108.24/94.19	MAYBE
110.68/94.86	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
110.68/94.86	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
110.68/94.86	
110.68/94.86	
110.68/94.86	H-Termination with start terms of the given HASKELL could not be shown:
110.68/94.86	
110.68/94.86	(0) HASKELL
110.68/94.86	(1) LR [EQUIVALENT, 0 ms]
110.68/94.86	(2) HASKELL
110.68/94.86	(3) IFR [EQUIVALENT, 0 ms]
110.68/94.86	(4) HASKELL
110.68/94.86	(5) BR [EQUIVALENT, 0 ms]
110.68/94.86	(6) HASKELL
110.68/94.86	(7) COR [EQUIVALENT, 1 ms]
110.68/94.86	(8) HASKELL
110.68/94.86	(9) LetRed [EQUIVALENT, 19 ms]
110.68/94.86	(10) HASKELL
110.68/94.86	(11) NumRed [SOUND, 0 ms]
110.68/94.86	(12) HASKELL
110.68/94.86	
110.68/94.86	
110.68/94.86	----------------------------------------
110.68/94.86	
110.68/94.86	(0)
110.68/94.86	Obligation:
110.68/94.86	mainModule Main 
110.68/94.86	module Main where {
110.68/94.86	import qualified Prelude;
110.68/94.86	}
110.68/94.86	
110.68/94.86	----------------------------------------
110.68/94.86	
110.68/94.86	(1) LR (EQUIVALENT)
110.68/94.86	Lambda Reductions:
110.68/94.86	The following Lambda expression
110.68/94.86	"\_->q"
110.68/94.86	is transformed to
110.68/94.86	"gtGt0 q _ = q;
110.68/94.86	"
110.68/94.86	The following Lambda expression
110.68/94.86	"\ab->(a,b)"
110.68/94.86	is transformed to
110.68/94.86	"zip0 a b = (a,b);
110.68/94.86	"
110.68/94.86	
110.68/94.86	----------------------------------------
110.68/94.86	
110.68/94.86	(2)
110.68/94.86	Obligation:
110.68/94.86	mainModule Main 
110.68/94.86	module Main where {
110.68/94.86	import qualified Prelude;
110.68/94.86	}
110.68/94.86	
110.68/94.86	----------------------------------------
110.68/94.86	
110.68/94.86	(3) IFR (EQUIVALENT)
110.68/94.86	If Reductions:
110.68/94.86	The following If expression
110.68/94.86	"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
110.68/94.86	is transformed to
110.68/94.86	"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
110.68/94.86	primDivNatS0 x y False = Zero;
110.68/94.86	"
110.68/94.86	The following If expression
110.68/94.86	"if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x"
110.68/94.86	is transformed to
110.68/94.86	"primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y);
110.68/94.86	primModNatS0 x y False = Succ x;
110.68/94.86	"
110.68/94.86	The following If expression
110.68/94.86	"if primGEqNatS x y then primModNatP (primMinusNatS x y) (Succ y) else primMinusNatS y x"
110.68/94.86	is transformed to
110.68/94.86	"primModNatP0 x y True = primModNatP (primMinusNatS x y) (Succ y);
110.68/94.86	primModNatP0 x y False = primMinusNatS y x;
110.68/94.86	"
110.68/94.86	
110.68/94.86	----------------------------------------
110.68/94.86	
110.68/94.86	(4)
110.68/94.86	Obligation:
110.68/94.86	mainModule Main 
110.68/94.86	module Main where {
110.68/94.86	import qualified Prelude;
110.68/94.86	}
110.68/94.86	
110.68/94.86	----------------------------------------
110.68/94.86	
110.68/94.86	(5) BR (EQUIVALENT)
110.68/94.86	Replaced joker patterns by fresh variables and removed binding patterns.
