.53	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.53	   new_show1(x0)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.53	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.53	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_show6(x0, x1)
32.88/16.53	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.53	   new_show13(x0)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.53	   new_primModNatS3(Zero, Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.53	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.53	   new_div(x0, x1)
32.88/16.53	   new_primIntToChar(x0, x1)
32.88/16.53	   new_show14(x0, x1, x2, x3)
32.88/16.53	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.53	   new_primModNatS3(Zero, Succ(x0))
32.88/16.53	   new_showsPrec(x0, x1, ty_Int)
32.88/16.53	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.53	   new_show5(x0)
32.88/16.53	   new_primShowInt0(Pos(Zero))
32.88/16.53	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.53	   new_primDivNatS02(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.53	   new_show12(x0, x1)
32.88/16.53	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.53	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.53	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.53	   new_primModNatS2(Zero, Zero, x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.53	   new_psPs0([], x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.53	   new_show2(x0)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.53	   new_show7(x0)
32.88/16.53	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.53	   new_show4(x0, x1, x2)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.53	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.53	   new_showsPrec(x0, x1, ty_Char)
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.53	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.53	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.53	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.53	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.53	   new_primDivNatS4(x0)
32.88/16.53	   new_primDivNatS3(Zero, Zero)
32.88/16.53	
32.88/16.53	We have to consider all minimal (P,Q,R)-chains.
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(74) DependencyGraphProof (EQUIVALENT)
32.88/16.53	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.53	----------------------------------------
32.88/16.53	
32.88/16.53	(75)
32.88/16.53	Obligation:
32.88/16.53	Q DP problem:
32.88/16.53	The TRS P consists of the following rules:
32.88/16.53	
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.53	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.53	   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)
32.88/16.53	   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)
32.88/16.53	
32.88/16.53	The TRS R consists of the following rules:
32.88/16.53	
32.88/16.53	   new_show2(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show6(ww17, be) -> error([])
32.88/16.53	   new_show(ww17, bg, bh) -> error([])
32.88/16.53	   new_show7(ww17) -> error([])
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.53	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show1(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.53	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.53	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.53	   new_show3(ww17, ba) -> error([])
32.88/16.53	   new_show8(ww17) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.53	   new_primModNatS4(ww122) -> Zero
32.88/16.53	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.53	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.53	   new_show0(ww17) -> error([])
32.88/16.53	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.53	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.53	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.53	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.53	   new_show9(ww17) -> error([])
32.88/16.53	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show13(ww17) -> error([])
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.53	   new_psPs0([], ww56) -> ww56
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.53	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.53	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.53	   new_show5(ww17) -> error([])
32.88/16.53	   new_show12(ww17, ca) -> error([])
32.88/16.53	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.53	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.53	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.53	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.53	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.53	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.53	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.53	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.53	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.53	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.54	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.54	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.54	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.54	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_show11(ww17) -> error([])
32.88/16.54	   new_show4(ww17, bc, bd) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.54	   new_show15(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.54	   new_primDivNatS4(ww126) -> Zero
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.54	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.54	
32.88/16.54	The set Q consists of the following terms:
32.88/16.54	
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.54	   new_primShowInt0(Neg(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.54	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.54	   new_primModNatS3(Succ(x0), Zero)
32.88/16.54	   new_show0(x0)
32.88/16.54	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Double)
32.88/16.54	   new_showsPrec(x0, x1, ty_Float)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_@0)
32.88/16.54	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.54	   new_show9(x0)
32.88/16.54	   new_primModNatS02(x0, x1)
32.88/16.54	   new_show15(x0)
32.88/16.54	   new_show3(x0, x1)
32.88/16.54	   new_show8(x0)
32.88/16.54	   new_show11(x0)
32.88/16.54	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.54	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.54	   new_show(x0, x1, x2)
32.88/16.54	   new_show10(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.54	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.54	   new_psPs0(:(x0, x1), x2)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_primModNatS4(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.54	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_show1(x0)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.54	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.54	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_show6(x0, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.54	   new_show13(x0)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.54	   new_primModNatS3(Zero, Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.54	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.54	   new_div(x0, x1)
32.88/16.54	   new_primIntToChar(x0, x1)
32.88/16.54	   new_show14(x0, x1, x2, x3)
32.88/16.54	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.54	   new_primModNatS3(Zero, Succ(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_Int)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.54	   new_show5(x0)
32.88/16.54	   new_primShowInt0(Pos(Zero))
32.88/16.54	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.54	   new_primDivNatS02(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_show12(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.54	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_primModNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.54	   new_psPs0([], x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.54	   new_show2(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.54	   new_show7(x0)
32.88/16.54	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.54	   new_show4(x0, x1, x2)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.54	   new_showsPrec(x0, x1, ty_Char)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.54	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.54	   new_primDivNatS4(x0)
32.88/16.54	   new_primDivNatS3(Zero, Zero)
32.88/16.54	
32.88/16.54	We have to consider all minimal (P,Q,R)-chains.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(76) TransformationProof (EQUIVALENT)
32.88/16.54	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.54	
32.88/16.54	   (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))
32.88/16.54	   (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))
32.88/16.54	
32.88/16.54	
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(77)
32.88/16.54	Obligation:
32.88/16.54	Q DP problem:
32.88/16.54	The TRS P consists of the following rules:
32.88/16.54	
32.88/16.54	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	
32.88/16.54	The TRS R consists of the following rules:
32.88/16.54	
32.88/16.54	   new_show2(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show6(ww17, be) -> error([])
32.88/16.54	   new_show(ww17, bg, bh) -> error([])
32.88/16.54	   new_show7(ww17) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.54	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show1(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.54	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.54	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_show3(ww17, ba) -> error([])
32.88/16.54	   new_show8(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.54	   new_primModNatS4(ww122) -> Zero
32.88/16.54	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.54	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.54	   new_show0(ww17) -> error([])
32.88/16.54	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.54	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.54	   new_show9(ww17) -> error([])
32.88/16.54	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show13(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.54	   new_psPs0([], ww56) -> ww56
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.54	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.54	   new_show5(ww17) -> error([])
32.88/16.54	   new_show12(ww17, ca) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.54	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.54	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.54	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.54	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.54	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.54	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.54	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.54	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_show11(ww17) -> error([])
32.88/16.54	   new_show4(ww17, bc, bd) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.54	   new_show15(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.54	   new_primDivNatS4(ww126) -> Zero
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.54	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.54	
32.88/16.54	The set Q consists of the following terms:
32.88/16.54	
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.54	   new_primShowInt0(Neg(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.54	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.54	   new_primModNatS3(Succ(x0), Zero)
32.88/16.54	   new_show0(x0)
32.88/16.54	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Double)
32.88/16.54	   new_showsPrec(x0, x1, ty_Float)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_@0)
32.88/16.54	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.54	   new_show9(x0)
32.88/16.54	   new_primModNatS02(x0, x1)
32.88/16.54	   new_show15(x0)
32.88/16.54	   new_show3(x0, x1)
32.88/16.54	   new_show8(x0)
32.88/16.54	   new_show11(x0)
32.88/16.54	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.54	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.54	   new_show(x0, x1, x2)
32.88/16.54	   new_show10(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.54	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.54	   new_psPs0(:(x0, x1), x2)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_primModNatS4(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.54	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_show1(x0)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.54	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.54	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_show6(x0, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.54	   new_show13(x0)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.54	   new_primModNatS3(Zero, Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.54	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.54	   new_div(x0, x1)
32.88/16.54	   new_primIntToChar(x0, x1)
32.88/16.54	   new_show14(x0, x1, x2, x3)
32.88/16.54	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.54	   new_primModNatS3(Zero, Succ(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_Int)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.54	   new_show5(x0)
32.88/16.54	   new_primShowInt0(Pos(Zero))
32.88/16.54	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.54	   new_primDivNatS02(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_show12(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.54	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_primModNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.54	   new_psPs0([], x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.54	   new_show2(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.54	   new_show7(x0)
32.88/16.54	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.54	   new_show4(x0, x1, x2)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.54	   new_showsPrec(x0, x1, ty_Char)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.54	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.54	   new_primDivNatS4(x0)
32.88/16.54	   new_primDivNatS3(Zero, Zero)
32.88/16.54	
32.88/16.54	We have to consider all minimal (P,Q,R)-chains.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(78) DependencyGraphProof (EQUIVALENT)
32.88/16.54	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(79)
32.88/16.54	Obligation:
32.88/16.54	Q DP problem:
32.88/16.54	The TRS P consists of the following rules:
32.88/16.54	
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	
32.88/16.54	The TRS R consists of the following rules:
32.88/16.54	
32.88/16.54	   new_show2(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show6(ww17, be) -> error([])
32.88/16.54	   new_show(ww17, bg, bh) -> error([])
32.88/16.54	   new_show7(ww17) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.54	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show1(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.54	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.54	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_show3(ww17, ba) -> error([])
32.88/16.54	   new_show8(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.54	   new_primModNatS4(ww122) -> Zero
32.88/16.54	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.54	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.54	   new_show0(ww17) -> error([])
32.88/16.54	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.54	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.54	   new_show9(ww17) -> error([])
32.88/16.54	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show13(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.54	   new_psPs0([], ww56) -> ww56
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.54	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.54	   new_show5(ww17) -> error([])
32.88/16.54	   new_show12(ww17, ca) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.54	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.54	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.54	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.54	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.54	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.54	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.54	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.54	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_show11(ww17) -> error([])
32.88/16.54	   new_show4(ww17, bc, bd) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.54	   new_show15(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.54	   new_primDivNatS4(ww126) -> Zero
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.54	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.54	
32.88/16.54	The set Q consists of the following terms:
32.88/16.54	
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.54	   new_primShowInt0(Neg(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.54	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.54	   new_primModNatS3(Succ(x0), Zero)
32.88/16.54	   new_show0(x0)
32.88/16.54	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Double)
32.88/16.54	   new_showsPrec(x0, x1, ty_Float)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_@0)
32.88/16.54	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.54	   new_show9(x0)
32.88/16.54	   new_primModNatS02(x0, x1)
32.88/16.54	   new_show15(x0)
32.88/16.54	   new_show3(x0, x1)
32.88/16.54	   new_show8(x0)
32.88/16.54	   new_show11(x0)
32.88/16.54	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.54	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.54	   new_show(x0, x1, x2)
32.88/16.54	   new_show10(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.54	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.54	   new_psPs0(:(x0, x1), x2)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_primModNatS4(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.54	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_show1(x0)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.54	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.54	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_show6(x0, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.54	   new_show13(x0)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.54	   new_primModNatS3(Zero, Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.54	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.54	   new_div(x0, x1)
32.88/16.54	   new_primIntToChar(x0, x1)
32.88/16.54	   new_show14(x0, x1, x2, x3)
32.88/16.54	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.54	   new_primModNatS3(Zero, Succ(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_Int)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.54	   new_show5(x0)
32.88/16.54	   new_primShowInt0(Pos(Zero))
32.88/16.54	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.54	   new_primDivNatS02(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_show12(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.54	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_primModNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.54	   new_psPs0([], x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.54	   new_show2(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.54	   new_show7(x0)
32.88/16.54	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.54	   new_show4(x0, x1, x2)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.54	   new_showsPrec(x0, x1, ty_Char)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.54	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.54	   new_primDivNatS4(x0)
32.88/16.54	   new_primDivNatS3(Zero, Zero)
32.88/16.54	
32.88/16.54	We have to consider all minimal (P,Q,R)-chains.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(80) TransformationProof (EQUIVALENT)
32.88/16.54	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.54	
32.88/16.54	   (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)))
32.88/16.54	   (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)))
32.88/16.54	
32.88/16.54	
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(81)
32.88/16.54	Obligation:
32.88/16.54	Q DP problem:
32.88/16.54	The TRS P consists of the following rules:
32.88/16.54	
32.88/16.54	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	   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))
32.88/16.54	   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))
32.88/16.54	
32.88/16.54	The TRS R consists of the following rules:
32.88/16.54	
32.88/16.54	   new_show2(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show6(ww17, be) -> error([])
32.88/16.54	   new_show(ww17, bg, bh) -> error([])
32.88/16.54	   new_show7(ww17) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.54	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show1(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.54	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.54	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_show3(ww17, ba) -> error([])
32.88/16.54	   new_show8(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.54	   new_primModNatS4(ww122) -> Zero
32.88/16.54	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.54	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.54	   new_show0(ww17) -> error([])
32.88/16.54	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.54	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.54	   new_show9(ww17) -> error([])
32.88/16.54	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show13(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.54	   new_psPs0([], ww56) -> ww56
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.54	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.54	   new_show5(ww17) -> error([])
32.88/16.54	   new_show12(ww17, ca) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.54	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.54	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.54	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.54	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.54	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.54	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.54	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.54	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_show11(ww17) -> error([])
32.88/16.54	   new_show4(ww17, bc, bd) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.54	   new_show15(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.54	   new_primDivNatS4(ww126) -> Zero
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.54	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.54	
32.88/16.54	The set Q consists of the following terms:
32.88/16.54	
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.54	   new_primShowInt0(Neg(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.54	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.54	   new_primModNatS3(Succ(x0), Zero)
32.88/16.54	   new_show0(x0)
32.88/16.54	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Double)
32.88/16.54	   new_showsPrec(x0, x1, ty_Float)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_@0)
32.88/16.54	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.54	   new_show9(x0)
32.88/16.54	   new_primModNatS02(x0, x1)
32.88/16.54	   new_show15(x0)
32.88/16.54	   new_show3(x0, x1)
32.88/16.54	   new_show8(x0)
32.88/16.54	   new_show11(x0)
32.88/16.54	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.54	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.54	   new_show(x0, x1, x2)
32.88/16.54	   new_show10(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.54	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.54	   new_psPs0(:(x0, x1), x2)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_primModNatS4(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.54	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_show1(x0)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.54	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.54	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_show6(x0, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.54	   new_show13(x0)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.54	   new_primModNatS3(Zero, Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.54	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.54	   new_div(x0, x1)
32.88/16.54	   new_primIntToChar(x0, x1)
32.88/16.54	   new_show14(x0, x1, x2, x3)
32.88/16.54	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.54	   new_primModNatS3(Zero, Succ(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_Int)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.54	   new_show5(x0)
32.88/16.54	   new_primShowInt0(Pos(Zero))
32.88/16.54	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.54	   new_primDivNatS02(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_show12(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.54	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_primModNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.54	   new_psPs0([], x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.54	   new_show2(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.54	   new_show7(x0)
32.88/16.54	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.54	   new_show4(x0, x1, x2)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.54	   new_showsPrec(x0, x1, ty_Char)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.54	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.54	   new_primDivNatS4(x0)
32.88/16.54	   new_primDivNatS3(Zero, Zero)
32.88/16.54	
32.88/16.54	We have to consider all minimal (P,Q,R)-chains.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(82) DependencyGraphProof (EQUIVALENT)
32.88/16.54	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(83)
32.88/16.54	Obligation:
32.88/16.54	Q DP problem:
32.88/16.54	The TRS P consists of the following rules:
32.88/16.54	
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	
32.88/16.54	The TRS R consists of the following rules:
32.88/16.54	
32.88/16.54	   new_show2(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show6(ww17, be) -> error([])
32.88/16.54	   new_show(ww17, bg, bh) -> error([])
32.88/16.54	   new_show7(ww17) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.54	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show1(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.54	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.54	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_show3(ww17, ba) -> error([])
32.88/16.54	   new_show8(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.54	   new_primModNatS4(ww122) -> Zero
32.88/16.54	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.54	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.54	   new_show0(ww17) -> error([])
32.88/16.54	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.54	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.54	   new_show9(ww17) -> error([])
32.88/16.54	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show13(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.54	   new_psPs0([], ww56) -> ww56
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.54	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.54	   new_show5(ww17) -> error([])
