103.20/91.27	MAYBE
105.52/91.93	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
105.52/91.93	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
105.52/91.93	
105.52/91.93	
105.52/91.93	H-Termination with start terms of the given HASKELL could not be shown:
105.52/91.93	
105.52/91.93	(0) HASKELL
105.52/91.93	(1) LR [EQUIVALENT, 0 ms]
105.52/91.93	(2) HASKELL
105.52/91.93	(3) IFR [EQUIVALENT, 0 ms]
105.52/91.93	(4) HASKELL
105.52/91.93	(5) BR [EQUIVALENT, 0 ms]
105.52/91.93	(6) HASKELL
105.52/91.93	(7) COR [EQUIVALENT, 5 ms]
105.52/91.93	(8) HASKELL
105.52/91.93	(9) LetRed [EQUIVALENT, 0 ms]
105.52/91.93	(10) HASKELL
105.52/91.93	(11) NumRed [SOUND, 1 ms]
105.52/91.93	(12) HASKELL
105.52/91.93	
105.52/91.93	
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(0)
105.52/91.93	Obligation:
105.52/91.93	mainModule Main 
105.52/91.93	module Main where {
105.52/91.93	import qualified Prelude;
105.52/91.93	}
105.52/91.93	
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(1) LR (EQUIVALENT)
105.52/91.93	Lambda Reductions:
105.52/91.93	The following Lambda expression
105.52/91.93	"\ab->(a,b)"
105.52/91.93	is transformed to
105.52/91.93	"zip0 a b = (a,b);
105.52/91.93	"
105.52/91.93	
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(2)
105.52/91.93	Obligation:
105.52/91.93	mainModule Main 
105.52/91.93	module Main where {
105.52/91.93	import qualified Prelude;
105.52/91.93	}
105.52/91.93	
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(3) IFR (EQUIVALENT)
105.52/91.93	If Reductions:
105.52/91.93	The following If expression
105.52/91.93	"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
105.52/91.93	is transformed to
105.52/91.93	"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
105.52/91.93	primDivNatS0 x y False = Zero;
105.52/91.93	"
105.52/91.93	The following If expression
105.52/91.93	"if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x"
105.52/91.93	is transformed to
105.52/91.93	"primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y);
105.52/91.93	primModNatS0 x y False = Succ x;
105.52/91.93	"
105.52/91.93	The following If expression
105.52/91.93	"if primGEqNatS x y then primModNatP (primMinusNatS x y) (Succ y) else primMinusNatS y x"
105.52/91.93	is transformed to
105.52/91.93	"primModNatP0 x y True = primModNatP (primMinusNatS x y) (Succ y);
105.52/91.93	primModNatP0 x y False = primMinusNatS y x;
105.52/91.93	"
105.52/91.93	
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(4)
105.52/91.93	Obligation:
105.52/91.93	mainModule Main 
105.52/91.93	module Main where {
105.52/91.93	import qualified Prelude;
105.52/91.93	}
105.52/91.93	
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(5) BR (EQUIVALENT)
105.52/91.93	Replaced joker patterns by fresh variables and removed binding patterns.
105.52/91.93	
105.52/91.93	Binding Reductions:
105.52/91.93	The bind variable of the following binding Pattern
105.52/91.93	"s@(wy : wz)"
105.52/91.93	is replaced by the following term
105.52/91.93	"wy : wz"
105.52/91.93	
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(6)
105.52/91.93	Obligation:
105.52/91.93	mainModule Main 
105.52/91.93	module Main where {
105.52/91.93	import qualified Prelude;
105.52/91.93	}
105.52/91.93	
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(7) COR (EQUIVALENT)
105.52/91.93	Cond Reductions:
105.52/91.93	The following Function with conditions
105.52/91.93	"showsPrec p ''' = showString (''' : '\' : ''' : ''' : []);