110.68/94.86	
110.68/94.86	Binding Reductions:
110.68/94.86	The bind variable of the following binding Pattern
110.68/94.86	"s@(wy : wz)"
110.68/94.86	is replaced by the following term
110.68/94.86	"wy : wz"
110.68/94.86	
110.68/94.86	----------------------------------------
110.68/94.86	
110.68/94.86	(6)
110.68/94.86	Obligation:
110.68/94.86	mainModule Main 
110.68/94.86	module Main where {
110.68/94.86	import qualified Prelude;
110.68/94.86	}
110.68/94.86	
110.68/94.86	----------------------------------------
110.68/94.86	
110.68/94.86	(7) COR (EQUIVALENT)
110.68/94.86	Cond Reductions:
110.68/94.86	The following Function with conditions
110.68/94.86	"showsPrec p ''' = showString (''' : '\' : ''' : ''' : []);
110.68/94.86	showsPrec p c = (showChar ''') . (showLitChar c) . showChar ''';
110.68/94.86	"
110.68/94.86	is transformed to
110.68/94.86	"showsPrec p zu = showsPrec2 p zu;
110.68/94.86	showsPrec p c = showsPrec0 p c;
110.68/94.86	"
110.68/94.86	"showsPrec0 p c = (showChar ''') . (showLitChar c) . showChar ''';
110.68/94.86	"
110.68/94.86	"showsPrec1 True p zu = showString (''' : '\' : ''' : ''' : []);
110.68/94.86	showsPrec1 zv zw zx = showsPrec0 zw zx;
110.68/94.86	"
110.68/94.86	"showsPrec2 p zu = showsPrec1 (zu == ''') p zu;
110.68/94.86	showsPrec2 zy zz = showsPrec0 zy zz;
110.68/94.86	"
110.68/94.86	The following Function with conditions
110.68/94.86	"randomSelect (x : []) = x;
110.68/94.86	randomSelect (x : xs)|terminatorrandomSelect xs|otherwisex;
110.68/94.86	"
110.68/94.86	is transformed to
110.68/94.86	"randomSelect (x : []) = randomSelect3 (x : []);
110.68/94.86	randomSelect (x : xs) = randomSelect2 (x : xs);
110.68/94.86	"
110.68/94.86	"randomSelect0 x xs True = x;
110.68/94.86	"
110.68/94.86	"randomSelect1 x xs True = randomSelect xs;
110.68/94.86	randomSelect1 x xs False = randomSelect0 x xs otherwise;
110.68/94.86	"
110.68/94.86	"randomSelect2 (x : xs) = randomSelect1 x xs terminator;
110.68/94.86	"
110.68/94.86	"randomSelect3 (x : []) = x;
110.68/94.86	randomSelect3 vux = randomSelect2 vux;
110.68/94.86	"
110.68/94.86	The following Function with conditions
110.68/94.86	"takeWhile p [] = [];
110.68/94.86	takeWhile p (x : xs)|p xx : takeWhile p xs|otherwise[];
110.68/94.86	"
110.68/94.86	is transformed to
110.68/94.86	"takeWhile p [] = takeWhile3 p [];
110.68/94.86	takeWhile p (x : xs) = takeWhile2 p (x : xs);
110.68/94.86	"
110.68/94.86	"takeWhile0 p x xs True = [];
110.68/94.86	"
110.68/94.86	"takeWhile1 p x xs True = x : takeWhile p xs;
110.68/94.86	takeWhile1 p x xs False = takeWhile0 p x xs otherwise;
110.68/94.86	"
110.68/94.86	"takeWhile2 p (x : xs) = takeWhile1 p x xs (p x);
110.68/94.86	"
110.68/94.86	"takeWhile3 p [] = [];
110.68/94.86	takeWhile3 vvu vvv = takeWhile2 vvu vvv;
110.68/94.86	"
110.68/94.86	The following Function with conditions
110.68/94.86	"!! (x : vx) 0 = x;
110.68/94.86	!! (vy : xs) n|n > 0xs !! (n - 1);
110.68/94.86	!! (vz : wu) wv = error [];
110.68/94.86	!! [] ww = error [];