32.88/16.54	   new_show12(ww17, ca) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.54	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.54	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.54	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.54	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.54	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.54	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.54	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.54	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_show11(ww17) -> error([])
32.88/16.54	   new_show4(ww17, bc, bd) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.54	   new_show15(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.54	   new_primDivNatS4(ww126) -> Zero
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.54	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.54	
32.88/16.54	The set Q consists of the following terms:
32.88/16.54	
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.54	   new_primShowInt0(Neg(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.54	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.54	   new_primModNatS3(Succ(x0), Zero)
32.88/16.54	   new_show0(x0)
32.88/16.54	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Double)
32.88/16.54	   new_showsPrec(x0, x1, ty_Float)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_@0)
32.88/16.54	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.54	   new_show9(x0)
32.88/16.54	   new_primModNatS02(x0, x1)
32.88/16.54	   new_show15(x0)
32.88/16.54	   new_show3(x0, x1)
32.88/16.54	   new_show8(x0)
32.88/16.54	   new_show11(x0)
32.88/16.54	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.54	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.54	   new_show(x0, x1, x2)
32.88/16.54	   new_show10(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.54	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.54	   new_psPs0(:(x0, x1), x2)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_primModNatS4(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.54	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_show1(x0)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.54	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.54	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_show6(x0, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.54	   new_show13(x0)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.54	   new_primModNatS3(Zero, Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.54	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.54	   new_div(x0, x1)
32.88/16.54	   new_primIntToChar(x0, x1)
32.88/16.54	   new_show14(x0, x1, x2, x3)
32.88/16.54	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.54	   new_primModNatS3(Zero, Succ(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_Int)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.54	   new_show5(x0)
32.88/16.54	   new_primShowInt0(Pos(Zero))
32.88/16.54	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.54	   new_primDivNatS02(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_show12(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.54	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_primModNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.54	   new_psPs0([], x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.54	   new_show2(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.54	   new_show7(x0)
32.88/16.54	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.54	   new_show4(x0, x1, x2)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.54	   new_showsPrec(x0, x1, ty_Char)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.54	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.54	   new_primDivNatS4(x0)
32.88/16.54	   new_primDivNatS3(Zero, Zero)
32.88/16.54	
32.88/16.54	We have to consider all minimal (P,Q,R)-chains.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(84) TransformationProof (EQUIVALENT)
32.88/16.54	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.54	
32.88/16.54	   (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))
32.88/16.54	   (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))
32.88/16.54	
32.88/16.54	
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(85)
32.88/16.54	Obligation:
32.88/16.54	Q DP problem:
32.88/16.54	The TRS P consists of the following rules:
32.88/16.54	
32.88/16.54	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	
32.88/16.54	The TRS R consists of the following rules:
32.88/16.54	
32.88/16.54	   new_show2(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show6(ww17, be) -> error([])
32.88/16.54	   new_show(ww17, bg, bh) -> error([])
32.88/16.54	   new_show7(ww17) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.54	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show1(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.54	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.54	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_show3(ww17, ba) -> error([])
32.88/16.54	   new_show8(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.54	   new_primModNatS4(ww122) -> Zero
32.88/16.54	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.54	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.54	   new_show0(ww17) -> error([])
32.88/16.54	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.54	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.54	   new_show9(ww17) -> error([])
32.88/16.54	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show13(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.54	   new_psPs0([], ww56) -> ww56
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.54	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.54	   new_show5(ww17) -> error([])
32.88/16.54	   new_show12(ww17, ca) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.54	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.54	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.54	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.54	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.54	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.54	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.54	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.54	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_show11(ww17) -> error([])
32.88/16.54	   new_show4(ww17, bc, bd) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.54	   new_show15(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.54	   new_primDivNatS4(ww126) -> Zero
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.54	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.54	
32.88/16.54	The set Q consists of the following terms:
32.88/16.54	
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.54	   new_primShowInt0(Neg(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.54	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.54	   new_primModNatS3(Succ(x0), Zero)
32.88/16.54	   new_show0(x0)
32.88/16.54	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Double)
32.88/16.54	   new_showsPrec(x0, x1, ty_Float)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_@0)
32.88/16.54	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.54	   new_show9(x0)
32.88/16.54	   new_primModNatS02(x0, x1)
32.88/16.54	   new_show15(x0)
32.88/16.54	   new_show3(x0, x1)
32.88/16.54	   new_show8(x0)
32.88/16.54	   new_show11(x0)
32.88/16.54	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.54	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.54	   new_show(x0, x1, x2)
32.88/16.54	   new_show10(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.54	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.54	   new_psPs0(:(x0, x1), x2)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_primModNatS4(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.54	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_show1(x0)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.54	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.54	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_show6(x0, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.54	   new_show13(x0)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.54	   new_primModNatS3(Zero, Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.54	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.54	   new_div(x0, x1)
32.88/16.54	   new_primIntToChar(x0, x1)
32.88/16.54	   new_show14(x0, x1, x2, x3)
32.88/16.54	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.54	   new_primModNatS3(Zero, Succ(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_Int)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.54	   new_show5(x0)
32.88/16.54	   new_primShowInt0(Pos(Zero))
32.88/16.54	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.54	   new_primDivNatS02(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_show12(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.54	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_primModNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.54	   new_psPs0([], x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.54	   new_show2(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.54	   new_show7(x0)
32.88/16.54	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.54	   new_show4(x0, x1, x2)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.54	   new_showsPrec(x0, x1, ty_Char)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.54	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.54	   new_primDivNatS4(x0)
32.88/16.54	   new_primDivNatS3(Zero, Zero)
32.88/16.54	
32.88/16.54	We have to consider all minimal (P,Q,R)-chains.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(86) DependencyGraphProof (EQUIVALENT)
32.88/16.54	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(87)
32.88/16.54	Obligation:
32.88/16.54	Q DP problem:
32.88/16.54	The TRS P consists of the following rules:
32.88/16.54	
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	
32.88/16.54	The TRS R consists of the following rules:
32.88/16.54	
32.88/16.54	   new_show2(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show6(ww17, be) -> error([])
32.88/16.54	   new_show(ww17, bg, bh) -> error([])
32.88/16.54	   new_show7(ww17) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.54	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show1(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.54	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.54	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_show3(ww17, ba) -> error([])
32.88/16.54	   new_show8(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.54	   new_primModNatS4(ww122) -> Zero
32.88/16.54	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.54	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.54	   new_show0(ww17) -> error([])
32.88/16.54	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.54	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.54	   new_show9(ww17) -> error([])
32.88/16.54	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show13(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.54	   new_psPs0([], ww56) -> ww56
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.54	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.54	   new_show5(ww17) -> error([])
32.88/16.54	   new_show12(ww17, ca) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.54	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.54	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.54	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.54	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.54	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.54	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.54	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.54	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_show11(ww17) -> error([])
32.88/16.54	   new_show4(ww17, bc, bd) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.54	   new_show15(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.54	   new_primDivNatS4(ww126) -> Zero
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.54	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.54	
32.88/16.54	The set Q consists of the following terms:
32.88/16.54	
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.54	   new_primShowInt0(Neg(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.54	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.54	   new_primModNatS3(Succ(x0), Zero)
32.88/16.54	   new_show0(x0)
32.88/16.54	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Double)
32.88/16.54	   new_showsPrec(x0, x1, ty_Float)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_@0)
32.88/16.54	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.54	   new_show9(x0)
32.88/16.54	   new_primModNatS02(x0, x1)
32.88/16.54	   new_show15(x0)
32.88/16.54	   new_show3(x0, x1)
32.88/16.54	   new_show8(x0)
32.88/16.54	   new_show11(x0)
32.88/16.54	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.54	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.54	   new_show(x0, x1, x2)
32.88/16.54	   new_show10(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.54	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.54	   new_psPs0(:(x0, x1), x2)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_primModNatS4(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.54	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_show1(x0)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.54	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.54	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_show6(x0, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.54	   new_show13(x0)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.54	   new_primModNatS3(Zero, Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.54	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.54	   new_div(x0, x1)
32.88/16.54	   new_primIntToChar(x0, x1)
32.88/16.54	   new_show14(x0, x1, x2, x3)
32.88/16.54	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.54	   new_primModNatS3(Zero, Succ(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_Int)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.54	   new_show5(x0)
32.88/16.54	   new_primShowInt0(Pos(Zero))
32.88/16.54	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.54	   new_primDivNatS02(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_show12(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.54	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_primModNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.54	   new_psPs0([], x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.54	   new_show2(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.54	   new_show7(x0)
32.88/16.54	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.54	   new_show4(x0, x1, x2)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.54	   new_showsPrec(x0, x1, ty_Char)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.54	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.54	   new_primDivNatS4(x0)
32.88/16.54	   new_primDivNatS3(Zero, Zero)
32.88/16.54	
32.88/16.54	We have to consider all minimal (P,Q,R)-chains.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(88) TransformationProof (EQUIVALENT)
32.88/16.54	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.54	
32.88/16.54	   (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))
32.88/16.54	   (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))
32.88/16.54	
32.88/16.54	
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(89)
32.88/16.54	Obligation:
32.88/16.54	Q DP problem:
32.88/16.54	The TRS P consists of the following rules:
32.88/16.54	
32.88/16.54	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	
32.88/16.54	The TRS R consists of the following rules:
32.88/16.54	
32.88/16.54	   new_show2(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show6(ww17, be) -> error([])
32.88/16.54	   new_show(ww17, bg, bh) -> error([])
32.88/16.54	   new_show7(ww17) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.54	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show1(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.54	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.54	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_show3(ww17, ba) -> error([])
32.88/16.54	   new_show8(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.54	   new_primModNatS4(ww122) -> Zero
32.88/16.54	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.54	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.54	   new_show0(ww17) -> error([])
32.88/16.54	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.54	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.54	   new_show9(ww17) -> error([])
32.88/16.54	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show13(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.54	   new_psPs0([], ww56) -> ww56
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.54	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.54	   new_show5(ww17) -> error([])
32.88/16.54	   new_show12(ww17, ca) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.54	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.54	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.54	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.54	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.54	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.54	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.54	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.54	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_show11(ww17) -> error([])
32.88/16.54	   new_show4(ww17, bc, bd) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.54	   new_show15(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.54	   new_primDivNatS4(ww126) -> Zero
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.54	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.54	
32.88/16.54	The set Q consists of the following terms:
32.88/16.54	
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.54	   new_primShowInt0(Neg(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.54	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.54	   new_primModNatS3(Succ(x0), Zero)
32.88/16.54	   new_show0(x0)
32.88/16.54	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Double)
32.88/16.54	   new_showsPrec(x0, x1, ty_Float)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_@0)
32.88/16.54	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.54	   new_show9(x0)
32.88/16.54	   new_primModNatS02(x0, x1)
32.88/16.54	   new_show15(x0)
32.88/16.54	   new_show3(x0, x1)
32.88/16.54	   new_show8(x0)
32.88/16.54	   new_show11(x0)
32.88/16.54	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.54	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.54	   new_show(x0, x1, x2)
32.88/16.54	   new_show10(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.54	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.54	   new_psPs0(:(x0, x1), x2)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_primModNatS4(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.54	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_show1(x0)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.54	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.54	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_show6(x0, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.54	   new_show13(x0)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.54	   new_primModNatS3(Zero, Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.54	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.54	   new_div(x0, x1)
32.88/16.54	   new_primIntToChar(x0, x1)
32.88/16.54	   new_show14(x0, x1, x2, x3)
32.88/16.54	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.54	   new_primModNatS3(Zero, Succ(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_Int)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.54	   new_show5(x0)
32.88/16.54	   new_primShowInt0(Pos(Zero))
32.88/16.54	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.54	   new_primDivNatS02(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_show12(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.54	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_primModNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.54	   new_psPs0([], x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.54	   new_show2(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.54	   new_show7(x0)
32.88/16.54	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.54	   new_show4(x0, x1, x2)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.54	   new_showsPrec(x0, x1, ty_Char)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.54	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.54	   new_primDivNatS4(x0)
32.88/16.54	   new_primDivNatS3(Zero, Zero)
32.88/16.54	
32.88/16.54	We have to consider all minimal (P,Q,R)-chains.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(90) DependencyGraphProof (EQUIVALENT)
32.88/16.54	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(91)
32.88/16.54	Obligation:
32.88/16.54	Q DP problem:
32.88/16.54	The TRS P consists of the following rules:
32.88/16.54	
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.54	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.54	   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)
32.88/16.54	   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)
32.88/16.54	
32.88/16.54	The TRS R consists of the following rules:
32.88/16.54	
32.88/16.54	   new_show2(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show6(ww17, be) -> error([])
32.88/16.54	   new_show(ww17, bg, bh) -> error([])
32.88/16.54	   new_show7(ww17) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.54	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show1(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.54	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.54	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.54	   new_show3(ww17, ba) -> error([])
32.88/16.54	   new_show8(ww17) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.54	   new_primModNatS4(ww122) -> Zero
32.88/16.54	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.54	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.54	   new_show0(ww17) -> error([])
32.88/16.54	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.54	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.54	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.54	   new_show9(ww17) -> error([])
32.88/16.54	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show13(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.54	   new_psPs0([], ww56) -> ww56
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.54	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.54	   new_show5(ww17) -> error([])
32.88/16.54	   new_show12(ww17, ca) -> error([])
32.88/16.54	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.54	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.54	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.54	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.54	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.54	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.54	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.54	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.54	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.54	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.54	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.54	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.54	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.54	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.54	   new_show11(ww17) -> error([])
32.88/16.54	   new_show4(ww17, bc, bd) -> error([])
32.88/16.54	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.54	   new_show15(ww17) -> error([])
32.88/16.54	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.54	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.54	   new_primDivNatS4(ww126) -> Zero
32.88/16.54	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.54	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.54	
32.88/16.54	The set Q consists of the following terms:
32.88/16.54	
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.54	   new_primShowInt0(Neg(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.54	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.54	   new_primModNatS3(Succ(x0), Zero)
32.88/16.54	   new_show0(x0)
32.88/16.54	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Double)
32.88/16.54	   new_showsPrec(x0, x1, ty_Float)
32.88/16.54	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_@0)
32.88/16.54	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.54	   new_show9(x0)
32.88/16.54	   new_primModNatS02(x0, x1)
32.88/16.54	   new_show15(x0)
32.88/16.54	   new_show3(x0, x1)
32.88/16.54	   new_show8(x0)
32.88/16.54	   new_show11(x0)
32.88/16.54	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.54	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.54	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.54	   new_show(x0, x1, x2)
32.88/16.54	   new_show10(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.54	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.54	   new_psPs0(:(x0, x1), x2)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_primModNatS4(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.54	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.54	   new_show1(x0)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.54	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.54	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_show6(x0, x1)
32.88/16.54	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.54	   new_show13(x0)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.54	   new_primModNatS3(Zero, Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.54	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.54	   new_div(x0, x1)
32.88/16.54	   new_primIntToChar(x0, x1)
32.88/16.54	   new_show14(x0, x1, x2, x3)
32.88/16.54	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.54	   new_primModNatS3(Zero, Succ(x0))
32.88/16.54	   new_showsPrec(x0, x1, ty_Int)
32.88/16.54	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.54	   new_show5(x0)
32.88/16.54	   new_primShowInt0(Pos(Zero))
32.88/16.54	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.54	   new_primDivNatS02(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.54	   new_show12(x0, x1)
32.88/16.54	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.54	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.54	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.54	   new_primModNatS2(Zero, Zero, x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.54	   new_psPs0([], x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.54	   new_show2(x0)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.54	   new_show7(x0)
32.88/16.54	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.54	   new_show4(x0, x1, x2)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.54	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.54	   new_showsPrec(x0, x1, ty_Char)
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.54	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.54	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.54	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.54	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.54	   new_primDivNatS4(x0)
32.88/16.54	   new_primDivNatS3(Zero, Zero)
32.88/16.54	
32.88/16.54	We have to consider all minimal (P,Q,R)-chains.
