107.13/95.15	MAYBE
109.42/95.84	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
109.42/95.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
109.42/95.84	
109.42/95.84	
109.42/95.84	H-Termination with start terms of the given HASKELL could not be shown:
109.42/95.84	
109.42/95.84	(0) HASKELL
109.42/95.84	(1) LR [EQUIVALENT, 0 ms]
109.42/95.84	(2) HASKELL
109.42/95.84	(3) IFR [EQUIVALENT, 0 ms]
109.42/95.84	(4) HASKELL
109.42/95.84	(5) BR [EQUIVALENT, 0 ms]
109.42/95.84	(6) HASKELL
109.42/95.84	(7) COR [EQUIVALENT, 10 ms]
109.42/95.84	(8) HASKELL
109.42/95.84	(9) LetRed [EQUIVALENT, 0 ms]
109.42/95.84	(10) HASKELL
109.42/95.84	(11) NumRed [SOUND, 4 ms]
109.42/95.84	(12) HASKELL
109.42/95.84	
109.42/95.84	
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(0)
109.42/95.84	Obligation:
109.42/95.84	mainModule Main 
109.42/95.84	module Main where {
109.42/95.84	import qualified Prelude;
109.42/95.84	}
109.42/95.84	
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(1) LR (EQUIVALENT)
109.42/95.84	Lambda Reductions:
109.42/95.84	The following Lambda expression
109.42/95.84	"\ab->(a,b)"
109.42/95.84	is transformed to
109.42/95.84	"zip0 a b = (a,b);
109.42/95.84	"
109.42/95.84	
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(2)
109.42/95.84	Obligation:
109.42/95.84	mainModule Main 
109.42/95.84	module Main where {
109.42/95.84	import qualified Prelude;
109.42/95.84	}
109.42/95.84	
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(3) IFR (EQUIVALENT)
109.42/95.84	If Reductions:
109.42/95.84	The following If expression
109.42/95.84	"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
109.42/95.84	is transformed to
109.42/95.84	"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
109.42/95.84	primDivNatS0 x y False = Zero;
109.42/95.84	"
109.42/95.84	The following If expression
109.42/95.84	"if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x"
109.42/95.84	is transformed to
109.42/95.84	"primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y);
109.42/95.84	primModNatS0 x y False = Succ x;
109.42/95.84	"
109.42/95.84	The following If expression
109.42/95.84	"if primGEqNatS x y then primModNatP (primMinusNatS x y) (Succ y) else primMinusNatS y x"
109.42/95.84	is transformed to
109.42/95.84	"primModNatP0 x y True = primModNatP (primMinusNatS x y) (Succ y);
109.42/95.84	primModNatP0 x y False = primMinusNatS y x;
109.42/95.84	"
109.42/95.84	
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(4)
109.42/95.84	Obligation:
109.42/95.84	mainModule Main 
109.42/95.84	module Main where {
109.42/95.84	import qualified Prelude;
109.42/95.84	}
109.42/95.84	
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(5) BR (EQUIVALENT)
109.42/95.84	Replaced joker patterns by fresh variables and removed binding patterns.
109.42/95.84	
109.42/95.84	Binding Reductions:
109.42/95.84	The bind variable of the following binding Pattern
109.42/95.84	"s@(wy : wz)"
109.42/95.84	is replaced by the following term
109.42/95.84	"wy : wz"
109.42/95.84	
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(6)
109.42/95.84	Obligation:
109.42/95.84	mainModule Main 
109.42/95.84	module Main where {
109.42/95.84	import qualified Prelude;
109.42/95.84	}
109.42/95.84	
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(7) COR (EQUIVALENT)
109.42/95.84	Cond Reductions:
109.42/95.84	The following Function with conditions
109.42/95.84	"showl [] = showChar '"';
109.42/95.84	showl ('"' : cs) = (showString ('\' : '"' : [])) . showl cs;
109.42/95.84	showl (c : cs) = (showLitChar c) . showl cs;
109.42/95.84	"
109.42/95.84	is transformed to
109.42/95.84	"showl [] = showl3 [];
109.42/95.84	showl (zv : cs) = showl2 (zv : cs);
109.42/95.84	showl (c : cs) = showl0 (c : cs);
109.42/95.84	"