110.68/94.86	"
110.68/94.86	is transformed to
110.68/94.86	"!! (x : vx) vwy = emEm5 (x : vx) vwy;
110.68/94.86	!! (vy : xs) n = emEm3 (vy : xs) n;
110.68/94.86	!! (vz : wu) wv = emEm1 (vz : wu) wv;
110.68/94.86	!! [] ww = emEm0 [] ww;
110.68/94.86	"
110.68/94.86	"emEm0 [] ww = error [];
110.68/94.86	"
110.68/94.86	"emEm1 (vz : wu) wv = error [];
110.68/94.86	emEm1 vvy vvz = emEm0 vvy vvz;
110.68/94.86	"
110.68/94.86	"emEm2 vy xs n True = xs !! (n - 1);
110.68/94.86	emEm2 vy xs n False = emEm1 (vy : xs) n;
110.68/94.86	"
110.68/94.86	"emEm3 (vy : xs) n = emEm2 vy xs n (n > 0);
110.68/94.86	emEm3 vwv vww = emEm1 vwv vww;
110.68/94.86	"
110.68/94.86	"emEm4 True (x : vx) vwy = x;
110.68/94.86	emEm4 vwz vxu vxv = emEm3 vxu vxv;
110.68/94.86	"
110.68/94.86	"emEm5 (x : vx) vwy = emEm4 (vwy == 0) (x : vx) vwy;
110.68/94.86	emEm5 vxw vxx = emEm3 vxw vxx;
110.68/94.86	"
110.68/94.86	The following Function with conditions
110.68/94.86	"showLitChar c|c > '\127'(showChar '\') . protectEsc isDigit (shows (fromEnum c));
110.68/94.86	showLitChar '\127' = showString ('\' : 'D' : 'E' : 'L' : []);
110.68/94.86	showLitChar '\' = showString ('\' : '\' : []);
110.68/94.86	showLitChar c|c >= '\32'showChar c;
110.68/94.86	showLitChar '\7' = showString ('\' : 'a' : []);
110.68/94.86	showLitChar '\8' = showString ('\' : 'b' : []);
110.68/94.86	showLitChar '\12' = showString ('\' : 'f' : []);
110.68/94.86	showLitChar '\10' = showString ('\' : 'n' : []);
110.68/94.86	showLitChar '\13' = showString ('\' : 'r' : []);
110.68/94.86	showLitChar '\9' = showString ('\' : 't' : []);
110.68/94.86	showLitChar '\11' = showString ('\' : 'v' : []);
110.68/94.86	showLitChar '\14' = protectEsc ('H' ==) (showString ('\' : 'S' : 'O' : []));
110.68/94.86	showLitChar c = showString ('\' : snd (asciiTab !! (fromEnum c)));
110.68/94.86	"
110.68/94.86	is transformed to
110.68/94.86	"showLitChar c = showLitChar24 c;
110.68/94.86	showLitChar wxz = showLitChar22 wxz;
110.68/94.86	showLitChar wxv = showLitChar20 wxv;
110.68/94.86	showLitChar c = showLitChar18 c;
110.68/94.86	showLitChar www = showLitChar16 www;
110.68/94.86	showLitChar wvy = showLitChar14 wvy;
110.68/94.86	showLitChar wvu = showLitChar12 wvu;
110.68/94.86	showLitChar wuw = showLitChar10 wuw;
110.68/94.86	showLitChar vzy = showLitChar8 vzy;
110.68/94.86	showLitChar vzu = showLitChar6 vzu;
110.68/94.86	showLitChar vyw = showLitChar4 vyw;
110.68/94.86	showLitChar vxy = showLitChar2 vxy;
110.68/94.86	showLitChar c = showLitChar0 c;
110.68/94.86	"
110.68/94.86	"showLitChar0 c = showString ('\' : snd (asciiTab !! (fromEnum c)));
110.68/94.86	"
110.68/94.86	"showLitChar1 True vxy = protectEsc ('H' ==) (showString ('\' : 'S' : 'O' : []));
110.68/94.86	showLitChar1 vxz vyu = showLitChar0 vyu;
110.68/94.86	"
110.68/94.86	"showLitChar2 vxy = showLitChar1 (vxy == '\14') vxy;
110.68/94.86	showLitChar2 vyv = showLitChar0 vyv;
110.68/94.86	"
110.68/94.86	"showLitChar3 True vyw = showString ('\' : 'v' : []);