32.88/16.54	----------------------------------------
32.88/16.54	
32.88/16.54	(92) TransformationProof (EQUIVALENT)
32.88/16.54	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.55	
32.88/16.55	   (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))
32.88/16.55	   (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))
32.88/16.55	
32.88/16.55	
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(93)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.55	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.55	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.55	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	
32.88/16.55	The TRS R consists of the following rules:
32.88/16.55	
32.88/16.55	   new_show2(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show6(ww17, be) -> error([])
32.88/16.55	   new_show(ww17, bg, bh) -> error([])
32.88/16.55	   new_show7(ww17) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.55	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show1(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.55	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.55	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_show3(ww17, ba) -> error([])
32.88/16.55	   new_show8(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.55	   new_primModNatS4(ww122) -> Zero
32.88/16.55	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.55	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.55	   new_show0(ww17) -> error([])
32.88/16.55	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.55	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.55	   new_show9(ww17) -> error([])
32.88/16.55	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show13(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.55	   new_psPs0([], ww56) -> ww56
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.55	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.55	   new_show5(ww17) -> error([])
32.88/16.55	   new_show12(ww17, ca) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.55	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.55	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.55	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.55	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.55	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.55	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.55	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.55	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.55	   new_show11(ww17) -> error([])
32.88/16.55	   new_show4(ww17, bc, bd) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.55	   new_show15(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.55	   new_primDivNatS4(ww126) -> Zero
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.55	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.55	
32.88/16.55	The set Q consists of the following terms:
32.88/16.55	
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.55	   new_primShowInt0(Neg(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.55	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.55	   new_primModNatS3(Succ(x0), Zero)
32.88/16.55	   new_show0(x0)
32.88/16.55	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Double)
32.88/16.55	   new_showsPrec(x0, x1, ty_Float)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_@0)
32.88/16.55	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.55	   new_show9(x0)
32.88/16.55	   new_primModNatS02(x0, x1)
32.88/16.55	   new_show15(x0)
32.88/16.55	   new_show3(x0, x1)
32.88/16.55	   new_show8(x0)
32.88/16.55	   new_show11(x0)
32.88/16.55	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.55	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.55	   new_show(x0, x1, x2)
32.88/16.55	   new_show10(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.55	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.55	   new_psPs0(:(x0, x1), x2)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_primModNatS4(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.55	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_show1(x0)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.55	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.55	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_show6(x0, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.55	   new_show13(x0)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.55	   new_primModNatS3(Zero, Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.55	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.55	   new_div(x0, x1)
32.88/16.55	   new_primIntToChar(x0, x1)
32.88/16.55	   new_show14(x0, x1, x2, x3)
32.88/16.55	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.55	   new_primModNatS3(Zero, Succ(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_Int)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.55	   new_show5(x0)
32.88/16.55	   new_primShowInt0(Pos(Zero))
32.88/16.55	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.55	   new_primDivNatS02(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_show12(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.55	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_primModNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.55	   new_psPs0([], x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.55	   new_show2(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.55	   new_show7(x0)
32.88/16.55	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.55	   new_show4(x0, x1, x2)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.55	   new_showsPrec(x0, x1, ty_Char)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.55	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.55	   new_primDivNatS4(x0)
32.88/16.55	   new_primDivNatS3(Zero, Zero)
32.88/16.55	
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(94) DependencyGraphProof (EQUIVALENT)
32.88/16.55	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(95)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.55	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.55	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.55	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	
32.88/16.55	The TRS R consists of the following rules:
32.88/16.55	
32.88/16.55	   new_show2(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show6(ww17, be) -> error([])
32.88/16.55	   new_show(ww17, bg, bh) -> error([])
32.88/16.55	   new_show7(ww17) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.55	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show1(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.55	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.55	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_show3(ww17, ba) -> error([])
32.88/16.55	   new_show8(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.55	   new_primModNatS4(ww122) -> Zero
32.88/16.55	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.55	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.55	   new_show0(ww17) -> error([])
32.88/16.55	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.55	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.55	   new_show9(ww17) -> error([])
32.88/16.55	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show13(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.55	   new_psPs0([], ww56) -> ww56
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.55	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.55	   new_show5(ww17) -> error([])
32.88/16.55	   new_show12(ww17, ca) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.55	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.55	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.55	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.55	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.55	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.55	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.55	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.55	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.55	   new_show11(ww17) -> error([])
32.88/16.55	   new_show4(ww17, bc, bd) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.55	   new_show15(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.55	   new_primDivNatS4(ww126) -> Zero
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.55	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.55	
32.88/16.55	The set Q consists of the following terms:
32.88/16.55	
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.55	   new_primShowInt0(Neg(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.55	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.55	   new_primModNatS3(Succ(x0), Zero)
32.88/16.55	   new_show0(x0)
32.88/16.55	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Double)
32.88/16.55	   new_showsPrec(x0, x1, ty_Float)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_@0)
32.88/16.55	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.55	   new_show9(x0)
32.88/16.55	   new_primModNatS02(x0, x1)
32.88/16.55	   new_show15(x0)
32.88/16.55	   new_show3(x0, x1)
32.88/16.55	   new_show8(x0)
32.88/16.55	   new_show11(x0)
32.88/16.55	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.55	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.55	   new_show(x0, x1, x2)
32.88/16.55	   new_show10(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.55	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.55	   new_psPs0(:(x0, x1), x2)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_primModNatS4(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.55	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_show1(x0)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.55	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.55	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_show6(x0, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.55	   new_show13(x0)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.55	   new_primModNatS3(Zero, Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.55	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.55	   new_div(x0, x1)
32.88/16.55	   new_primIntToChar(x0, x1)
32.88/16.55	   new_show14(x0, x1, x2, x3)
32.88/16.55	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.55	   new_primModNatS3(Zero, Succ(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_Int)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.55	   new_show5(x0)
32.88/16.55	   new_primShowInt0(Pos(Zero))
32.88/16.55	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.55	   new_primDivNatS02(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_show12(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.55	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_primModNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.55	   new_psPs0([], x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.55	   new_show2(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.55	   new_show7(x0)
32.88/16.55	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.55	   new_show4(x0, x1, x2)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.55	   new_showsPrec(x0, x1, ty_Char)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.55	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.55	   new_primDivNatS4(x0)
32.88/16.55	   new_primDivNatS3(Zero, Zero)
32.88/16.55	
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(96) TransformationProof (EQUIVALENT)
32.88/16.55	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.55	
32.88/16.55	   (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))
32.88/16.55	   (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))
32.88/16.55	
32.88/16.55	
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(97)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.55	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.55	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	
32.88/16.55	The TRS R consists of the following rules:
32.88/16.55	
32.88/16.55	   new_show2(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show6(ww17, be) -> error([])
32.88/16.55	   new_show(ww17, bg, bh) -> error([])
32.88/16.55	   new_show7(ww17) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.55	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show1(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.55	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.55	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_show3(ww17, ba) -> error([])
32.88/16.55	   new_show8(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.55	   new_primModNatS4(ww122) -> Zero
32.88/16.55	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.55	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.55	   new_show0(ww17) -> error([])
32.88/16.55	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.55	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.55	   new_show9(ww17) -> error([])
32.88/16.55	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show13(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.55	   new_psPs0([], ww56) -> ww56
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.55	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.55	   new_show5(ww17) -> error([])
32.88/16.55	   new_show12(ww17, ca) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.55	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.55	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.55	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.55	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.55	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.55	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.55	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.55	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.55	   new_show11(ww17) -> error([])
32.88/16.55	   new_show4(ww17, bc, bd) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.55	   new_show15(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.55	   new_primDivNatS4(ww126) -> Zero
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.55	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.55	
32.88/16.55	The set Q consists of the following terms:
32.88/16.55	
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.55	   new_primShowInt0(Neg(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.55	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.55	   new_primModNatS3(Succ(x0), Zero)
32.88/16.55	   new_show0(x0)
32.88/16.55	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Double)
32.88/16.55	   new_showsPrec(x0, x1, ty_Float)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_@0)
32.88/16.55	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.55	   new_show9(x0)
32.88/16.55	   new_primModNatS02(x0, x1)
32.88/16.55	   new_show15(x0)
32.88/16.55	   new_show3(x0, x1)
32.88/16.55	   new_show8(x0)
32.88/16.55	   new_show11(x0)
32.88/16.55	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.55	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.55	   new_show(x0, x1, x2)
32.88/16.55	   new_show10(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.55	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.55	   new_psPs0(:(x0, x1), x2)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_primModNatS4(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.55	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_show1(x0)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.55	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.55	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_show6(x0, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.55	   new_show13(x0)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.55	   new_primModNatS3(Zero, Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.55	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.55	   new_div(x0, x1)
32.88/16.55	   new_primIntToChar(x0, x1)
32.88/16.55	   new_show14(x0, x1, x2, x3)
32.88/16.55	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.55	   new_primModNatS3(Zero, Succ(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_Int)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.55	   new_show5(x0)
32.88/16.55	   new_primShowInt0(Pos(Zero))
32.88/16.55	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.55	   new_primDivNatS02(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_show12(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.55	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_primModNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.55	   new_psPs0([], x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.55	   new_show2(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.55	   new_show7(x0)
32.88/16.55	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.55	   new_show4(x0, x1, x2)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.55	   new_showsPrec(x0, x1, ty_Char)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.55	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.55	   new_primDivNatS4(x0)
32.88/16.55	   new_primDivNatS3(Zero, Zero)
32.88/16.55	
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(98) DependencyGraphProof (EQUIVALENT)
32.88/16.55	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(99)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb)
32.88/16.55	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.55	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	
32.88/16.55	The TRS R consists of the following rules:
32.88/16.55	
32.88/16.55	   new_show2(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show6(ww17, be) -> error([])
32.88/16.55	   new_show(ww17, bg, bh) -> error([])
32.88/16.55	   new_show7(ww17) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.55	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show1(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.55	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.55	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_show3(ww17, ba) -> error([])
32.88/16.55	   new_show8(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.55	   new_primModNatS4(ww122) -> Zero
32.88/16.55	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.55	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.55	   new_show0(ww17) -> error([])
32.88/16.55	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.55	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.55	   new_show9(ww17) -> error([])
32.88/16.55	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show13(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.55	   new_psPs0([], ww56) -> ww56
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.55	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.55	   new_show5(ww17) -> error([])
32.88/16.55	   new_show12(ww17, ca) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.55	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.55	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.55	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.55	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.55	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.55	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.55	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.55	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.55	   new_show11(ww17) -> error([])
32.88/16.55	   new_show4(ww17, bc, bd) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.55	   new_show15(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.55	   new_primDivNatS4(ww126) -> Zero
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.55	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.55	
32.88/16.55	The set Q consists of the following terms:
32.88/16.55	
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.55	   new_primShowInt0(Neg(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.55	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.55	   new_primModNatS3(Succ(x0), Zero)
32.88/16.55	   new_show0(x0)
32.88/16.55	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Double)
32.88/16.55	   new_showsPrec(x0, x1, ty_Float)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_@0)
32.88/16.55	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.55	   new_show9(x0)
32.88/16.55	   new_primModNatS02(x0, x1)
32.88/16.55	   new_show15(x0)
32.88/16.55	   new_show3(x0, x1)
32.88/16.55	   new_show8(x0)
32.88/16.55	   new_show11(x0)
32.88/16.55	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.55	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.55	   new_show(x0, x1, x2)
32.88/16.55	   new_show10(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.55	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.55	   new_psPs0(:(x0, x1), x2)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_primModNatS4(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.55	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_show1(x0)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.55	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.55	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_show6(x0, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.55	   new_show13(x0)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.55	   new_primModNatS3(Zero, Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.55	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.55	   new_div(x0, x1)
32.88/16.55	   new_primIntToChar(x0, x1)
32.88/16.55	   new_show14(x0, x1, x2, x3)
32.88/16.55	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.55	   new_primModNatS3(Zero, Succ(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_Int)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.55	   new_show5(x0)
32.88/16.55	   new_primShowInt0(Pos(Zero))
32.88/16.55	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.55	   new_primDivNatS02(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_show12(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.55	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_primModNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.55	   new_psPs0([], x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.55	   new_show2(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.55	   new_show7(x0)
32.88/16.55	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.55	   new_show4(x0, x1, x2)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.55	   new_showsPrec(x0, x1, ty_Char)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.55	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.55	   new_primDivNatS4(x0)
32.88/16.55	   new_primDivNatS3(Zero, Zero)
32.88/16.55	
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(100) TransformationProof (EQUIVALENT)
32.88/16.55	By instantiating [LPAR04] the rule new_showParen(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_pt(ww18, ww19, ww20, ww21, ww22, bb) we obtained the following new rules [LPAR04]:
32.88/16.55	
32.88/16.55	   (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)))
32.88/16.55	   (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)))
32.88/16.55	
32.88/16.55	
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(101)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_pt(ww18, ww19, ww20, :%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.55	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	   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))
32.88/16.55	   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))
32.88/16.55	
32.88/16.55	The TRS R consists of the following rules:
32.88/16.55	
32.88/16.55	   new_show2(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show6(ww17, be) -> error([])
32.88/16.55	   new_show(ww17, bg, bh) -> error([])
32.88/16.55	   new_show7(ww17) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.55	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show1(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.55	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.55	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_show3(ww17, ba) -> error([])
32.88/16.55	   new_show8(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.55	   new_primModNatS4(ww122) -> Zero
32.88/16.55	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.55	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.55	   new_show0(ww17) -> error([])
32.88/16.55	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.55	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.55	   new_show9(ww17) -> error([])
32.88/16.55	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show13(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.55	   new_psPs0([], ww56) -> ww56
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.55	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.55	   new_show5(ww17) -> error([])
32.88/16.55	   new_show12(ww17, ca) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.55	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.55	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.55	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.55	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.55	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.55	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.55	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.55	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.55	   new_show11(ww17) -> error([])
32.88/16.55	   new_show4(ww17, bc, bd) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.55	   new_show15(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.55	   new_primDivNatS4(ww126) -> Zero
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.55	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.55	
32.88/16.55	The set Q consists of the following terms:
32.88/16.55	
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.55	   new_primShowInt0(Neg(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.55	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.55	   new_primModNatS3(Succ(x0), Zero)
32.88/16.55	   new_show0(x0)
32.88/16.55	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Double)
32.88/16.55	   new_showsPrec(x0, x1, ty_Float)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_@0)
32.88/16.55	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.55	   new_show9(x0)
32.88/16.55	   new_primModNatS02(x0, x1)
32.88/16.55	   new_show15(x0)
32.88/16.55	   new_show3(x0, x1)
32.88/16.55	   new_show8(x0)
32.88/16.55	   new_show11(x0)
32.88/16.55	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.55	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.55	   new_show(x0, x1, x2)
32.88/16.55	   new_show10(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.55	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.55	   new_psPs0(:(x0, x1), x2)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_primModNatS4(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.55	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_show1(x0)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.55	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.55	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_show6(x0, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.55	   new_show13(x0)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.55	   new_primModNatS3(Zero, Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.55	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.55	   new_div(x0, x1)
32.88/16.55	   new_primIntToChar(x0, x1)
32.88/16.55	   new_show14(x0, x1, x2, x3)
32.88/16.55	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.55	   new_primModNatS3(Zero, Succ(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_Int)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.55	   new_show5(x0)
32.88/16.55	   new_primShowInt0(Pos(Zero))
32.88/16.55	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.55	   new_primDivNatS02(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_show12(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.55	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_primModNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.55	   new_psPs0([], x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.55	   new_show2(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.55	   new_show7(x0)
32.88/16.55	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.55	   new_show4(x0, x1, x2)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.55	   new_showsPrec(x0, x1, ty_Char)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.55	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.55	   new_primDivNatS4(x0)
32.88/16.55	   new_primDivNatS3(Zero, Zero)
32.88/16.55	
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(102) DependencyGraphProof (EQUIVALENT)
32.88/16.55	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(103)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf)
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	
32.88/16.55	The TRS R consists of the following rules:
32.88/16.55	
32.88/16.55	   new_show2(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show6(ww17, be) -> error([])
32.88/16.55	   new_show(ww17, bg, bh) -> error([])