105.52/91.93	showsPrec p c = (showChar ''') . (showLitChar c) . showChar ''';
105.52/91.93	"
105.52/91.93	is transformed to
105.52/91.93	"showsPrec p yz = showsPrec2 p yz;
105.52/91.93	showsPrec p c = showsPrec0 p c;
105.52/91.93	"
105.52/91.93	"showsPrec0 p c = (showChar ''') . (showLitChar c) . showChar ''';
105.52/91.93	"
105.52/91.93	"showsPrec1 True p yz = showString (''' : '\' : ''' : ''' : []);
105.52/91.93	showsPrec1 zu zv zw = showsPrec0 zv zw;
105.52/91.93	"
105.52/91.93	"showsPrec2 p yz = showsPrec1 (yz == ''') p yz;
105.52/91.93	showsPrec2 zx zy = showsPrec0 zx zy;
105.52/91.93	"
105.52/91.93	The following Function with conditions
105.52/91.93	"takeWhile p [] = [];
105.52/91.93	takeWhile p (x : xs)|p xx : takeWhile p xs|otherwise[];
105.52/91.93	"
105.52/91.93	is transformed to
105.52/91.93	"takeWhile p [] = takeWhile3 p [];
105.52/91.93	takeWhile p (x : xs) = takeWhile2 p (x : xs);
105.52/91.93	"
105.52/91.93	"takeWhile0 p x xs True = [];
105.52/91.93	"
105.52/91.93	"takeWhile1 p x xs True = x : takeWhile p xs;
105.52/91.93	takeWhile1 p x xs False = takeWhile0 p x xs otherwise;
105.52/91.93	"
105.52/91.93	"takeWhile2 p (x : xs) = takeWhile1 p x xs (p x);
105.52/91.93	"
105.52/91.93	"takeWhile3 p [] = [];
105.52/91.93	takeWhile3 vuv vuw = takeWhile2 vuv vuw;
105.52/91.93	"
105.52/91.93	The following Function with conditions
105.52/91.93	"!! (x : vx) 0 = x;
105.52/91.93	!! (vy : xs) n|n > 0xs !! (n - 1);
105.52/91.93	!! (vz : wu) wv = error [];
105.52/91.93	!! [] ww = error [];
105.52/91.93	"
105.52/91.93	is transformed to
105.52/91.93	"!! (x : vx) vvz = emEm5 (x : vx) vvz;
105.52/91.93	!! (vy : xs) n = emEm3 (vy : xs) n;
105.52/91.93	!! (vz : wu) wv = emEm1 (vz : wu) wv;
105.52/91.93	!! [] ww = emEm0 [] ww;
105.52/91.93	"
105.52/91.93	"emEm0 [] ww = error [];
105.52/91.93	"
105.52/91.93	"emEm1 (vz : wu) wv = error [];
105.52/91.93	emEm1 vuz vvu = emEm0 vuz vvu;
105.52/91.93	"
105.52/91.93	"emEm2 vy xs n True = xs !! (n - 1);
105.52/91.93	emEm2 vy xs n False = emEm1 (vy : xs) n;
105.52/91.93	"
105.52/91.93	"emEm3 (vy : xs) n = emEm2 vy xs n (n > 0);
105.52/91.93	emEm3 vvw vvx = emEm1 vvw vvx;
105.52/91.93	"
105.52/91.93	"emEm4 True (x : vx) vvz = x;
105.52/91.93	emEm4 vwu vwv vww = emEm3 vwv vww;
105.52/91.93	"
105.52/91.93	"emEm5 (x : vx) vvz = emEm4 (vvz == 0) (x : vx) vvz;
105.52/91.93	emEm5 vwx vwy = emEm3 vwx vwy;
105.52/91.93	"
105.52/91.93	The following Function with conditions
105.52/91.93	"showLitChar c|c > '\127'(showChar '\') . protectEsc isDigit (shows (fromEnum c));
105.52/91.93	showLitChar '\127' = showString ('\' : 'D' : 'E' : 'L' : []);
105.52/91.93	showLitChar '\' = showString ('\' : '\' : []);
105.52/91.93	showLitChar c|c >= '\32'showChar c;
105.52/91.93	showLitChar '\7' = showString ('\' : 'a' : []);
105.52/91.93	showLitChar '\8' = showString ('\' : 'b' : []);
105.52/91.93	showLitChar '\12' = showString ('\' : 'f' : []);
105.52/91.93	showLitChar '\10' = showString ('\' : 'n' : []);
105.52/91.93	showLitChar '\13' = showString ('\' : 'r' : []);
105.52/91.93	showLitChar '\9' = showString ('\' : 't' : []);
105.52/91.93	showLitChar '\11' = showString ('\' : 'v' : []);
105.52/91.93	showLitChar '\14' = protectEsc ('H' ==) (showString ('\' : 'S' : 'O' : []));
105.52/91.93	showLitChar c = showString ('\' : snd (asciiTab !! (fromEnum c)));
105.52/91.93	"
105.52/91.93	is transformed to
105.52/91.93	"showLitChar c = showLitChar24 c;