110.68/94.86	showLitChar3 vyx vyy = showLitChar2 vyy;
110.68/94.87	"
110.68/94.87	"showLitChar4 vyw = showLitChar3 (vyw == '\11') vyw;
110.68/94.87	showLitChar4 vyz = showLitChar2 vyz;
110.68/94.87	"
110.68/94.87	"showLitChar5 True vzu = showString ('\' : 't' : []);
110.68/94.87	showLitChar5 vzv vzw = showLitChar4 vzw;
110.68/94.87	"
110.68/94.87	"showLitChar6 vzu = showLitChar5 (vzu == '\9') vzu;
110.68/94.87	showLitChar6 vzx = showLitChar4 vzx;
110.68/94.87	"
110.68/94.87	"showLitChar7 True vzy = showString ('\' : 'r' : []);
110.68/94.87	showLitChar7 vzz wuu = showLitChar6 wuu;
110.68/94.87	"
110.68/94.87	"showLitChar8 vzy = showLitChar7 (vzy == '\13') vzy;
110.68/94.87	showLitChar8 wuv = showLitChar6 wuv;
110.68/94.87	"
110.68/94.87	"showLitChar9 True wuw = showString ('\' : 'n' : []);
110.68/94.87	showLitChar9 wux wuy = showLitChar8 wuy;
110.68/94.87	"
110.68/94.87	"showLitChar10 wuw = showLitChar9 (wuw == '\10') wuw;
110.68/94.87	showLitChar10 wuz = showLitChar8 wuz;
110.68/94.87	"
110.68/94.87	"showLitChar11 True wvu = showString ('\' : 'f' : []);
110.68/94.87	showLitChar11 wvv wvw = showLitChar10 wvw;
110.68/94.87	"
110.68/94.87	"showLitChar12 wvu = showLitChar11 (wvu == '\12') wvu;
110.68/94.87	showLitChar12 wvx = showLitChar10 wvx;
110.68/94.87	"
110.68/94.87	"showLitChar13 True wvy = showString ('\' : 'b' : []);
110.68/94.87	showLitChar13 wvz wwu = showLitChar12 wwu;
110.68/94.87	"
110.68/94.87	"showLitChar14 wvy = showLitChar13 (wvy == '\8') wvy;
110.68/94.87	showLitChar14 wwv = showLitChar12 wwv;
110.68/94.87	"
110.68/94.87	"showLitChar15 True www = showString ('\' : 'a' : []);
110.68/94.87	showLitChar15 wwx wwy = showLitChar14 wwy;
110.68/94.87	"
110.68/94.87	"showLitChar16 www = showLitChar15 (www == '\7') www;
110.68/94.87	showLitChar16 wwz = showLitChar14 wwz;
110.68/94.87	"
110.68/94.87	"showLitChar17 c True = showChar c;
110.68/94.87	showLitChar17 c False = showLitChar16 c;
110.68/94.87	"
110.68/94.87	"showLitChar18 c = showLitChar17 c (c >= '\32');
110.68/94.87	showLitChar18 wxu = showLitChar16 wxu;
110.68/94.87	"
110.68/94.87	"showLitChar19 True wxv = showString ('\' : '\' : []);
110.68/94.87	showLitChar19 wxw wxx = showLitChar18 wxx;
110.68/94.87	"
110.68/94.87	"showLitChar20 wxv = showLitChar19 (wxv == '\') wxv;
110.68/94.87	showLitChar20 wxy = showLitChar18 wxy;
110.68/94.87	"
110.68/94.87	"showLitChar21 True wxz = showString ('\' : 'D' : 'E' : 'L' : []);
110.68/94.87	showLitChar21 wyu wyv = showLitChar20 wyv;
110.68/94.87	"
110.68/94.87	"showLitChar22 wxz = showLitChar21 (wxz == '\127') wxz;
110.68/94.87	showLitChar22 wyw = showLitChar20 wyw;
110.68/94.87	"
110.68/94.87	"showLitChar23 c True = (showChar '\') . protectEsc isDigit (shows (fromEnum c));
110.68/94.87	showLitChar23 c False = showLitChar22 c;
110.68/94.87	"
110.68/94.87	"showLitChar24 c = showLitChar23 c (c > '\127');
110.68/94.87	showLitChar24 wyx = showLitChar22 wyx;
110.68/94.87	"
110.68/94.87	The following Function with conditions