32.88/16.55	   new_show7(ww17) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.55	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show1(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.55	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.55	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_show3(ww17, ba) -> error([])
32.88/16.55	   new_show8(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.55	   new_primModNatS4(ww122) -> Zero
32.88/16.55	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.55	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.55	   new_show0(ww17) -> error([])
32.88/16.55	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.55	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.55	   new_show9(ww17) -> error([])
32.88/16.55	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show13(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.55	   new_psPs0([], ww56) -> ww56
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.55	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.55	   new_show5(ww17) -> error([])
32.88/16.55	   new_show12(ww17, ca) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.55	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.55	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.55	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.55	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.55	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.55	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.55	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.55	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.55	   new_show11(ww17) -> error([])
32.88/16.55	   new_show4(ww17, bc, bd) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.55	   new_show15(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.55	   new_primDivNatS4(ww126) -> Zero
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.55	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.55	
32.88/16.55	The set Q consists of the following terms:
32.88/16.55	
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.55	   new_primShowInt0(Neg(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.55	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.55	   new_primModNatS3(Succ(x0), Zero)
32.88/16.55	   new_show0(x0)
32.88/16.55	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Double)
32.88/16.55	   new_showsPrec(x0, x1, ty_Float)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_@0)
32.88/16.55	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.55	   new_show9(x0)
32.88/16.55	   new_primModNatS02(x0, x1)
32.88/16.55	   new_show15(x0)
32.88/16.55	   new_show3(x0, x1)
32.88/16.55	   new_show8(x0)
32.88/16.55	   new_show11(x0)
32.88/16.55	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.55	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.55	   new_show(x0, x1, x2)
32.88/16.55	   new_show10(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.55	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.55	   new_psPs0(:(x0, x1), x2)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_primModNatS4(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.55	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_show1(x0)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.55	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.55	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_show6(x0, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.55	   new_show13(x0)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.55	   new_primModNatS3(Zero, Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.55	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.55	   new_div(x0, x1)
32.88/16.55	   new_primIntToChar(x0, x1)
32.88/16.55	   new_show14(x0, x1, x2, x3)
32.88/16.55	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.55	   new_primModNatS3(Zero, Succ(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_Int)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.55	   new_show5(x0)
32.88/16.55	   new_primShowInt0(Pos(Zero))
32.88/16.55	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.55	   new_primDivNatS02(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_show12(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.55	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_primModNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.55	   new_psPs0([], x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.55	   new_show2(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.55	   new_show7(x0)
32.88/16.55	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.55	   new_show4(x0, x1, x2)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.55	   new_showsPrec(x0, x1, ty_Char)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.55	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.55	   new_primDivNatS4(x0)
32.88/16.55	   new_primDivNatS3(Zero, Zero)
32.88/16.55	
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(104) TransformationProof (EQUIVALENT)
32.88/16.55	By instantiating [LPAR04] the rule new_showParen(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, :(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), new_showsPrec(ww21, ww22, bf)))), bf, bf) we obtained the following new rules [LPAR04]:
32.88/16.55	
32.88/16.55	   (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))
32.88/16.55	   (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))
32.88/16.55	
32.88/16.55	
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(105)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	   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)
32.88/16.55	
32.88/16.55	The TRS R consists of the following rules:
32.88/16.55	
32.88/16.55	   new_show2(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Zero, Succ(ww1210), ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Char, bb) -> new_psPs0(new_show13(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(app(ty_@3, cb), cc), cd), bb) -> new_psPs0(new_show14(ww17, cb, cc, cd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show6(ww17, be) -> error([])
32.88/16.55	   new_show(ww17, bg, bh) -> error([])
32.88/16.55	   new_show7(ww17) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Ordering) -> new_psPs0(new_show9(ww21), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOError, bb) -> new_psPs0(new_show5(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_IOErrorKind, bb) -> new_psPs0(new_show7(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primShowInt0(Neg(ww170)) -> :(Char(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))))))))))))), new_primShowInt0(Pos(ww170)))
32.88/16.55	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_Either, bg), bh), bb) -> new_psPs0(new_show(ww17, bg, bh), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show1(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Double, bb) -> new_psPs0(new_show11(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_HugsException, bb) -> new_psPs0(new_show0(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.55	   new_primModNatS3(Succ(ww660), Zero) -> new_primModNatS2(Succ(ww660), Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Bool) -> new_psPs0(new_show2(ww21), ww22)
32.88/16.55	   new_primModNatS2(Zero, Zero, ww122) -> new_primModNatS4(ww122)
32.88/16.55	   new_show3(ww17, ba) -> error([])
32.88/16.55	   new_show8(ww17) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS2(ww1200, ww1210, ww122)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(app(ty_@3, de), df), dg)) -> new_psPs0(new_show14(ww21, de, df, dg), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Float) -> new_psPs0(new_show15(ww21), ww22)
32.88/16.55	   new_primModNatS4(ww122) -> Zero
32.88/16.55	   new_psPs0(:(ww580, ww581), ww56) -> :(ww580, new_psPs0(ww581, ww56))
32.88/16.55	   new_primModNatS3(Zero, Succ(ww670)) -> Succ(Zero)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_Maybe, ca), bb) -> new_psPs0(new_show12(ww17, ca), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_[], ce)) -> new_psPs0(new_show3(ww21, ce), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_IO, da)) -> new_psPs0(new_show6(ww21, da), ww22)
32.88/16.55	   new_show0(ww17) -> error([])
32.88/16.55	   new_primIntToChar(ww66, ww67) -> Char(new_primModNatS3(ww66, ww67))
32.88/16.55	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS01(ww115, ww116, ww1170, ww1180)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_@0, bb) -> new_psPs0(new_show1(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.55	   new_showsPrec(ww21, ww22, ty_HugsException) -> new_psPs0(new_show0(ww21), ww22)
32.88/16.55	   new_show9(ww17) -> error([])
32.88/16.55	   new_showParen0(:%(ww170, ww171), ww18, ww19, ww20, ww21, ww22, app(ty_Ratio, bf), bb) -> new_showParen0(ww170, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww171, new_pt0(ww18, ww19, ww20, ww21, ww22, bf), bf, bf)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Int, bb) -> new_psPs0(new_show10(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show13(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(app(ty_@2, bc), bd), bb) -> new_psPs0(new_show4(ww17, bc, bd), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_show14(ww17, cb, cc, cd) -> error([])
32.88/16.55	   new_psPs0([], ww56) -> ww56
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_[], ba), bb) -> new_psPs0(new_show3(ww17, ba), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOErrorKind) -> new_psPs0(new_show7(ww21), ww22)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Succ(ww1180)) -> Succ(Succ(ww115))
32.88/16.55	   new_pt0(ww18, ww19, ww20, ww21, ww22, bb) -> new_psPs0(:(Char(Succ(ww18)), :(Char(Succ(ww19)), :(Char(Succ(ww20)), []))), new_showsPrec(ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Integer) -> new_psPs0(new_show8(ww21), ww22)
32.88/16.55	   new_show5(ww17) -> error([])
32.88/16.55	   new_show12(ww17, ca) -> error([])
32.88/16.55	   new_primModNatS2(Succ(ww1200), Zero, ww122) -> new_primModNatS3(ww1200, ww122)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Int) -> new_psPs0(new_show10(ww21), ww22)
32.88/16.55	   new_show10(ww17) -> new_primShowInt0(ww17)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_Either, db), dc)) -> new_psPs0(new_show(ww21, db, dc), ww22)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Bool, bb) -> new_psPs0(new_show2(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Char) -> new_psPs0(new_show13(ww21), ww22)
32.88/16.55	   new_showsPrec(ww21, ww22, app(ty_Maybe, dd)) -> new_psPs0(new_show12(ww21, dd), ww22)
32.88/16.55	   new_primModNatS02(ww115, ww116) -> new_primModNatS2(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Ordering, bb) -> new_psPs0(new_show9(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_Double) -> new_psPs0(new_show11(ww21), ww22)
32.88/16.55	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.55	   new_primShowInt0(Pos(Succ(ww1700))) -> new_psPs0(new_primShowInt0(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), :(new_primIntToChar(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), []))
32.88/16.55	   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))))))))))))))))))))))))))))))))))))))))))))))))), [])
32.88/16.55	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primModNatS01(ww115, ww116, Zero, Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primModNatS01(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS02(ww115, ww116)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, app(ty_IO, be), bb) -> new_psPs0(new_show6(ww17, be), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Float, bb) -> new_psPs0(new_show15(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.55	   new_primModNatS3(Zero, Zero) -> new_primModNatS2(Zero, Zero, Zero)
32.88/16.55	   new_showsPrec(ww21, ww22, app(app(ty_@2, cf), cg)) -> new_psPs0(new_show4(ww21, cf, cg), ww22)
32.88/16.55	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.55	   new_showsPrec(:%(ww210, ww211), ww22, app(ty_Ratio, h)) -> new_showParen0(ww210, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))))))))))))))))))))))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))))))))))))))))))))), ww211, ww22, h, h)
32.88/16.55	   new_show11(ww17) -> error([])
32.88/16.55	   new_show4(ww17, bc, bd) -> error([])
32.88/16.55	   new_showsPrec(ww21, ww22, ty_IOError) -> new_psPs0(new_show5(ww21), ww22)
32.88/16.55	   new_show15(ww17) -> error([])
32.88/16.55	   new_showParen0(ww17, ww18, ww19, ww20, ww21, ww22, ty_Integer, bb) -> new_psPs0(new_show8(ww17), new_pt0(ww18, ww19, ww20, ww21, ww22, bb))
32.88/16.55	   new_showsPrec(ww21, ww22, ty_@0) -> new_psPs0(new_show1(ww21), ww22)
32.88/16.55	   new_primDivNatS4(ww126) -> Zero
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.55	   new_primModNatS3(Succ(ww660), Succ(ww670)) -> new_primModNatS01(ww660, ww670, ww660, ww670)
32.88/16.55	
32.88/16.55	The set Q consists of the following terms:
32.88/16.55	
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(app(ty_@3, x6), x7), x8), x9)
32.88/16.55	   new_primShowInt0(Neg(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_IOError)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(:%(x0, x1), x2, x3, x4, x5, x6, app(ty_Ratio, x7), x8)
32.88/16.55	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.55	   new_primModNatS3(Succ(x0), Zero)
32.88/16.55	   new_show0(x0)
32.88/16.55	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Double)
32.88/16.55	   new_showsPrec(x0, x1, ty_Float)
32.88/16.55	   new_primModNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_@0)
32.88/16.55	   new_showsPrec(x0, x1, ty_Ordering)
32.88/16.55	   new_show9(x0)
32.88/16.55	   new_primModNatS02(x0, x1)
32.88/16.55	   new_show15(x0)
32.88/16.55	   new_show3(x0, x1)
32.88/16.55	   new_show8(x0)
32.88/16.55	   new_show11(x0)
32.88/16.55	   new_primModNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_showsPrec(x0, x1, ty_IOErrorKind)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Bool, x6)
32.88/16.55	   new_primModNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOError, x6)
32.88/16.55	   new_show(x0, x1, x2)
32.88/16.55	   new_show10(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Int, x6)
32.88/16.55	   new_showsPrec(x0, x1, ty_Integer)
32.88/16.55	   new_psPs0(:(x0, x1), x2)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_primModNatS4(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Ordering, x6)
32.88/16.55	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_show1(x0)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_IOErrorKind, x6)
32.88/16.55	   new_showsPrec(:%(x0, x1), x2, app(ty_Ratio, x3))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_@0, x6)
32.88/16.55	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_show6(x0, x1)
32.88/16.55	   new_showsPrec(x0, x1, ty_Bool)
32.88/16.55	   new_show13(x0)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_Maybe, x2))
32.88/16.55	   new_primModNatS3(Zero, Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_Either, x6), x7), x8)
32.88/16.55	   new_primShowInt0(Pos(Succ(x0)))
32.88/16.55	   new_div(x0, x1)
32.88/16.55	   new_primIntToChar(x0, x1)
32.88/16.55	   new_show14(x0, x1, x2, x3)
32.88/16.55	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.55	   new_primModNatS3(Zero, Succ(x0))
32.88/16.55	   new_showsPrec(x0, x1, ty_Int)
32.88/16.55	   new_primModNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Char, x6)
32.88/16.55	   new_show5(x0)
32.88/16.55	   new_primShowInt0(Pos(Zero))
32.88/16.55	   new_showsPrec(x0, x1, app(app(app(ty_@3, x2), x3), x4))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Integer, x6)
32.88/16.55	   new_primDivNatS02(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_show12(x0, x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_showsPrec(x0, x1, ty_HugsException)
32.88/16.55	   new_primModNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_primModNatS2(Zero, Zero, x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_Maybe, x6), x7)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_IO, x6), x7)
32.88/16.55	   new_psPs0([], x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(ty_[], x6), x7)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_@2, x2), x3))
32.88/16.55	   new_show2(x0)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Float, x6)
32.88/16.55	   new_show7(x0)
32.88/16.55	   new_pt0(x0, x1, x2, x3, x4, x5)
32.88/16.55	   new_show4(x0, x1, x2)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_[], x2))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_HugsException, x6)
32.88/16.55	   new_showsPrec(x0, x1, app(app(ty_Either, x2), x3))
32.88/16.55	   new_showsPrec(x0, x1, ty_Char)
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, ty_Double, x6)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_showsPrec(x0, x1, app(ty_IO, x2))
32.88/16.55	   new_primModNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_showParen0(x0, x1, x2, x3, x4, x5, app(app(ty_@2, x6), x7), x8)
32.88/16.55	   new_primDivNatS4(x0)
32.88/16.55	   new_primDivNatS3(Zero, Zero)
32.88/16.55	
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(106) QDPSizeChangeProof (EQUIVALENT)
32.88/16.55	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. 
32.88/16.55	
32.88/16.55	From the DPs we obtained the following set of size-change graphs:
32.88/16.55	*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)
32.88/16.55	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
32.88/16.55	
32.88/16.55	
32.88/16.55	*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)
32.88/16.55	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
32.88/16.55	
32.88/16.55	
32.88/16.55	*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)
32.88/16.55	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
32.88/16.55	
32.88/16.55	
32.88/16.55	*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)
32.88/16.55	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
32.88/16.55	
32.88/16.55	
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(107)
32.88/16.55	YES
32.88/16.55	
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(108)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primModNatS(Succ(ww1200), Zero, ww122) -> new_primModNatS1(ww1200, ww122)
32.88/16.55	   new_primModNatS1(Zero, Zero) -> new_primModNatS(Zero, Zero, Zero)
32.88/16.55	   new_primModNatS00(ww115, ww116) -> new_primModNatS(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	   new_primModNatS0(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	   new_primModNatS(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS(ww1200, ww1210, ww122)
32.88/16.55	   new_primModNatS0(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS0(ww115, ww116, ww1170, ww1180)
32.88/16.55	   new_primModNatS1(Succ(ww660), Succ(ww670)) -> new_primModNatS0(ww660, ww670, ww660, ww670)
32.88/16.55	   new_primModNatS0(ww115, ww116, Zero, Zero) -> new_primModNatS00(ww115, ww116)
32.88/16.55	   new_primModNatS1(Succ(ww660), Zero) -> new_primModNatS(Succ(ww660), Zero, Zero)
32.88/16.55	
32.88/16.55	R is empty.
32.88/16.55	Q is empty.
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(109) DependencyGraphProof (EQUIVALENT)
32.88/16.55	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(110)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primModNatS1(Succ(ww660), Succ(ww670)) -> new_primModNatS0(ww660, ww670, ww660, ww670)
32.88/16.55	   new_primModNatS0(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	   new_primModNatS(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS(ww1200, ww1210, ww122)
32.88/16.55	   new_primModNatS(Succ(ww1200), Zero, ww122) -> new_primModNatS1(ww1200, ww122)
32.88/16.55	   new_primModNatS1(Succ(ww660), Zero) -> new_primModNatS(Succ(ww660), Zero, Zero)
32.88/16.55	   new_primModNatS0(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS0(ww115, ww116, ww1170, ww1180)
32.88/16.55	   new_primModNatS0(ww115, ww116, Zero, Zero) -> new_primModNatS00(ww115, ww116)
32.88/16.55	   new_primModNatS00(ww115, ww116) -> new_primModNatS(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	
32.88/16.55	R is empty.
32.88/16.55	Q is empty.
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(111) QDPOrderProof (EQUIVALENT)
32.88/16.55	We use the reduction pair processor [LPAR04,JAR06].
32.88/16.55	
32.88/16.55	
32.88/16.55	The following pairs can be oriented strictly and are deleted.
32.88/16.55	
32.88/16.55	   new_primModNatS1(Succ(ww660), Succ(ww670)) -> new_primModNatS0(ww660, ww670, ww660, ww670)
32.88/16.55	   new_primModNatS(Succ(ww1200), Succ(ww1210), ww122) -> new_primModNatS(ww1200, ww1210, ww122)
32.88/16.55	   new_primModNatS1(Succ(ww660), Zero) -> new_primModNatS(Succ(ww660), Zero, Zero)
32.88/16.55	The remaining pairs can at least be oriented weakly.
32.88/16.55	Used ordering:  Polynomial interpretation [POLO]:
32.88/16.55	
32.88/16.55	   POL(Succ(x_1)) = 1 + x_1
32.88/16.55	   POL(Zero) = 0
32.88/16.55	   POL(new_primModNatS(x_1, x_2, x_3)) = x_1
32.88/16.55	   POL(new_primModNatS0(x_1, x_2, x_3, x_4)) = 1 + x_1
32.88/16.55	   POL(new_primModNatS00(x_1, x_2)) = 1 + x_1
32.88/16.55	   POL(new_primModNatS1(x_1, x_2)) = 1 + x_1
32.88/16.55	
32.88/16.55	The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented:
32.88/16.55	none
32.88/16.55	
32.88/16.55	
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(112)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primModNatS0(ww115, ww116, Succ(ww1170), Zero) -> new_primModNatS(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	   new_primModNatS(Succ(ww1200), Zero, ww122) -> new_primModNatS1(ww1200, ww122)
32.88/16.55	   new_primModNatS0(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS0(ww115, ww116, ww1170, ww1180)
32.88/16.55	   new_primModNatS0(ww115, ww116, Zero, Zero) -> new_primModNatS00(ww115, ww116)
32.88/16.55	   new_primModNatS00(ww115, ww116) -> new_primModNatS(Succ(ww115), Succ(ww116), Succ(ww116))
32.88/16.55	
32.88/16.55	R is empty.
32.88/16.55	Q is empty.
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(113) DependencyGraphProof (EQUIVALENT)
32.88/16.55	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(114)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primModNatS0(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS0(ww115, ww116, ww1170, ww1180)
32.88/16.55	
32.88/16.55	R is empty.
32.88/16.55	Q is empty.
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(115) QDPSizeChangeProof (EQUIVALENT)
32.88/16.55	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. 
32.88/16.55	
32.88/16.55	From the DPs we obtained the following set of size-change graphs:
32.88/16.55	*new_primModNatS0(ww115, ww116, Succ(ww1170), Succ(ww1180)) -> new_primModNatS0(ww115, ww116, ww1170, ww1180)
32.88/16.55	The graph contains the following edges 1 >= 1, 2 >= 2, 3 > 3, 4 > 4
32.88/16.55	
32.88/16.55	
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(116)
32.88/16.55	YES
32.88/16.55	
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(117)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primShowInt(Neg(ww170)) -> new_primShowInt(Pos(ww170))
32.88/16.55	   new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))
32.88/16.55	
32.88/16.55	The TRS R consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.55	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.55	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.55	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.55	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.55	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.55	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_primDivNatS4(ww126) -> Zero
32.88/16.55	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.55	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.55	
32.88/16.55	The set Q consists of the following terms:
32.88/16.55	
32.88/16.55	   new_div(x0, x1)
32.88/16.55	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.55	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.55	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.55	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_primDivNatS02(x0, x1)
32.88/16.55	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_primDivNatS4(x0)
32.88/16.55	   new_primDivNatS3(Zero, Zero)
32.88/16.55	
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(118) DependencyGraphProof (EQUIVALENT)
32.88/16.55	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(119)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))
32.88/16.55	
32.88/16.55	The TRS R consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.55	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.55	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.55	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.55	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.55	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.55	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_primDivNatS4(ww126) -> Zero
32.88/16.55	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.55	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.55	
32.88/16.55	The set Q consists of the following terms:
32.88/16.55	
32.88/16.55	   new_div(x0, x1)
32.88/16.55	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.55	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.55	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.55	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_primDivNatS02(x0, x1)
32.88/16.55	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_primDivNatS4(x0)
32.88/16.55	   new_primDivNatS3(Zero, Zero)
32.88/16.55	
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(120) TransformationProof (EQUIVALENT)
32.88/16.55	By rewriting [LPAR04] the rule new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(new_div(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0] we obtained the following new rules [LPAR04]:
32.88/16.55	
32.88/16.55	   (new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))),new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
32.88/16.55	
32.88/16.55	
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(121)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
32.88/16.55	
32.88/16.55	The TRS R consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.55	   new_div(ww60, ww61) -> Pos(new_primDivNatS3(ww60, ww61))
32.88/16.55	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.55	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.55	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.55	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.55	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_primDivNatS4(ww126) -> Zero
32.88/16.55	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.55	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.55	
32.88/16.55	The set Q consists of the following terms:
32.88/16.55	
32.88/16.55	   new_div(x0, x1)
32.88/16.55	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.55	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.55	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.55	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_primDivNatS02(x0, x1)
32.88/16.55	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_primDivNatS4(x0)
32.88/16.55	   new_primDivNatS3(Zero, Zero)
32.88/16.55	
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(122) UsableRulesProof (EQUIVALENT)
32.88/16.55	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.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(123)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
32.88/16.55	
32.88/16.55	The TRS R consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.55	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.55	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.55	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.55	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.55	   new_primDivNatS4(ww126) -> Zero
32.88/16.55	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.55	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.55	
32.88/16.55	The set Q consists of the following terms:
32.88/16.55	
32.88/16.55	   new_div(x0, x1)
32.88/16.55	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.55	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.55	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.55	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.55	   new_primDivNatS02(x0, x1)
32.88/16.55	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.55	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.55	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.55	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.55	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.55	   new_primDivNatS4(x0)
32.88/16.55	   new_primDivNatS3(Zero, Zero)
32.88/16.55	
32.88/16.55	We have to consider all minimal (P,Q,R)-chains.
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(124) QReductionProof (EQUIVALENT)
32.88/16.55	We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN].