105.52/91.93	showLitChar wxu = showLitChar22 wxu;
105.52/91.93	showLitChar www = showLitChar20 www;
105.52/91.93	showLitChar c = showLitChar18 c;
105.52/91.93	showLitChar wvx = showLitChar16 wvx;
105.52/91.93	showLitChar wuz = showLitChar14 wuz;
105.52/91.93	showLitChar wuv = showLitChar12 wuv;
105.52/91.93	showLitChar vzx = showLitChar10 vzx;
105.52/91.93	showLitChar vyz = showLitChar8 vyz;
105.52/91.93	showLitChar vyv = showLitChar6 vyv;
105.52/91.93	showLitChar vxx = showLitChar4 vxx;
105.52/91.93	showLitChar vwz = showLitChar2 vwz;
105.52/91.93	showLitChar c = showLitChar0 c;
105.52/91.93	"
105.52/91.93	"showLitChar0 c = showString ('\' : snd (asciiTab !! (fromEnum c)));
105.52/91.93	"
105.52/91.93	"showLitChar1 True vwz = protectEsc ('H' ==) (showString ('\' : 'S' : 'O' : []));
105.52/91.93	showLitChar1 vxu vxv = showLitChar0 vxv;
105.52/91.93	"
105.52/91.93	"showLitChar2 vwz = showLitChar1 (vwz == '\14') vwz;
105.52/91.93	showLitChar2 vxw = showLitChar0 vxw;
105.52/91.93	"
105.52/91.93	"showLitChar3 True vxx = showString ('\' : 'v' : []);
105.52/91.93	showLitChar3 vxy vxz = showLitChar2 vxz;
105.52/91.93	"
105.52/91.93	"showLitChar4 vxx = showLitChar3 (vxx == '\11') vxx;
105.52/91.93	showLitChar4 vyu = showLitChar2 vyu;
105.52/91.93	"
105.52/91.93	"showLitChar5 True vyv = showString ('\' : 't' : []);
105.52/91.93	showLitChar5 vyw vyx = showLitChar4 vyx;
105.52/91.93	"
105.52/91.93	"showLitChar6 vyv = showLitChar5 (vyv == '\9') vyv;
105.52/91.93	showLitChar6 vyy = showLitChar4 vyy;
105.52/91.93	"
105.52/91.93	"showLitChar7 True vyz = showString ('\' : 'r' : []);
105.52/91.93	showLitChar7 vzu vzv = showLitChar6 vzv;
105.52/91.93	"
105.52/91.93	"showLitChar8 vyz = showLitChar7 (vyz == '\13') vyz;
105.52/91.93	showLitChar8 vzw = showLitChar6 vzw;
105.52/91.93	"
105.52/91.93	"showLitChar9 True vzx = showString ('\' : 'n' : []);
105.52/91.93	showLitChar9 vzy vzz = showLitChar8 vzz;
105.52/91.93	"
105.52/91.93	"showLitChar10 vzx = showLitChar9 (vzx == '\10') vzx;
105.52/91.93	showLitChar10 wuu = showLitChar8 wuu;
105.52/91.93	"
105.52/91.93	"showLitChar11 True wuv = showString ('\' : 'f' : []);
105.52/91.93	showLitChar11 wuw wux = showLitChar10 wux;
105.52/91.93	"
105.52/91.93	"showLitChar12 wuv = showLitChar11 (wuv == '\12') wuv;
105.52/91.93	showLitChar12 wuy = showLitChar10 wuy;
105.52/91.93	"
105.52/91.93	"showLitChar13 True wuz = showString ('\' : 'b' : []);
105.52/91.93	showLitChar13 wvu wvv = showLitChar12 wvv;
105.52/91.93	"
105.52/91.93	"showLitChar14 wuz = showLitChar13 (wuz == '\8') wuz;
105.52/91.93	showLitChar14 wvw = showLitChar12 wvw;
105.52/91.93	"
105.52/91.93	"showLitChar15 True wvx = showString ('\' : 'a' : []);
105.52/91.93	showLitChar15 wvy wvz = showLitChar14 wvz;
105.52/91.93	"
105.52/91.93	"showLitChar16 wvx = showLitChar15 (wvx == '\7') wvx;
105.52/91.93	showLitChar16 wwu = showLitChar14 wwu;
105.52/91.93	"
105.52/91.93	"showLitChar17 c True = showChar c;
105.52/91.93	showLitChar17 c False = showLitChar16 c;
105.52/91.93	"
105.52/91.93	"showLitChar18 c = showLitChar17 c (c >= '\32');
105.52/91.93	showLitChar18 wwv = showLitChar16 wwv;
105.52/91.93	"
105.52/91.93	"showLitChar19 True www = showString ('\' : '\' : []);
105.52/91.93	showLitChar19 wwx wwy = showLitChar18 wwy;
105.52/91.93	"
105.52/91.93	"showLitChar20 www = showLitChar19 (www == '\') www;
105.52/91.93	showLitChar20 wwz = showLitChar18 wwz;
105.52/91.93	"