110.68/94.87	"cont (wy : wz)|p wy('\' : '&' : []) ++ wy : wz;
110.68/94.87	cont s = s;
110.68/94.87	"
110.68/94.87	is transformed to
110.68/94.87	"cont (wy : wz) = cont2 (wy : wz);
110.68/94.87	cont s = cont0 s;
110.68/94.87	"
110.68/94.87	"cont0 s = s;
110.68/94.87	"
110.68/94.87	"cont1 wy wz True = ('\' : '&' : []) ++ wy : wz;
110.68/94.87	cont1 wy wz False = cont0 (wy : wz);
110.68/94.87	"
110.68/94.87	"cont2 (wy : wz) = cont1 wy wz (p wy);
110.68/94.87	cont2 wyz = cont0 wyz;
110.68/94.87	"
110.68/94.87	The following Function with conditions
110.68/94.87	"undefined |Falseundefined;
110.68/94.87	"
110.68/94.87	is transformed to
110.68/94.87	"undefined  = undefined1;
110.68/94.87	"
110.68/94.87	"undefined0 True = undefined;
110.68/94.87	"
110.68/94.87	"undefined1  = undefined0 False;
110.68/94.87	"
110.68/94.87	
110.68/94.87	----------------------------------------
110.68/94.87	
110.68/94.87	(8)
110.68/94.87	Obligation:
110.68/94.87	mainModule Main 
110.68/94.87	module Main where {
110.68/94.87	import qualified Prelude;
110.68/94.87	}
110.68/94.87	
110.68/94.87	----------------------------------------
110.68/94.87	
110.68/94.87	(9) LetRed (EQUIVALENT)
110.68/94.87	Let/Where Reductions:
110.68/94.87	The bindings of the following Let/Where expression
110.68/94.87	"f . cont where {
110.68/94.87	cont (wy : wz) = cont2 (wy : wz);
110.68/94.87	cont s = cont0 s;
110.68/94.87	;
110.68/94.87	cont0 s = s;
110.68/94.87	;
110.68/94.87	cont1 wy wz True = ('\' : '&' : []) ++ wy : wz;
110.68/94.87	cont1 wy wz False = cont0 (wy : wz);
110.68/94.87	;
110.68/94.87	cont2 (wy : wz) = cont1 wy wz (p wy);
110.68/94.87	cont2 wyz = cont0 wyz;
110.68/94.87	} 
110.68/94.87	"
110.68/94.87	are unpacked to the following functions on top level
110.68/94.87	"protectEscCont2 wzu (wy : wz) = protectEscCont1 wzu wy wz (wzu wy);
110.68/94.87	protectEscCont2 wzu wyz = protectEscCont0 wzu wyz;
110.68/94.87	"
110.68/94.87	"protectEscCont0 wzu s = s;
110.68/94.87	"
110.68/94.87	"protectEscCont1 wzu wy wz True = ('\' : '&' : []) ++ wy : wz;
110.68/94.87	protectEscCont1 wzu wy wz False = protectEscCont0 wzu (wy : wz);
110.68/94.87	"
110.68/94.87	"protectEscCont wzu (wy : wz) = protectEscCont2 wzu (wy : wz);
110.68/94.87	protectEscCont wzu s = protectEscCont0 wzu s;
110.68/94.87	"
110.68/94.87	
110.68/94.87	----------------------------------------
110.68/94.87	
110.68/94.87	(10)
110.68/94.87	Obligation:
110.68/94.87	mainModule Main 
110.68/94.87	module Main where {
110.68/94.87	import qualified Prelude;
110.68/94.87	}
110.68/94.87	
110.68/94.87	----------------------------------------
110.68/94.87	
110.68/94.87	(11) NumRed (SOUND)
110.68/94.87	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
110.68/94.87	----------------------------------------
110.68/94.87	
110.68/94.87	(12)
110.68/94.87	Obligation:
110.68/94.87	mainModule Main 
110.68/94.87	module Main where {
110.68/94.87	import qualified Prelude;
110.68/94.87	}
110.73/94.92	EOF