32.88/16.55	
32.88/16.55	   new_div(x0, x1)
32.88/16.55	
32.88/16.55	
32.88/16.55	----------------------------------------
32.88/16.55	
32.88/16.55	(125)
32.88/16.55	Obligation:
32.88/16.55	Q DP problem:
32.88/16.55	The TRS P consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
32.88/16.55	
32.88/16.55	The TRS R consists of the following rules:
32.88/16.55	
32.88/16.55	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.55	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.55	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	The set Q consists of the following terms:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.56	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.56	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.56	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.56	   new_primDivNatS02(x0, x1)
32.88/16.56	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.56	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.56	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.56	   new_primDivNatS4(x0)
32.88/16.56	   new_primDivNatS3(Zero, Zero)
32.88/16.56	
32.88/16.56	We have to consider all minimal (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(126) MNOCProof (EQUIVALENT)
32.88/16.56	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(127)
32.88/16.56	Obligation:
32.88/16.56	Q DP problem:
32.88/16.56	The TRS P consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
32.88/16.56	
32.88/16.56	The TRS R consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.56	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	Q is empty.
32.88/16.56	We have to consider all (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(128) InductionCalculusProof (EQUIVALENT)
32.88/16.56	Note that final constraints are written in bold face.
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	For Pair new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) the following chains were created:
32.88/16.56	*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:
32.88/16.56	
32.88/16.56	(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)))))))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint:
32.88/16.56	
32.88/16.56	(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)))))))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	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:
32.88/16.56	
32.88/16.56	(3)    (new_primDivNatS01(x4, x3, x4, x3)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))=Succ(x3)  ==>  new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
32.88/16.56	
32.88/16.56	(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)))))))))))))
32.88/16.56	
32.88/16.56	(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)))))))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	We simplified constraint (3) using rules (I), (II), (VII) which results in the following new constraint:
32.88/16.56	
32.88/16.56	(6)    (x4=x7 & x3=x8 & new_primDivNatS01(x4, x3, x7, x8)=Succ(x1) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3  ==>  new_primShowInt(Pos(Succ(Succ(x4))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x4), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	We solved constraint (4) using rules (I), (II).We solved constraint (5) using rules (I), (II).We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x4, x3, x7, x8)=Succ(x1) which results in the following new constraints:
32.88/16.56	
32.88/16.56	(7)    (new_primDivNatS02(x10, x9)=Succ(x1) & x10=Zero & x9=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x9  ==>  new_primShowInt(Pos(Succ(Succ(x10))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x10), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
32.88/16.56	
32.88/16.56	(8)    (new_primDivNatS02(x16, x15)=Succ(x1) & x16=Succ(x14) & x15=Zero & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15  ==>  new_primShowInt(Pos(Succ(Succ(x16))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x16), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
32.88/16.56	
32.88/16.56	(9)    (new_primDivNatS01(x20, x19, x18, x17)=Succ(x1) & x20=Succ(x18) & x19=Succ(x17) & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x19 & (\/x21:new_primDivNatS01(x20, x19, x18, x17)=Succ(x21) & x20=x18 & x19=x17 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x19  ==>  new_primShowInt(Pos(Succ(Succ(x20))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x20), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))  ==>  new_primShowInt(Pos(Succ(Succ(x20))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(x20), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	We solved constraint (7) using rules (I), (II), (III).We solved constraint (8) using rules (I), (II), (III).We simplified constraint (9) using rules (I), (II), (III), (IV), (VII) which results in the following new constraint:
32.88/16.56	
32.88/16.56	(10)    (new_primShowInt(Pos(Succ(Succ(Succ(x18)))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(Succ(x18)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	To summarize, we get the following constraints P__>=_ for the following pairs.
32.88/16.56	
32.88/16.56	*new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
32.88/16.56	
32.88/16.56	*(new_primShowInt(Pos(Succ(Succ(Succ(x18)))))_>=_new_primShowInt(Pos(new_primDivNatS3(Succ(Succ(x18)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	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. 
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(129)
32.88/16.56	Obligation:
32.88/16.56	Q DP problem:
32.88/16.56	The TRS P consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
32.88/16.56	
32.88/16.56	The TRS R consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.56	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	The set Q consists of the following terms:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.56	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.56	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.56	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.56	   new_primDivNatS02(x0, x1)
32.88/16.56	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.56	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.56	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.56	   new_primDivNatS4(x0)
32.88/16.56	   new_primDivNatS3(Zero, Zero)
32.88/16.56	
32.88/16.56	We have to consider all minimal (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(130) TransformationProof (EQUIVALENT)
32.88/16.56	By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(ww1700))) -> new_primShowInt(Pos(new_primDivNatS3(ww1700, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))) at position [0,0] we obtained the following new rules [LPAR04]:
32.88/16.56	
32.88/16.56	   (new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))),new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))))
32.88/16.56	   (new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero)))
32.88/16.56	
32.88/16.56	
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(131)
32.88/16.56	Obligation:
32.88/16.56	Q DP problem:
32.88/16.56	The TRS P consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))
32.88/16.56	   new_primShowInt(Pos(Succ(Zero))) -> new_primShowInt(Pos(Zero))
32.88/16.56	
32.88/16.56	The TRS R consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.56	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	The set Q consists of the following terms:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.56	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.56	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.56	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.56	   new_primDivNatS02(x0, x1)
32.88/16.56	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.56	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.56	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.56	   new_primDivNatS4(x0)
32.88/16.56	   new_primDivNatS3(Zero, Zero)
32.88/16.56	
32.88/16.56	We have to consider all minimal (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(132) DependencyGraphProof (EQUIVALENT)
32.88/16.56	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(133)
32.88/16.56	Obligation:
32.88/16.56	Q DP problem:
32.88/16.56	The TRS P consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))
32.88/16.56	
32.88/16.56	The TRS R consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.56	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	The set Q consists of the following terms:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.56	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.56	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.56	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.56	   new_primDivNatS02(x0, x1)
32.88/16.56	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.56	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.56	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.56	   new_primDivNatS4(x0)
32.88/16.56	   new_primDivNatS3(Zero, Zero)
32.88/16.56	
32.88/16.56	We have to consider all minimal (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(134) TransformationProof (EQUIVALENT)
32.88/16.56	By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(x0)))) -> new_primShowInt(Pos(new_primDivNatS01(x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))) at position [0,0] we obtained the following new rules [LPAR04]:
32.88/16.56	
32.88/16.56	   (new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero)))
32.88/16.56	   (new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))),new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(135)
32.88/16.56	Obligation:
32.88/16.56	Q DP problem:
32.88/16.56	The TRS P consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(Zero)))) -> new_primShowInt(Pos(Zero))
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))
32.88/16.56	
32.88/16.56	The TRS R consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.56	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	The set Q consists of the following terms:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.56	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.56	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.56	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.56	   new_primDivNatS02(x0, x1)
32.88/16.56	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.56	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.56	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.56	   new_primDivNatS4(x0)
32.88/16.56	   new_primDivNatS3(Zero, Zero)
32.88/16.56	
32.88/16.56	We have to consider all minimal (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(136) DependencyGraphProof (EQUIVALENT)
32.88/16.56	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(137)
32.88/16.56	Obligation:
32.88/16.56	Q DP problem:
32.88/16.56	The TRS P consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))
32.88/16.56	
32.88/16.56	The TRS R consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.56	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	The set Q consists of the following terms:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.56	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.56	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.56	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.56	   new_primDivNatS02(x0, x1)
32.88/16.56	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.56	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.56	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.56	   new_primDivNatS4(x0)
32.88/16.56	   new_primDivNatS3(Zero, Zero)
32.88/16.56	
32.88/16.56	We have to consider all minimal (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(138) TransformationProof (EQUIVALENT)
32.88/16.56	By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(x2))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(x2), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))) at position [0,0] we obtained the following new rules [LPAR04]:
32.88/16.56	
32.88/16.56	   (new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero)))
32.88/16.56	   (new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))),new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(139)
32.88/16.56	Obligation:
32.88/16.56	Q DP problem:
32.88/16.56	The TRS P consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(Succ(Zero))))) -> new_primShowInt(Pos(Zero))
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	The TRS R consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.56	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	The set Q consists of the following terms:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.56	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.56	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.56	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.56	   new_primDivNatS02(x0, x1)
32.88/16.56	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.56	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.56	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.56	   new_primDivNatS4(x0)
32.88/16.56	   new_primDivNatS3(Zero, Zero)
32.88/16.56	
32.88/16.56	We have to consider all minimal (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(140) DependencyGraphProof (EQUIVALENT)
32.88/16.56	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(141)
32.88/16.56	Obligation:
32.88/16.56	Q DP problem:
32.88/16.56	The TRS P consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	The TRS R consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.56	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	The set Q consists of the following terms:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.56	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.56	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.56	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.56	   new_primDivNatS02(x0, x1)
32.88/16.56	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.56	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.56	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.56	   new_primDivNatS4(x0)
32.88/16.56	   new_primDivNatS3(Zero, Zero)
32.88/16.56	
32.88/16.56	We have to consider all minimal (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(142) TransformationProof (EQUIVALENT)
32.88/16.56	By narrowing [LPAR04] the rule new_primShowInt(Pos(Succ(Succ(Succ(Succ(x2)))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(x2)), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))) at position [0,0] we obtained the following new rules [LPAR04]:
32.88/16.56	
32.88/16.56	   (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero)))
32.88/16.56	   (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))),new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(143)
32.88/16.56	Obligation:
32.88/16.56	Q DP problem:
32.88/16.56	The TRS P consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(Zero)))))) -> new_primShowInt(Pos(Zero))
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))
32.88/16.56	
32.88/16.56	The TRS R consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.56	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	The set Q consists of the following terms:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.56	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.56	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.56	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.56	   new_primDivNatS02(x0, x1)
32.88/16.56	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.56	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.56	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.56	   new_primDivNatS4(x0)
32.88/16.56	   new_primDivNatS3(Zero, Zero)
32.88/16.56	
32.88/16.56	We have to consider all minimal (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(144) DependencyGraphProof (EQUIVALENT)
32.88/16.56	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(145)
32.88/16.56	Obligation:
32.88/16.56	Q DP problem:
32.88/16.56	The TRS P consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))
32.88/16.56	
32.88/16.56	The TRS R consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.56	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	The set Q consists of the following terms:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.56	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.56	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.56	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.56	   new_primDivNatS02(x0, x1)
32.88/16.56	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.56	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.56	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.56	   new_primDivNatS4(x0)
32.88/16.56	   new_primDivNatS3(Zero, Zero)
32.88/16.56	
32.88/16.56	We have to consider all minimal (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(146) MNOCProof (EQUIVALENT)
32.88/16.56	We use the modular non-overlap check [FROCOS05] to decrease Q to the empty set.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(147)
32.88/16.56	Obligation:
32.88/16.56	Q DP problem:
32.88/16.56	The TRS P consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))
32.88/16.56	
32.88/16.56	The TRS R consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.56	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	Q is empty.
32.88/16.56	We have to consider all (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(148) InductionCalculusProof (EQUIVALENT)
32.88/16.56	Note that final constraints are written in bold face.
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	For Pair new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero)))))))) the following chains were created:
32.88/16.56	*We consider the chain new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero)))))))), new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x1))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x1))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x1, Succ(Succ(Succ(Succ(Succ(Zero)))))))) which results in the following constraint:
32.88/16.56	
32.88/16.56	(1)    (new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero))))))))=new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x1)))))))  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	We simplified constraint (1) using rules (I), (II), (VII) which results in the following new constraint:
32.88/16.56	
32.88/16.56	(2)    (Succ(Succ(Succ(x0)))=x2 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x3 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x4 & new_primDivNatS01(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1)))))  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x0)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x0))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x0, Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	We simplified constraint (2) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x2, x3, x0, x4)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints:
32.88/16.56	
32.88/16.56	(3)    (new_primDivNatS02(x6, x5)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Zero)))=x6 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x5 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Zero)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Zero))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Zero, Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	(4)    (new_primDivNatS02(x12, x11)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x10))))=x12 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x11 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Zero  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x10))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x10)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x10), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	(5)    (new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x14))))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Succ(Zero)))))=Succ(x13) & (\/x17:new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x17))))) & Succ(Succ(Succ(x14)))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Succ(Zero)))))=x13  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x14)))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x14))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x14, Succ(Succ(Succ(Succ(Succ(Zero)))))))))  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x14))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x14)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x14), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	We solved constraint (3) using rules (I), (II).We solved constraint (4) using rules (I), (II).We simplified constraint (5) using rules (I), (II), (IV) which results in the following new constraint:
32.88/16.56	
32.88/16.56	(6)    (new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(x14))))=x16 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x15 & Succ(Succ(Succ(Succ(Zero))))=x13  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x14))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x14)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x14), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	We simplified constraint (6) using rule (V) (with possible (I) afterwards) using induction on new_primDivNatS01(x16, x15, x14, x13)=Succ(Succ(Succ(Succ(Succ(x1))))) which results in the following new constraints:
32.88/16.56	
32.88/16.56	(7)    (new_primDivNatS02(x19, x18)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Zero))))=x19 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x18 & Succ(Succ(Succ(Succ(Zero))))=Zero  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Zero)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Zero), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	(8)    (new_primDivNatS02(x25, x24)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x23)))))=x25 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x24 & Succ(Succ(Succ(Succ(Zero))))=Zero  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x23)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x23))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x23)), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	(9)    (new_primDivNatS01(x29, x28, x27, x26)=Succ(Succ(Succ(Succ(Succ(x1))))) & Succ(Succ(Succ(Succ(Succ(x27)))))=x29 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x28 & Succ(Succ(Succ(Succ(Zero))))=Succ(x26) & (\/x30:new_primDivNatS01(x29, x28, x27, x26)=Succ(Succ(Succ(Succ(Succ(x30))))) & Succ(Succ(Succ(Succ(x27))))=x29 & Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))=x28 & Succ(Succ(Succ(Succ(Zero))))=x26  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(x27))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(x27)))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(x27), Succ(Succ(Succ(Succ(Succ(Zero)))))))))  ==>  new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	We solved constraint (7) using rules (I), (II).We solved constraint (8) using rules (I), (II).We simplified constraint (9) using rules (I), (II), (III), (IV) which results in the following new constraint:
32.88/16.56	
32.88/16.56	(10)    (new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	To summarize, we get the following constraints P__>=_ for the following pairs.
32.88/16.56	
32.88/16.56	*new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))
32.88/16.56	
32.88/16.56	*(new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(Succ(Succ(x27)))))))))_>=_new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(Succ(Succ(x27))))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), Succ(Succ(x27)), Succ(Succ(Succ(Succ(Succ(Zero)))))))))
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	
32.88/16.56	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. 
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(149)
32.88/16.56	Obligation:
32.88/16.56	Q DP problem:
32.88/16.56	The TRS P consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primShowInt(Pos(Succ(Succ(Succ(Succ(Succ(x2))))))) -> new_primShowInt(Pos(new_primDivNatS01(Succ(Succ(Succ(x2))), Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), x2, Succ(Succ(Succ(Succ(Succ(Zero))))))))
32.88/16.56	
32.88/16.56	The TRS R consists of the following rules:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Succ(ww600), Succ(ww610)) -> new_primDivNatS01(ww600, ww610, ww600, ww610)
32.88/16.56	   new_primDivNatS3(Zero, Succ(ww610)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Zero, Succ(ww1130)) -> Zero
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Zero) -> new_primDivNatS02(ww110, ww111)
32.88/16.56	   new_primDivNatS01(ww110, ww111, Succ(ww1120), Succ(ww1130)) -> new_primDivNatS01(ww110, ww111, ww1120, ww1130)
32.88/16.56	   new_primDivNatS02(ww110, ww111) -> Succ(new_primDivNatS2(Succ(ww110), Succ(ww111), Succ(ww111)))
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Succ(ww1250), ww126) -> new_primDivNatS2(ww1240, ww1250, ww126)
32.88/16.56	   new_primDivNatS2(Succ(ww1240), Zero, ww126) -> new_primDivNatS3(ww1240, ww126)
32.88/16.56	   new_primDivNatS2(Zero, Zero, ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS2(Zero, Succ(ww1250), ww126) -> new_primDivNatS4(ww126)
32.88/16.56	   new_primDivNatS4(ww126) -> Zero
32.88/16.56	   new_primDivNatS3(Succ(ww600), Zero) -> Succ(new_primDivNatS2(Succ(ww600), Zero, Zero))
32.88/16.56	   new_primDivNatS3(Zero, Zero) -> Succ(new_primDivNatS2(Zero, Zero, Zero))
32.88/16.56	
32.88/16.56	The set Q consists of the following terms:
32.88/16.56	
32.88/16.56	   new_primDivNatS3(Zero, Succ(x0))
32.88/16.56	   new_primDivNatS2(Zero, Zero, x0)
32.88/16.56	   new_primDivNatS3(Succ(x0), Zero)
32.88/16.56	   new_primDivNatS2(Succ(x0), Zero, x1)
32.88/16.56	   new_primDivNatS02(x0, x1)
32.88/16.56	   new_primDivNatS2(Succ(x0), Succ(x1), x2)
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Succ(x3))
32.88/16.56	   new_primDivNatS2(Zero, Succ(x0), x1)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Zero)
32.88/16.56	   new_primDivNatS01(x0, x1, Zero, Succ(x2))
32.88/16.56	   new_primDivNatS3(Succ(x0), Succ(x1))
32.88/16.56	   new_primDivNatS01(x0, x1, Succ(x2), Zero)
32.88/16.56	   new_primDivNatS4(x0)
32.88/16.56	   new_primDivNatS3(Zero, Zero)
32.88/16.56	
32.88/16.56	We have to consider all minimal (P,Q,R)-chains.