105.52/91.93	"showLitChar21 True wxu = showString ('\' : 'D' : 'E' : 'L' : []);
105.52/91.93	showLitChar21 wxv wxw = showLitChar20 wxw;
105.52/91.93	"
105.52/91.93	"showLitChar22 wxu = showLitChar21 (wxu == '\127') wxu;
105.52/91.93	showLitChar22 wxx = showLitChar20 wxx;
105.52/91.93	"
105.52/91.93	"showLitChar23 c True = (showChar '\') . protectEsc isDigit (shows (fromEnum c));
105.52/91.93	showLitChar23 c False = showLitChar22 c;
105.52/91.93	"
105.52/91.93	"showLitChar24 c = showLitChar23 c (c > '\127');
105.52/91.93	showLitChar24 wxy = showLitChar22 wxy;
105.52/91.93	"
105.52/91.93	The following Function with conditions
105.52/91.93	"cont (wy : wz)|p wy('\' : '&' : []) ++ wy : wz;
105.52/91.93	cont s = s;
105.52/91.93	"
105.52/91.93	is transformed to
105.52/91.93	"cont (wy : wz) = cont2 (wy : wz);
105.52/91.93	cont s = cont0 s;
105.52/91.93	"
105.52/91.93	"cont0 s = s;
105.52/91.93	"
105.52/91.93	"cont1 wy wz True = ('\' : '&' : []) ++ wy : wz;
105.52/91.93	cont1 wy wz False = cont0 (wy : wz);
105.52/91.93	"
105.52/91.93	"cont2 (wy : wz) = cont1 wy wz (p wy);
105.52/91.93	cont2 wyu = cont0 wyu;
105.52/91.93	"
105.52/91.93	The following Function with conditions
105.52/91.93	"undefined |Falseundefined;
105.52/91.93	"
105.52/91.93	is transformed to
105.52/91.93	"undefined  = undefined1;
105.52/91.93	"
105.52/91.93	"undefined0 True = undefined;
105.52/91.93	"
105.52/91.93	"undefined1  = undefined0 False;
105.52/91.93	"
105.52/91.93	
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(8)
105.52/91.93	Obligation:
105.52/91.93	mainModule Main 
105.52/91.93	module Main where {
105.52/91.93	import qualified Prelude;
105.52/91.93	}
105.52/91.93	
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(9) LetRed (EQUIVALENT)
105.52/91.93	Let/Where Reductions:
105.52/91.93	The bindings of the following Let/Where expression
105.52/91.93	"f . cont where {
105.52/91.93	cont (wy : wz) = cont2 (wy : wz);
105.52/91.93	cont s = cont0 s;
105.52/91.93	;
105.52/91.93	cont0 s = s;
105.52/91.93	;
105.52/91.93	cont1 wy wz True = ('\' : '&' : []) ++ wy : wz;
105.52/91.93	cont1 wy wz False = cont0 (wy : wz);
105.52/91.93	;
105.52/91.93	cont2 (wy : wz) = cont1 wy wz (p wy);
105.52/91.93	cont2 wyu = cont0 wyu;
105.52/91.93	} 
105.52/91.93	"
105.52/91.93	are unpacked to the following functions on top level
105.52/91.93	"protectEscCont wyv (wy : wz) = protectEscCont2 wyv (wy : wz);
105.52/91.93	protectEscCont wyv s = protectEscCont0 wyv s;
105.52/91.93	"
105.52/91.93	"protectEscCont2 wyv (wy : wz) = protectEscCont1 wyv wy wz (wyv wy);
105.52/91.93	protectEscCont2 wyv wyu = protectEscCont0 wyv wyu;
105.52/91.93	"
105.52/91.93	"protectEscCont0 wyv s = s;
105.52/91.93	"
105.52/91.93	"protectEscCont1 wyv wy wz True = ('\' : '&' : []) ++ wy : wz;
105.52/91.93	protectEscCont1 wyv wy wz False = protectEscCont0 wyv (wy : wz);
105.52/91.93	"
105.52/91.93	
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(10)
105.52/91.93	Obligation:
105.52/91.93	mainModule Main 
105.52/91.93	module Main where {
105.52/91.93	import qualified Prelude;
105.52/91.93	}
105.52/91.93	
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(11) NumRed (SOUND)
105.52/91.93	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
105.52/91.93	----------------------------------------
105.52/91.93	
105.52/91.93	(12)
105.52/91.93	Obligation:
105.52/91.93	mainModule Main 
105.52/91.93	module Main where {
105.52/91.93	import qualified Prelude;
105.52/91.93	}
105.60/91.97	EOF