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(150) Narrow (COMPLETE)
32.88/16.56	Haskell To QDPs
32.88/16.56	
32.88/16.56	digraph dp_graph {
32.88/16.56	node [outthreshold=100, inthreshold=100];1[label="shows",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
32.88/16.56	3[label="shows ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
32.88/16.56	4[label="shows ww3 ww4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
32.88/16.56	5[label="showsPrec (Pos Zero) ww3 ww4",fontsize=16,color="burlywood",shape="box"];1224[label="ww3/ww30 :% ww31",fontsize=10,color="white",style="solid",shape="box"];5 -> 1224[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1224 -> 6[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	6[label="showsPrec (Pos Zero) (ww30 :% ww31) ww4",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
32.88/16.56	7 -> 24[label="",style="dashed", color="red", weight=0];
32.88/16.56	7[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww30) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww31) ww4",fontsize=16,color="magenta"];7 -> 25[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	7 -> 26[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	7 -> 27[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	7 -> 28[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	7 -> 29[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	7 -> 30[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	25[label="ww30",fontsize=16,color="green",shape="box"];26[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];27[label="ww4",fontsize=16,color="green",shape="box"];28[label="ww31",fontsize=16,color="green",shape="box"];29[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];30[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];24[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) ww22",fontsize=16,color="black",shape="triangle"];24 -> 37[label="",style="solid", color="black", weight=3];
32.88/16.56	37[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ww22",fontsize=16,color="black",shape="box"];37 -> 38[label="",style="solid", color="black", weight=3];
32.88/16.56	38[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (compare (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww22",fontsize=16,color="black",shape="box"];38 -> 39[label="",style="solid", color="black", weight=3];
32.88/16.56	39[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (primCmpInt (Pos Zero) (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) == GT) ww22",fontsize=16,color="black",shape="box"];39 -> 40[label="",style="solid", color="black", weight=3];
32.88/16.56	40[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (primCmpNat Zero (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))) == GT) ww22",fontsize=16,color="black",shape="box"];40 -> 41[label="",style="solid", color="black", weight=3];
32.88/16.56	41[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) (LT == GT) ww22",fontsize=16,color="black",shape="box"];41 -> 42[label="",style="solid", color="black", weight=3];
32.88/16.56	42[label="showParen0 ((shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21) False ww22",fontsize=16,color="black",shape="box"];42 -> 43[label="",style="solid", color="black", weight=3];
32.88/16.56	43[label="(shows ww17) . (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="black",shape="box"];43 -> 44[label="",style="solid", color="black", weight=3];
32.88/16.56	44[label="shows ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];44 -> 45[label="",style="solid", color="black", weight=3];
32.88/16.56	45[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="blue",shape="box"];1225[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1225[label="",style="solid", color="blue", weight=9];
32.88/16.56	1225 -> 46[label="",style="solid", color="blue", weight=3];
32.88/16.56	1226[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1226[label="",style="solid", color="blue", weight=9];
32.88/16.56	1226 -> 47[label="",style="solid", color="blue", weight=3];
32.88/16.56	1227[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1227[label="",style="solid", color="blue", weight=9];
32.88/16.56	1227 -> 48[label="",style="solid", color="blue", weight=3];
32.88/16.56	1228[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1228[label="",style="solid", color="blue", weight=9];
32.88/16.56	1228 -> 49[label="",style="solid", color="blue", weight=3];
32.88/16.56	1229[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1229[label="",style="solid", color="blue", weight=9];
32.88/16.56	1229 -> 50[label="",style="solid", color="blue", weight=3];
32.88/16.56	1230[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1230[label="",style="solid", color="blue", weight=9];
32.88/16.56	1230 -> 51[label="",style="solid", color="blue", weight=3];
32.88/16.56	1231[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1231[label="",style="solid", color="blue", weight=9];
32.88/16.56	1231 -> 52[label="",style="solid", color="blue", weight=3];
32.88/16.56	1232[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1232[label="",style="solid", color="blue", weight=9];
32.88/16.56	1232 -> 53[label="",style="solid", color="blue", weight=3];
32.88/16.56	1233[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1233[label="",style="solid", color="blue", weight=9];
32.88/16.56	1233 -> 54[label="",style="solid", color="blue", weight=3];
32.88/16.56	1234[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1234[label="",style="solid", color="blue", weight=9];
32.88/16.56	1234 -> 55[label="",style="solid", color="blue", weight=3];
32.88/16.56	1235[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1235[label="",style="solid", color="blue", weight=9];
32.88/16.56	1235 -> 56[label="",style="solid", color="blue", weight=3];
32.88/16.56	1236[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1236[label="",style="solid", color="blue", weight=9];
32.88/16.56	1236 -> 57[label="",style="solid", color="blue", weight=3];
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32.88/16.56	1237 -> 58[label="",style="solid", color="blue", weight=3];
32.88/16.56	1238[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1238[label="",style="solid", color="blue", weight=9];
32.88/16.56	1238 -> 59[label="",style="solid", color="blue", weight=3];
32.88/16.56	1239[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1239[label="",style="solid", color="blue", weight=9];
32.88/16.56	1239 -> 60[label="",style="solid", color="blue", weight=3];
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32.88/16.56	1240 -> 61[label="",style="solid", color="blue", weight=3];
32.88/16.56	1241[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];45 -> 1241[label="",style="solid", color="blue", weight=9];
32.88/16.56	1241 -> 62[label="",style="solid", color="blue", weight=3];
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32.88/16.56	1242 -> 63[label="",style="solid", color="blue", weight=3];
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32.88/16.56	47[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];47 -> 65[label="",style="solid", color="black", weight=3];
32.88/16.56	48[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];48 -> 66[label="",style="solid", color="black", weight=3];
32.88/16.56	49[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];49 -> 67[label="",style="solid", color="black", weight=3];
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32.88/16.56	52[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];52 -> 70[label="",style="solid", color="black", weight=3];
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32.88/16.56	57[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];57 -> 75[label="",style="solid", color="black", weight=3];
32.88/16.56	58[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];58 -> 76[label="",style="solid", color="black", weight=3];
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32.88/16.56	61[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];61 -> 79[label="",style="solid", color="black", weight=3];
32.88/16.56	62[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];62 -> 80[label="",style="solid", color="black", weight=3];
32.88/16.56	63[label="showsPrec (Pos Zero) ww17 ((showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21)",fontsize=16,color="black",shape="box"];63 -> 81[label="",style="solid", color="black", weight=3];
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32.88/16.56	65 -> 186[label="",style="dashed", color="magenta", weight=3];
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32.88/16.56	66 -> 188[label="",style="dashed", color="magenta", weight=3];
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32.88/16.56	67 -> 190[label="",style="dashed", color="magenta", weight=3];
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32.88/16.56	68 -> 192[label="",style="dashed", color="magenta", weight=3];
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32.88/16.56	69 -> 194[label="",style="dashed", color="magenta", weight=3];
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32.88/16.56	70 -> 196[label="",style="dashed", color="magenta", weight=3];
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32.88/16.56	72 -> 182[label="",style="dashed", color="red", weight=0];
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32.88/16.56	72 -> 198[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	73 -> 182[label="",style="dashed", color="red", weight=0];
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32.88/16.56	73 -> 200[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	74 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	74[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];74 -> 201[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	74 -> 202[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	75 -> 182[label="",style="dashed", color="red", weight=0];
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32.88/16.56	75 -> 204[label="",style="dashed", color="magenta", weight=3];
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32.88/16.56	76 -> 206[label="",style="dashed", color="magenta", weight=3];
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32.88/16.56	77 -> 208[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	78 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	78[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];78 -> 209[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	78 -> 210[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	79 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	79[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];79 -> 211[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	79 -> 212[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	80 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	80[label="show ww17 ++ (showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];80 -> 213[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	80 -> 214[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	81 -> 182[label="",style="dashed", color="red", weight=0];
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32.88/16.56	81 -> 216[label="",style="dashed", color="magenta", weight=3];
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32.88/16.56	1244 -> 243[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1245[label="ww58/[]",fontsize=10,color="white",style="solid",shape="box"];182 -> 1245[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1245 -> 244[label="",style="solid", color="burlywood", weight=3];
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32.88/16.56	190 -> 102[label="",style="dashed", color="red", weight=0];
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32.88/16.56	192 -> 102[label="",style="dashed", color="red", weight=0];
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32.88/16.56	194 -> 102[label="",style="dashed", color="red", weight=0];
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32.88/16.56	206 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.56	206[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];207[label="show ww17",fontsize=16,color="black",shape="triangle"];207 -> 256[label="",style="solid", color="black", weight=3];
32.88/16.56	208 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.56	208[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];209[label="show ww17",fontsize=16,color="black",shape="triangle"];209 -> 257[label="",style="solid", color="black", weight=3];
32.88/16.56	210 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.56	210[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];211[label="show ww17",fontsize=16,color="black",shape="triangle"];211 -> 258[label="",style="solid", color="black", weight=3];
32.88/16.56	212 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.56	212[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];213[label="show ww17",fontsize=16,color="black",shape="triangle"];213 -> 259[label="",style="solid", color="black", weight=3];
32.88/16.56	214 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.56	214[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];215[label="show ww17",fontsize=16,color="black",shape="triangle"];215 -> 260[label="",style="solid", color="black", weight=3];
32.88/16.56	216 -> 102[label="",style="dashed", color="red", weight=0];
32.88/16.56	216[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="magenta"];242[label="error []",fontsize=16,color="red",shape="box"];102[label="(showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : [])) . shows ww21",fontsize=16,color="black",shape="triangle"];102 -> 108[label="",style="solid", color="black", weight=3];
32.88/16.56	243[label="(ww580 : ww581) ++ ww56",fontsize=16,color="black",shape="box"];243 -> 262[label="",style="solid", color="black", weight=3];
32.88/16.56	244[label="[] ++ ww56",fontsize=16,color="black",shape="box"];244 -> 263[label="",style="solid", color="black", weight=3];
32.88/16.56	245[label="error []",fontsize=16,color="red",shape="box"];246[label="error []",fontsize=16,color="red",shape="box"];247[label="error []",fontsize=16,color="red",shape="box"];248[label="error []",fontsize=16,color="red",shape="box"];249[label="error []",fontsize=16,color="red",shape="box"];250[label="error []",fontsize=16,color="red",shape="box"];100[label="ww170",fontsize=16,color="green",shape="box"];101[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];103[label="ww171",fontsize=16,color="green",shape="box"];104[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];105[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];251[label="error []",fontsize=16,color="red",shape="box"];252[label="error []",fontsize=16,color="red",shape="box"];253[label="error []",fontsize=16,color="red",shape="box"];254[label="primShowInt ww17",fontsize=16,color="burlywood",shape="triangle"];1246[label="ww17/Pos ww170",fontsize=10,color="white",style="solid",shape="box"];254 -> 1246[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1246 -> 264[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1247[label="ww17/Neg ww170",fontsize=10,color="white",style="solid",shape="box"];254 -> 1247[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1247 -> 265[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	255[label="error []",fontsize=16,color="red",shape="box"];256[label="error []",fontsize=16,color="red",shape="box"];257[label="error []",fontsize=16,color="red",shape="box"];258[label="error []",fontsize=16,color="red",shape="box"];259[label="error []",fontsize=16,color="red",shape="box"];260[label="error []",fontsize=16,color="red",shape="box"];108[label="showString (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : []) (shows ww21 ww22)",fontsize=16,color="black",shape="box"];108 -> 112[label="",style="solid", color="black", weight=3];
32.88/16.56	262[label="ww580 : ww581 ++ ww56",fontsize=16,color="green",shape="box"];262 -> 284[label="",style="dashed", color="green", weight=3];
32.88/16.56	263[label="ww56",fontsize=16,color="green",shape="box"];264[label="primShowInt (Pos ww170)",fontsize=16,color="burlywood",shape="box"];1248[label="ww170/Succ ww1700",fontsize=10,color="white",style="solid",shape="box"];264 -> 1248[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1248 -> 285[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1249[label="ww170/Zero",fontsize=10,color="white",style="solid",shape="box"];264 -> 1249[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1249 -> 286[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	265[label="primShowInt (Neg ww170)",fontsize=16,color="black",shape="box"];265 -> 287[label="",style="solid", color="black", weight=3];
32.88/16.56	112 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	112[label="(++) (Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : []) shows ww21 ww22",fontsize=16,color="magenta"];112 -> 221[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	112 -> 222[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	284 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	284[label="ww581 ++ ww56",fontsize=16,color="magenta"];284 -> 306[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	285[label="primShowInt (Pos (Succ ww1700))",fontsize=16,color="black",shape="box"];285 -> 307[label="",style="solid", color="black", weight=3];
32.88/16.56	286[label="primShowInt (Pos Zero)",fontsize=16,color="black",shape="box"];286 -> 308[label="",style="solid", color="black", weight=3];
32.88/16.56	287[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))))))))))) : primShowInt (Pos ww170)",fontsize=16,color="green",shape="box"];287 -> 309[label="",style="dashed", color="green", weight=3];
32.88/16.56	221[label="Char (Succ ww18) : Char (Succ ww19) : Char (Succ ww20) : []",fontsize=16,color="green",shape="box"];222[label="shows ww21 ww22",fontsize=16,color="black",shape="box"];222 -> 261[label="",style="solid", color="black", weight=3];
32.88/16.56	306[label="ww581",fontsize=16,color="green",shape="box"];307 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	307[label="primShowInt (div Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) ++ toEnum (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="magenta"];307 -> 345[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	307 -> 346[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	308[label="Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))))))))))))))) : []",fontsize=16,color="green",shape="box"];309 -> 254[label="",style="dashed", color="red", weight=0];
32.88/16.56	309[label="primShowInt (Pos ww170)",fontsize=16,color="magenta"];309 -> 347[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	261[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="blue",shape="box"];1250[label="showsPrec :: Int -> ([] a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1250[label="",style="solid", color="blue", weight=9];
32.88/16.56	1250 -> 266[label="",style="solid", color="blue", weight=3];
32.88/16.56	1251[label="showsPrec :: Int -> ((@2) a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1251[label="",style="solid", color="blue", weight=9];
32.88/16.56	1251 -> 267[label="",style="solid", color="blue", weight=3];
32.88/16.56	1252[label="showsPrec :: Int -> Bool -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1252[label="",style="solid", color="blue", weight=9];
32.88/16.56	1252 -> 268[label="",style="solid", color="blue", weight=3];
32.88/16.56	1253[label="showsPrec :: Int -> IOError -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1253[label="",style="solid", color="blue", weight=9];
32.88/16.56	1253 -> 269[label="",style="solid", color="blue", weight=3];
32.88/16.56	1254[label="showsPrec :: Int -> (IO a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1254[label="",style="solid", color="blue", weight=9];
32.88/16.56	1254 -> 270[label="",style="solid", color="blue", weight=3];
32.88/16.56	1255[label="showsPrec :: Int -> () -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1255[label="",style="solid", color="blue", weight=9];
32.88/16.56	1255 -> 271[label="",style="solid", color="blue", weight=3];
32.88/16.56	1256[label="showsPrec :: Int -> IOErrorKind -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1256[label="",style="solid", color="blue", weight=9];
32.88/16.56	1256 -> 272[label="",style="solid", color="blue", weight=3];
32.88/16.56	1257[label="showsPrec :: Int -> (Ratio a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1257[label="",style="solid", color="blue", weight=9];
32.88/16.56	1257 -> 273[label="",style="solid", color="blue", weight=3];
32.88/16.56	1258[label="showsPrec :: Int -> (Either a b) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1258[label="",style="solid", color="blue", weight=9];
32.88/16.56	1258 -> 274[label="",style="solid", color="blue", weight=3];
32.88/16.56	1259[label="showsPrec :: Int -> Integer -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1259[label="",style="solid", color="blue", weight=9];
32.88/16.56	1259 -> 275[label="",style="solid", color="blue", weight=3];
32.88/16.56	1260[label="showsPrec :: Int -> Ordering -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1260[label="",style="solid", color="blue", weight=9];
32.88/16.56	1260 -> 276[label="",style="solid", color="blue", weight=3];
32.88/16.56	1261[label="showsPrec :: Int -> Int -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1261[label="",style="solid", color="blue", weight=9];
32.88/16.56	1261 -> 277[label="",style="solid", color="blue", weight=3];
32.88/16.56	1262[label="showsPrec :: Int -> Double -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1262[label="",style="solid", color="blue", weight=9];
32.88/16.56	1262 -> 278[label="",style="solid", color="blue", weight=3];
32.88/16.56	1263[label="showsPrec :: Int -> (Maybe a) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1263[label="",style="solid", color="blue", weight=9];
32.88/16.56	1263 -> 279[label="",style="solid", color="blue", weight=3];
32.88/16.56	1264[label="showsPrec :: Int -> HugsException -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1264[label="",style="solid", color="blue", weight=9];
32.88/16.56	1264 -> 280[label="",style="solid", color="blue", weight=3];
32.88/16.56	1265[label="showsPrec :: Int -> Char -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1265[label="",style="solid", color="blue", weight=9];
32.88/16.56	1265 -> 281[label="",style="solid", color="blue", weight=3];
32.88/16.56	1266[label="showsPrec :: Int -> ((@3) a b c) -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1266[label="",style="solid", color="blue", weight=9];
32.88/16.56	1266 -> 282[label="",style="solid", color="blue", weight=3];
32.88/16.56	1267[label="showsPrec :: Int -> Float -> ([] Char) -> [] Char",fontsize=10,color="white",style="solid",shape="box"];261 -> 1267[label="",style="solid", color="blue", weight=9];
32.88/16.56	1267 -> 283[label="",style="solid", color="blue", weight=3];
32.88/16.56	345 -> 254[label="",style="dashed", color="red", weight=0];
32.88/16.56	345[label="primShowInt (div Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];345 -> 370[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	346[label="toEnum (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) : []",fontsize=16,color="green",shape="box"];346 -> 371[label="",style="dashed", color="green", weight=3];
32.88/16.56	347[label="Pos ww170",fontsize=16,color="green",shape="box"];266[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];266 -> 288[label="",style="solid", color="black", weight=3];
32.88/16.56	267[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];267 -> 289[label="",style="solid", color="black", weight=3];
32.88/16.56	268[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];268 -> 290[label="",style="solid", color="black", weight=3];
32.88/16.56	269[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];269 -> 291[label="",style="solid", color="black", weight=3];
32.88/16.56	270[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];270 -> 292[label="",style="solid", color="black", weight=3];
32.88/16.56	271[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];271 -> 293[label="",style="solid", color="black", weight=3];
32.88/16.56	272[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];272 -> 294[label="",style="solid", color="black", weight=3];
32.88/16.56	273[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="burlywood",shape="box"];1268[label="ww21/ww210 :% ww211",fontsize=10,color="white",style="solid",shape="box"];273 -> 1268[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1268 -> 295[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	274[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];274 -> 296[label="",style="solid", color="black", weight=3];
32.88/16.56	275[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];275 -> 297[label="",style="solid", color="black", weight=3];
32.88/16.56	276[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];276 -> 298[label="",style="solid", color="black", weight=3];
32.88/16.56	277[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];277 -> 299[label="",style="solid", color="black", weight=3];
32.88/16.56	278[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];278 -> 300[label="",style="solid", color="black", weight=3];
32.88/16.56	279[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];279 -> 301[label="",style="solid", color="black", weight=3];
32.88/16.56	280[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];280 -> 302[label="",style="solid", color="black", weight=3];
32.88/16.56	281[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];281 -> 303[label="",style="solid", color="black", weight=3];
32.88/16.56	282[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];282 -> 304[label="",style="solid", color="black", weight=3];
32.88/16.56	283[label="showsPrec (Pos Zero) ww21 ww22",fontsize=16,color="black",shape="box"];283 -> 305[label="",style="solid", color="black", weight=3];
32.88/16.56	370 -> 372[label="",style="dashed", color="red", weight=0];
32.88/16.56	370[label="div Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))",fontsize=16,color="magenta"];370 -> 373[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	370 -> 374[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	371[label="toEnum (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="black",shape="box"];371 -> 389[label="",style="solid", color="black", weight=3];
32.88/16.56	288 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	288[label="show ww21 ++ ww22",fontsize=16,color="magenta"];288 -> 310[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	288 -> 311[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	289 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	289[label="show ww21 ++ ww22",fontsize=16,color="magenta"];289 -> 312[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	289 -> 313[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	290 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	290[label="show ww21 ++ ww22",fontsize=16,color="magenta"];290 -> 314[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	290 -> 315[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	291 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	291[label="show ww21 ++ ww22",fontsize=16,color="magenta"];291 -> 316[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	291 -> 317[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	292 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	292[label="show ww21 ++ ww22",fontsize=16,color="magenta"];292 -> 318[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	292 -> 319[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	293 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	293[label="show ww21 ++ ww22",fontsize=16,color="magenta"];293 -> 320[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	293 -> 321[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	294 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	294[label="show ww21 ++ ww22",fontsize=16,color="magenta"];294 -> 322[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	294 -> 323[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	295[label="showsPrec (Pos Zero) (ww210 :% ww211) ww22",fontsize=16,color="black",shape="box"];295 -> 324[label="",style="solid", color="black", weight=3];
32.88/16.56	296 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	296[label="show ww21 ++ ww22",fontsize=16,color="magenta"];296 -> 325[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	296 -> 326[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	297 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	297[label="show ww21 ++ ww22",fontsize=16,color="magenta"];297 -> 327[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	297 -> 328[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	298 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	298[label="show ww21 ++ ww22",fontsize=16,color="magenta"];298 -> 329[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	298 -> 330[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	299 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	299[label="show ww21 ++ ww22",fontsize=16,color="magenta"];299 -> 331[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	299 -> 332[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	300 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	300[label="show ww21 ++ ww22",fontsize=16,color="magenta"];300 -> 333[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	300 -> 334[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	301 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	301[label="show ww21 ++ ww22",fontsize=16,color="magenta"];301 -> 335[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	301 -> 336[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	302 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	302[label="show ww21 ++ ww22",fontsize=16,color="magenta"];302 -> 337[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	302 -> 338[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	303 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	303[label="show ww21 ++ ww22",fontsize=16,color="magenta"];303 -> 339[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	303 -> 340[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	304 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	304[label="show ww21 ++ ww22",fontsize=16,color="magenta"];304 -> 341[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	304 -> 342[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	305 -> 182[label="",style="dashed", color="red", weight=0];
32.88/16.56	305[label="show ww21 ++ ww22",fontsize=16,color="magenta"];305 -> 343[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	305 -> 344[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	373[label="ww1700",fontsize=16,color="green",shape="box"];374[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];372[label="div Pos (Succ ww60) Pos (Succ ww61)",fontsize=16,color="black",shape="triangle"];372 -> 378[label="",style="solid", color="black", weight=3];
32.88/16.56	389 -> 400[label="",style="dashed", color="red", weight=0];
32.88/16.56	389[label="primIntToChar (mod Pos (Succ ww1700) Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))",fontsize=16,color="magenta"];389 -> 401[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	389 -> 402[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	310 -> 183[label="",style="dashed", color="red", weight=0];
32.88/16.56	310[label="show ww21",fontsize=16,color="magenta"];310 -> 348[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	311[label="ww22",fontsize=16,color="green",shape="box"];312 -> 185[label="",style="dashed", color="red", weight=0];
32.88/16.56	312[label="show ww21",fontsize=16,color="magenta"];312 -> 349[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	313[label="ww22",fontsize=16,color="green",shape="box"];314 -> 187[label="",style="dashed", color="red", weight=0];
32.88/16.56	314[label="show ww21",fontsize=16,color="magenta"];314 -> 350[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	315[label="ww22",fontsize=16,color="green",shape="box"];316 -> 189[label="",style="dashed", color="red", weight=0];
32.88/16.56	316[label="show ww21",fontsize=16,color="magenta"];316 -> 351[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	317[label="ww22",fontsize=16,color="green",shape="box"];318 -> 191[label="",style="dashed", color="red", weight=0];
32.88/16.56	318[label="show ww21",fontsize=16,color="magenta"];318 -> 352[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	319[label="ww22",fontsize=16,color="green",shape="box"];320 -> 193[label="",style="dashed", color="red", weight=0];
32.88/16.56	320[label="show ww21",fontsize=16,color="magenta"];320 -> 353[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	321[label="ww22",fontsize=16,color="green",shape="box"];322 -> 195[label="",style="dashed", color="red", weight=0];
32.88/16.56	322[label="show ww21",fontsize=16,color="magenta"];322 -> 354[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	323[label="ww22",fontsize=16,color="green",shape="box"];324 -> 24[label="",style="dashed", color="red", weight=0];
32.88/16.56	324[label="showParen (Pos Zero > Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) ((shows ww210) . (showString (Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))))))))) : Char (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))) : [])) . shows ww211) ww22",fontsize=16,color="magenta"];324 -> 355[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	324 -> 356[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	324 -> 357[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	324 -> 358[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	324 -> 359[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	325 -> 197[label="",style="dashed", color="red", weight=0];
32.88/16.56	325[label="show ww21",fontsize=16,color="magenta"];325 -> 360[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	326[label="ww22",fontsize=16,color="green",shape="box"];327 -> 199[label="",style="dashed", color="red", weight=0];
32.88/16.56	327[label="show ww21",fontsize=16,color="magenta"];327 -> 361[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	328[label="ww22",fontsize=16,color="green",shape="box"];329 -> 201[label="",style="dashed", color="red", weight=0];
32.88/16.56	329[label="show ww21",fontsize=16,color="magenta"];329 -> 362[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	330[label="ww22",fontsize=16,color="green",shape="box"];331 -> 203[label="",style="dashed", color="red", weight=0];
32.88/16.56	331[label="show ww21",fontsize=16,color="magenta"];331 -> 363[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	332[label="ww22",fontsize=16,color="green",shape="box"];333 -> 205[label="",style="dashed", color="red", weight=0];
32.88/16.56	333[label="show ww21",fontsize=16,color="magenta"];333 -> 364[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	334[label="ww22",fontsize=16,color="green",shape="box"];335 -> 207[label="",style="dashed", color="red", weight=0];
32.88/16.56	335[label="show ww21",fontsize=16,color="magenta"];335 -> 365[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	336[label="ww22",fontsize=16,color="green",shape="box"];337 -> 209[label="",style="dashed", color="red", weight=0];
32.88/16.56	337[label="show ww21",fontsize=16,color="magenta"];337 -> 366[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	338[label="ww22",fontsize=16,color="green",shape="box"];339 -> 211[label="",style="dashed", color="red", weight=0];
32.88/16.56	339[label="show ww21",fontsize=16,color="magenta"];339 -> 367[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	340[label="ww22",fontsize=16,color="green",shape="box"];341 -> 213[label="",style="dashed", color="red", weight=0];
32.88/16.56	341[label="show ww21",fontsize=16,color="magenta"];341 -> 368[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	342[label="ww22",fontsize=16,color="green",shape="box"];343 -> 215[label="",style="dashed", color="red", weight=0];
32.88/16.56	343[label="show ww21",fontsize=16,color="magenta"];343 -> 369[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	344[label="ww22",fontsize=16,color="green",shape="box"];378[label="primDivInt (Pos (Succ ww60)) (Pos (Succ ww61))",fontsize=16,color="black",shape="box"];378 -> 388[label="",style="solid", color="black", weight=3];
32.88/16.56	401[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))",fontsize=16,color="green",shape="box"];402[label="ww1700",fontsize=16,color="green",shape="box"];400[label="primIntToChar (mod Pos (Succ ww66) Pos (Succ ww67))",fontsize=16,color="black",shape="triangle"];400 -> 403[label="",style="solid", color="black", weight=3];
32.88/16.56	348[label="ww21",fontsize=16,color="green",shape="box"];349[label="ww21",fontsize=16,color="green",shape="box"];350[label="ww21",fontsize=16,color="green",shape="box"];351[label="ww21",fontsize=16,color="green",shape="box"];352[label="ww21",fontsize=16,color="green",shape="box"];353[label="ww21",fontsize=16,color="green",shape="box"];354[label="ww21",fontsize=16,color="green",shape="box"];355[label="ww210",fontsize=16,color="green",shape="box"];356[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];357[label="ww211",fontsize=16,color="green",shape="box"];358[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];359[label="Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))))))))))))))))))))",fontsize=16,color="green",shape="box"];360[label="ww21",fontsize=16,color="green",shape="box"];361[label="ww21",fontsize=16,color="green",shape="box"];362[label="ww21",fontsize=16,color="green",shape="box"];363[label="ww21",fontsize=16,color="green",shape="box"];364[label="ww21",fontsize=16,color="green",shape="box"];365[label="ww21",fontsize=16,color="green",shape="box"];366[label="ww21",fontsize=16,color="green",shape="box"];367[label="ww21",fontsize=16,color="green",shape="box"];368[label="ww21",fontsize=16,color="green",shape="box"];369[label="ww21",fontsize=16,color="green",shape="box"];388[label="Pos (primDivNatS (Succ ww60) (Succ ww61))",fontsize=16,color="green",shape="box"];388 -> 399[label="",style="dashed", color="green", weight=3];
32.88/16.56	403[label="primIntToChar (primModInt (Pos (Succ ww66)) (Pos (Succ ww67)))",fontsize=16,color="black",shape="box"];403 -> 405[label="",style="solid", color="black", weight=3];
32.88/16.56	399[label="primDivNatS (Succ ww60) (Succ ww61)",fontsize=16,color="black",shape="triangle"];399 -> 404[label="",style="solid", color="black", weight=3];
32.88/16.56	405[label="primIntToChar (Pos (primModNatS (Succ ww66) (Succ ww67)))",fontsize=16,color="black",shape="box"];405 -> 408[label="",style="solid", color="black", weight=3];
32.88/16.56	404[label="primDivNatS0 ww60 ww61 (primGEqNatS ww60 ww61)",fontsize=16,color="burlywood",shape="box"];1269[label="ww60/Succ ww600",fontsize=10,color="white",style="solid",shape="box"];404 -> 1269[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1269 -> 406[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1270[label="ww60/Zero",fontsize=10,color="white",style="solid",shape="box"];404 -> 1270[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1270 -> 407[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	408[label="Char (primModNatS (Succ ww66) (Succ ww67))",fontsize=16,color="green",shape="box"];408 -> 413[label="",style="dashed", color="green", weight=3];
32.88/16.56	406[label="primDivNatS0 (Succ ww600) ww61 (primGEqNatS (Succ ww600) ww61)",fontsize=16,color="burlywood",shape="box"];1271[label="ww61/Succ ww610",fontsize=10,color="white",style="solid",shape="box"];406 -> 1271[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1271 -> 409[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1272[label="ww61/Zero",fontsize=10,color="white",style="solid",shape="box"];406 -> 1272[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1272 -> 410[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	407[label="primDivNatS0 Zero ww61 (primGEqNatS Zero ww61)",fontsize=16,color="burlywood",shape="box"];1273[label="ww61/Succ ww610",fontsize=10,color="white",style="solid",shape="box"];407 -> 1273[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1273 -> 411[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1274[label="ww61/Zero",fontsize=10,color="white",style="solid",shape="box"];407 -> 1274[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1274 -> 412[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	413[label="primModNatS (Succ ww66) (Succ ww67)",fontsize=16,color="black",shape="triangle"];413 -> 418[label="",style="solid", color="black", weight=3];
32.88/16.56	409[label="primDivNatS0 (Succ ww600) (Succ ww610) (primGEqNatS (Succ ww600) (Succ ww610))",fontsize=16,color="black",shape="box"];409 -> 414[label="",style="solid", color="black", weight=3];
32.88/16.56	410[label="primDivNatS0 (Succ ww600) Zero (primGEqNatS (Succ ww600) Zero)",fontsize=16,color="black",shape="box"];410 -> 415[label="",style="solid", color="black", weight=3];
32.88/16.56	411[label="primDivNatS0 Zero (Succ ww610) (primGEqNatS Zero (Succ ww610))",fontsize=16,color="black",shape="box"];411 -> 416[label="",style="solid", color="black", weight=3];
32.88/16.56	412[label="primDivNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];412 -> 417[label="",style="solid", color="black", weight=3];
32.88/16.56	418[label="primModNatS0 ww66 ww67 (primGEqNatS ww66 ww67)",fontsize=16,color="burlywood",shape="box"];1275[label="ww66/Succ ww660",fontsize=10,color="white",style="solid",shape="box"];418 -> 1275[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1275 -> 424[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1276[label="ww66/Zero",fontsize=10,color="white",style="solid",shape="box"];418 -> 1276[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1276 -> 425[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	414 -> 930[label="",style="dashed", color="red", weight=0];
32.88/16.56	414[label="primDivNatS0 (Succ ww600) (Succ ww610) (primGEqNatS ww600 ww610)",fontsize=16,color="magenta"];414 -> 931[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	414 -> 932[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	414 -> 933[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	414 -> 934[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	415[label="primDivNatS0 (Succ ww600) Zero True",fontsize=16,color="black",shape="box"];415 -> 421[label="",style="solid", color="black", weight=3];
32.88/16.56	416[label="primDivNatS0 Zero (Succ ww610) False",fontsize=16,color="black",shape="box"];416 -> 422[label="",style="solid", color="black", weight=3];
32.88/16.56	417[label="primDivNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];417 -> 423[label="",style="solid", color="black", weight=3];
32.88/16.56	424[label="primModNatS0 (Succ ww660) ww67 (primGEqNatS (Succ ww660) ww67)",fontsize=16,color="burlywood",shape="box"];1277[label="ww67/Succ ww670",fontsize=10,color="white",style="solid",shape="box"];424 -> 1277[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1277 -> 432[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1278[label="ww67/Zero",fontsize=10,color="white",style="solid",shape="box"];424 -> 1278[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1278 -> 433[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	425[label="primModNatS0 Zero ww67 (primGEqNatS Zero ww67)",fontsize=16,color="burlywood",shape="box"];1279[label="ww67/Succ ww670",fontsize=10,color="white",style="solid",shape="box"];425 -> 1279[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1279 -> 434[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1280[label="ww67/Zero",fontsize=10,color="white",style="solid",shape="box"];425 -> 1280[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1280 -> 435[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	931[label="ww610",fontsize=16,color="green",shape="box"];932[label="ww600",fontsize=16,color="green",shape="box"];933[label="ww600",fontsize=16,color="green",shape="box"];934[label="ww610",fontsize=16,color="green",shape="box"];930[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS ww112 ww113)",fontsize=16,color="burlywood",shape="triangle"];1281[label="ww112/Succ ww1120",fontsize=10,color="white",style="solid",shape="box"];930 -> 1281[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1281 -> 971[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1282[label="ww112/Zero",fontsize=10,color="white",style="solid",shape="box"];930 -> 1282[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1282 -> 972[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	421[label="Succ (primDivNatS (primMinusNatS (Succ ww600) Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];421 -> 430[label="",style="dashed", color="green", weight=3];
32.88/16.56	422[label="Zero",fontsize=16,color="green",shape="box"];423[label="Succ (primDivNatS (primMinusNatS Zero Zero) (Succ Zero))",fontsize=16,color="green",shape="box"];423 -> 431[label="",style="dashed", color="green", weight=3];
32.88/16.56	432[label="primModNatS0 (Succ ww660) (Succ ww670) (primGEqNatS (Succ ww660) (Succ ww670))",fontsize=16,color="black",shape="box"];432 -> 442[label="",style="solid", color="black", weight=3];
32.88/16.56	433[label="primModNatS0 (Succ ww660) Zero (primGEqNatS (Succ ww660) Zero)",fontsize=16,color="black",shape="box"];433 -> 443[label="",style="solid", color="black", weight=3];
32.88/16.56	434[label="primModNatS0 Zero (Succ ww670) (primGEqNatS Zero (Succ ww670))",fontsize=16,color="black",shape="box"];434 -> 444[label="",style="solid", color="black", weight=3];
32.88/16.56	435[label="primModNatS0 Zero Zero (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];435 -> 445[label="",style="solid", color="black", weight=3];
32.88/16.56	971[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS (Succ ww1120) ww113)",fontsize=16,color="burlywood",shape="box"];1283[label="ww113/Succ ww1130",fontsize=10,color="white",style="solid",shape="box"];971 -> 1283[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1283 -> 983[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1284[label="ww113/Zero",fontsize=10,color="white",style="solid",shape="box"];971 -> 1284[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1284 -> 984[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	972[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS Zero ww113)",fontsize=16,color="burlywood",shape="box"];1285[label="ww113/Succ ww1130",fontsize=10,color="white",style="solid",shape="box"];972 -> 1285[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1285 -> 985[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1286[label="ww113/Zero",fontsize=10,color="white",style="solid",shape="box"];972 -> 1286[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1286 -> 986[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	430 -> 1184[label="",style="dashed", color="red", weight=0];
32.88/16.56	430[label="primDivNatS (primMinusNatS (Succ ww600) Zero) (Succ Zero)",fontsize=16,color="magenta"];430 -> 1185[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	430 -> 1186[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	430 -> 1187[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	431 -> 1184[label="",style="dashed", color="red", weight=0];
32.88/16.56	431[label="primDivNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];431 -> 1188[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	431 -> 1189[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	431 -> 1190[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	442 -> 1005[label="",style="dashed", color="red", weight=0];
32.88/16.56	442[label="primModNatS0 (Succ ww660) (Succ ww670) (primGEqNatS ww660 ww670)",fontsize=16,color="magenta"];442 -> 1006[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	442 -> 1007[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	442 -> 1008[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	442 -> 1009[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	443[label="primModNatS0 (Succ ww660) Zero True",fontsize=16,color="black",shape="box"];443 -> 456[label="",style="solid", color="black", weight=3];
32.88/16.56	444[label="primModNatS0 Zero (Succ ww670) False",fontsize=16,color="black",shape="box"];444 -> 457[label="",style="solid", color="black", weight=3];
32.88/16.56	445[label="primModNatS0 Zero Zero True",fontsize=16,color="black",shape="box"];445 -> 458[label="",style="solid", color="black", weight=3];
32.88/16.56	983[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS (Succ ww1120) (Succ ww1130))",fontsize=16,color="black",shape="box"];983 -> 997[label="",style="solid", color="black", weight=3];
32.88/16.56	984[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS (Succ ww1120) Zero)",fontsize=16,color="black",shape="box"];984 -> 998[label="",style="solid", color="black", weight=3];
32.88/16.56	985[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS Zero (Succ ww1130))",fontsize=16,color="black",shape="box"];985 -> 999[label="",style="solid", color="black", weight=3];
32.88/16.56	986[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];986 -> 1000[label="",style="solid", color="black", weight=3];
32.88/16.56	1185[label="Succ ww600",fontsize=16,color="green",shape="box"];1186[label="Zero",fontsize=16,color="green",shape="box"];1187[label="Zero",fontsize=16,color="green",shape="box"];1184[label="primDivNatS (primMinusNatS ww124 ww125) (Succ ww126)",fontsize=16,color="burlywood",shape="triangle"];1287[label="ww124/Succ ww1240",fontsize=10,color="white",style="solid",shape="box"];1184 -> 1287[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1287 -> 1209[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1288[label="ww124/Zero",fontsize=10,color="white",style="solid",shape="box"];1184 -> 1288[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1288 -> 1210[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1188[label="Zero",fontsize=16,color="green",shape="box"];1189[label="Zero",fontsize=16,color="green",shape="box"];1190[label="Zero",fontsize=16,color="green",shape="box"];1006[label="ww660",fontsize=16,color="green",shape="box"];1007[label="ww670",fontsize=16,color="green",shape="box"];1008[label="ww660",fontsize=16,color="green",shape="box"];1009[label="ww670",fontsize=16,color="green",shape="box"];1005[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS ww117 ww118)",fontsize=16,color="burlywood",shape="triangle"];1289[label="ww117/Succ ww1170",fontsize=10,color="white",style="solid",shape="box"];1005 -> 1289[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1289 -> 1046[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1290[label="ww117/Zero",fontsize=10,color="white",style="solid",shape="box"];1005 -> 1290[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1290 -> 1047[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	456 -> 1092[label="",style="dashed", color="red", weight=0];
32.88/16.56	456[label="primModNatS (primMinusNatS (Succ ww660) Zero) (Succ Zero)",fontsize=16,color="magenta"];456 -> 1093[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	456 -> 1094[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	456 -> 1095[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	457[label="Succ Zero",fontsize=16,color="green",shape="box"];458 -> 1092[label="",style="dashed", color="red", weight=0];
32.88/16.56	458[label="primModNatS (primMinusNatS Zero Zero) (Succ Zero)",fontsize=16,color="magenta"];458 -> 1096[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	458 -> 1097[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	458 -> 1098[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	997 -> 930[label="",style="dashed", color="red", weight=0];
32.88/16.56	997[label="primDivNatS0 (Succ ww110) (Succ ww111) (primGEqNatS ww1120 ww1130)",fontsize=16,color="magenta"];997 -> 1048[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	997 -> 1049[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	998[label="primDivNatS0 (Succ ww110) (Succ ww111) True",fontsize=16,color="black",shape="triangle"];998 -> 1050[label="",style="solid", color="black", weight=3];
32.88/16.56	999[label="primDivNatS0 (Succ ww110) (Succ ww111) False",fontsize=16,color="black",shape="box"];999 -> 1051[label="",style="solid", color="black", weight=3];
32.88/16.56	1000 -> 998[label="",style="dashed", color="red", weight=0];
32.88/16.56	1000[label="primDivNatS0 (Succ ww110) (Succ ww111) True",fontsize=16,color="magenta"];1209[label="primDivNatS (primMinusNatS (Succ ww1240) ww125) (Succ ww126)",fontsize=16,color="burlywood",shape="box"];1291[label="ww125/Succ ww1250",fontsize=10,color="white",style="solid",shape="box"];1209 -> 1291[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1291 -> 1211[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1292[label="ww125/Zero",fontsize=10,color="white",style="solid",shape="box"];1209 -> 1292[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1292 -> 1212[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1210[label="primDivNatS (primMinusNatS Zero ww125) (Succ ww126)",fontsize=16,color="burlywood",shape="box"];1293[label="ww125/Succ ww1250",fontsize=10,color="white",style="solid",shape="box"];1210 -> 1293[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1293 -> 1213[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1294[label="ww125/Zero",fontsize=10,color="white",style="solid",shape="box"];1210 -> 1294[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1294 -> 1214[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1046[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS (Succ ww1170) ww118)",fontsize=16,color="burlywood",shape="box"];1295[label="ww118/Succ ww1180",fontsize=10,color="white",style="solid",shape="box"];1046 -> 1295[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1295 -> 1056[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1296[label="ww118/Zero",fontsize=10,color="white",style="solid",shape="box"];1046 -> 1296[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1296 -> 1057[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1047[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS Zero ww118)",fontsize=16,color="burlywood",shape="box"];1297[label="ww118/Succ ww1180",fontsize=10,color="white",style="solid",shape="box"];1047 -> 1297[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1297 -> 1058[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1298[label="ww118/Zero",fontsize=10,color="white",style="solid",shape="box"];1047 -> 1298[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1298 -> 1059[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1093[label="Succ ww660",fontsize=16,color="green",shape="box"];1094[label="Zero",fontsize=16,color="green",shape="box"];1095[label="Zero",fontsize=16,color="green",shape="box"];1092[label="primModNatS (primMinusNatS ww120 ww121) (Succ ww122)",fontsize=16,color="burlywood",shape="triangle"];1299[label="ww120/Succ ww1200",fontsize=10,color="white",style="solid",shape="box"];1092 -> 1299[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1299 -> 1123[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1300[label="ww120/Zero",fontsize=10,color="white",style="solid",shape="box"];1092 -> 1300[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1300 -> 1124[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1096[label="Zero",fontsize=16,color="green",shape="box"];1097[label="Zero",fontsize=16,color="green",shape="box"];1098[label="Zero",fontsize=16,color="green",shape="box"];1048[label="ww1130",fontsize=16,color="green",shape="box"];1049[label="ww1120",fontsize=16,color="green",shape="box"];1050[label="Succ (primDivNatS (primMinusNatS (Succ ww110) (Succ ww111)) (Succ (Succ ww111)))",fontsize=16,color="green",shape="box"];1050 -> 1060[label="",style="dashed", color="green", weight=3];
32.88/16.56	1051[label="Zero",fontsize=16,color="green",shape="box"];1211[label="primDivNatS (primMinusNatS (Succ ww1240) (Succ ww1250)) (Succ ww126)",fontsize=16,color="black",shape="box"];1211 -> 1215[label="",style="solid", color="black", weight=3];
32.88/16.56	1212[label="primDivNatS (primMinusNatS (Succ ww1240) Zero) (Succ ww126)",fontsize=16,color="black",shape="box"];1212 -> 1216[label="",style="solid", color="black", weight=3];
32.88/16.56	1213[label="primDivNatS (primMinusNatS Zero (Succ ww1250)) (Succ ww126)",fontsize=16,color="black",shape="box"];1213 -> 1217[label="",style="solid", color="black", weight=3];
32.88/16.56	1214[label="primDivNatS (primMinusNatS Zero Zero) (Succ ww126)",fontsize=16,color="black",shape="box"];1214 -> 1218[label="",style="solid", color="black", weight=3];
32.88/16.56	1056[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS (Succ ww1170) (Succ ww1180))",fontsize=16,color="black",shape="box"];1056 -> 1067[label="",style="solid", color="black", weight=3];
32.88/16.56	1057[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS (Succ ww1170) Zero)",fontsize=16,color="black",shape="box"];1057 -> 1068[label="",style="solid", color="black", weight=3];
32.88/16.56	1058[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS Zero (Succ ww1180))",fontsize=16,color="black",shape="box"];1058 -> 1069[label="",style="solid", color="black", weight=3];
32.88/16.56	1059[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS Zero Zero)",fontsize=16,color="black",shape="box"];1059 -> 1070[label="",style="solid", color="black", weight=3];
32.88/16.56	1123[label="primModNatS (primMinusNatS (Succ ww1200) ww121) (Succ ww122)",fontsize=16,color="burlywood",shape="box"];1301[label="ww121/Succ ww1210",fontsize=10,color="white",style="solid",shape="box"];1123 -> 1301[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1301 -> 1129[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1302[label="ww121/Zero",fontsize=10,color="white",style="solid",shape="box"];1123 -> 1302[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1302 -> 1130[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1124[label="primModNatS (primMinusNatS Zero ww121) (Succ ww122)",fontsize=16,color="burlywood",shape="box"];1303[label="ww121/Succ ww1210",fontsize=10,color="white",style="solid",shape="box"];1124 -> 1303[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1303 -> 1131[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1304[label="ww121/Zero",fontsize=10,color="white",style="solid",shape="box"];1124 -> 1304[label="",style="solid", color="burlywood", weight=9];
32.88/16.56	1304 -> 1132[label="",style="solid", color="burlywood", weight=3];
32.88/16.56	1060 -> 1184[label="",style="dashed", color="red", weight=0];
32.88/16.56	1060[label="primDivNatS (primMinusNatS (Succ ww110) (Succ ww111)) (Succ (Succ ww111))",fontsize=16,color="magenta"];1060 -> 1191[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1060 -> 1192[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1060 -> 1193[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1215 -> 1184[label="",style="dashed", color="red", weight=0];
32.88/16.56	1215[label="primDivNatS (primMinusNatS ww1240 ww1250) (Succ ww126)",fontsize=16,color="magenta"];1215 -> 1219[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1215 -> 1220[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1216 -> 399[label="",style="dashed", color="red", weight=0];
32.88/16.56	1216[label="primDivNatS (Succ ww1240) (Succ ww126)",fontsize=16,color="magenta"];1216 -> 1221[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1216 -> 1222[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1217[label="primDivNatS Zero (Succ ww126)",fontsize=16,color="black",shape="triangle"];1217 -> 1223[label="",style="solid", color="black", weight=3];
32.88/16.56	1218 -> 1217[label="",style="dashed", color="red", weight=0];
32.88/16.56	1218[label="primDivNatS Zero (Succ ww126)",fontsize=16,color="magenta"];1067 -> 1005[label="",style="dashed", color="red", weight=0];
32.88/16.56	1067[label="primModNatS0 (Succ ww115) (Succ ww116) (primGEqNatS ww1170 ww1180)",fontsize=16,color="magenta"];1067 -> 1076[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1067 -> 1077[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1068[label="primModNatS0 (Succ ww115) (Succ ww116) True",fontsize=16,color="black",shape="triangle"];1068 -> 1078[label="",style="solid", color="black", weight=3];
32.88/16.56	1069[label="primModNatS0 (Succ ww115) (Succ ww116) False",fontsize=16,color="black",shape="box"];1069 -> 1079[label="",style="solid", color="black", weight=3];
32.88/16.56	1070 -> 1068[label="",style="dashed", color="red", weight=0];
32.88/16.56	1070[label="primModNatS0 (Succ ww115) (Succ ww116) True",fontsize=16,color="magenta"];1129[label="primModNatS (primMinusNatS (Succ ww1200) (Succ ww1210)) (Succ ww122)",fontsize=16,color="black",shape="box"];1129 -> 1139[label="",style="solid", color="black", weight=3];
32.88/16.56	1130[label="primModNatS (primMinusNatS (Succ ww1200) Zero) (Succ ww122)",fontsize=16,color="black",shape="box"];1130 -> 1140[label="",style="solid", color="black", weight=3];
32.88/16.56	1131[label="primModNatS (primMinusNatS Zero (Succ ww1210)) (Succ ww122)",fontsize=16,color="black",shape="box"];1131 -> 1141[label="",style="solid", color="black", weight=3];
32.88/16.56	1132[label="primModNatS (primMinusNatS Zero Zero) (Succ ww122)",fontsize=16,color="black",shape="box"];1132 -> 1142[label="",style="solid", color="black", weight=3];
32.88/16.56	1191[label="Succ ww110",fontsize=16,color="green",shape="box"];1192[label="Succ ww111",fontsize=16,color="green",shape="box"];1193[label="Succ ww111",fontsize=16,color="green",shape="box"];1219[label="ww1240",fontsize=16,color="green",shape="box"];1220[label="ww1250",fontsize=16,color="green",shape="box"];1221[label="ww1240",fontsize=16,color="green",shape="box"];1222[label="ww126",fontsize=16,color="green",shape="box"];1223[label="Zero",fontsize=16,color="green",shape="box"];1076[label="ww1170",fontsize=16,color="green",shape="box"];1077[label="ww1180",fontsize=16,color="green",shape="box"];1078 -> 1092[label="",style="dashed", color="red", weight=0];
32.88/16.56	1078[label="primModNatS (primMinusNatS (Succ ww115) (Succ ww116)) (Succ (Succ ww116))",fontsize=16,color="magenta"];1078 -> 1105[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1078 -> 1106[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1078 -> 1107[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1079[label="Succ (Succ ww115)",fontsize=16,color="green",shape="box"];1139 -> 1092[label="",style="dashed", color="red", weight=0];
32.88/16.56	1139[label="primModNatS (primMinusNatS ww1200 ww1210) (Succ ww122)",fontsize=16,color="magenta"];1139 -> 1147[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1139 -> 1148[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1140 -> 413[label="",style="dashed", color="red", weight=0];
32.88/16.56	1140[label="primModNatS (Succ ww1200) (Succ ww122)",fontsize=16,color="magenta"];1140 -> 1149[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1140 -> 1150[label="",style="dashed", color="magenta", weight=3];
32.88/16.56	1141[label="primModNatS Zero (Succ ww122)",fontsize=16,color="black",shape="triangle"];1141 -> 1151[label="",style="solid", color="black", weight=3];
32.88/16.56	1142 -> 1141[label="",style="dashed", color="red", weight=0];
32.88/16.56	1142[label="primModNatS Zero (Succ ww122)",fontsize=16,color="magenta"];1105[label="Succ ww115",fontsize=16,color="green",shape="box"];1106[label="Succ ww116",fontsize=16,color="green",shape="box"];1107[label="Succ ww116",fontsize=16,color="green",shape="box"];1147[label="ww1200",fontsize=16,color="green",shape="box"];1148[label="ww1210",fontsize=16,color="green",shape="box"];1149[label="ww122",fontsize=16,color="green",shape="box"];1150[label="ww1200",fontsize=16,color="green",shape="box"];1151[label="Zero",fontsize=16,color="green",shape="box"];}
32.88/16.56	
32.88/16.56	----------------------------------------
32.88/16.56	
32.88/16.56	(151)
32.88/16.56	TRUE
33.09/16.60	EOF