109.42/95.84	"showl0 (c : cs) = (showLitChar c) . showl cs;
109.42/95.84	"
109.42/95.84	"showl1 True (zv : cs) = (showString ('\' : '"' : [])) . showl cs;
109.42/95.84	showl1 zw zx = showl0 zx;
109.42/95.84	"
109.42/95.84	"showl2 (zv : cs) = showl1 (zv == '"') (zv : cs);
109.42/95.84	showl2 zy = showl0 zy;
109.42/95.84	"
109.42/95.84	"showl3 [] = showChar '"';
109.42/95.84	showl3 vuu = showl2 vuu;
109.42/95.84	"
109.42/95.84	The following Function with conditions
109.42/95.84	"takeWhile p [] = [];
109.42/95.84	takeWhile p (x : xs)|p xx : takeWhile p xs|otherwise[];
109.42/95.84	"
109.42/95.84	is transformed to
109.42/95.84	"takeWhile p [] = takeWhile3 p [];
109.42/95.84	takeWhile p (x : xs) = takeWhile2 p (x : xs);
109.42/95.84	"
109.42/95.84	"takeWhile0 p x xs True = [];
109.42/95.84	"
109.42/95.84	"takeWhile1 p x xs True = x : takeWhile p xs;
109.42/95.84	takeWhile1 p x xs False = takeWhile0 p x xs otherwise;
109.42/95.84	"
109.42/95.84	"takeWhile2 p (x : xs) = takeWhile1 p x xs (p x);
109.42/95.84	"
109.42/95.84	"takeWhile3 p [] = [];
109.42/95.84	takeWhile3 vux vuy = takeWhile2 vux vuy;
109.42/95.84	"
109.42/95.84	The following Function with conditions
109.42/95.84	"!! (x : vx) 0 = x;
109.42/95.84	!! (vy : xs) n|n > 0xs !! (n - 1);
109.42/95.84	!! (vz : wu) wv = error [];
109.42/95.84	!! [] ww = error [];
109.42/95.84	"
109.42/95.84	is transformed to
109.42/95.84	"!! (x : vx) vwv = emEm5 (x : vx) vwv;
109.42/95.84	!! (vy : xs) n = emEm3 (vy : xs) n;
109.42/95.84	!! (vz : wu) wv = emEm1 (vz : wu) wv;
109.42/95.84	!! [] ww = emEm0 [] ww;
109.42/95.84	"
109.42/95.84	"emEm0 [] ww = error [];
109.42/95.84	"
109.42/95.84	"emEm1 (vz : wu) wv = error [];
109.42/95.84	emEm1 vvv vvw = emEm0 vvv vvw;
109.42/95.84	"
109.42/95.84	"emEm2 vy xs n True = xs !! (n - 1);
109.42/95.84	emEm2 vy xs n False = emEm1 (vy : xs) n;
109.42/95.84	"
109.42/95.84	"emEm3 (vy : xs) n = emEm2 vy xs n (n > 0);
109.42/95.84	emEm3 vvy vvz = emEm1 vvy vvz;
109.42/95.84	"
109.42/95.84	"emEm4 True (x : vx) vwv = x;
109.42/95.84	emEm4 vww vwx vwy = emEm3 vwx vwy;
109.42/95.84	"
109.42/95.84	"emEm5 (x : vx) vwv = emEm4 (vwv == 0) (x : vx) vwv;
109.42/95.84	emEm5 vwz vxu = emEm3 vwz vxu;
109.42/95.84	"
109.42/95.84	The following Function with conditions
109.42/95.84	"showLitChar c|c > '\127'(showChar '\') . protectEsc isDigit (shows (fromEnum c));
109.42/95.84	showLitChar '\127' = showString ('\' : 'D' : 'E' : 'L' : []);
109.42/95.84	showLitChar '\' = showString ('\' : '\' : []);
109.42/95.84	showLitChar c|c >= '\32'showChar c;
109.42/95.84	showLitChar '\7' = showString ('\' : 'a' : []);
109.42/95.84	showLitChar '\8' = showString ('\' : 'b' : []);
109.42/95.84	showLitChar '\12' = showString ('\' : 'f' : []);
109.42/95.84	showLitChar '\10' = showString ('\' : 'n' : []);
109.42/95.84	showLitChar '\13' = showString ('\' : 'r' : []);
109.42/95.84	showLitChar '\9' = showString ('\' : 't' : []);
109.42/95.84	showLitChar '\11' = showString ('\' : 'v' : []);
109.42/95.84	showLitChar '\14' = protectEsc ('H' ==) (showString ('\' : 'S' : 'O' : []));
109.42/95.84	showLitChar c = showString ('\' : snd (asciiTab !! (fromEnum c)));
109.42/95.84	"
109.42/95.84	is transformed to
109.42/95.84	"showLitChar c = showLitChar24 c;
109.42/95.84	showLitChar wxw = showLitChar22 wxw;
109.42/95.84	showLitChar wwy = showLitChar20 wwy;
109.42/95.84	showLitChar c = showLitChar18 c;
109.42/95.84	showLitChar wvz = showLitChar16 wvz;
109.42/95.84	showLitChar wvv = showLitChar14 wvv;
109.42/95.84	showLitChar wux = showLitChar12 wux;
109.42/95.84	showLitChar vzz = showLitChar10 vzz;
109.42/95.84	showLitChar vzv = showLitChar8 vzv;
109.42/95.84	showLitChar vyx = showLitChar6 vyx;
109.42/95.84	showLitChar vxz = showLitChar4 vxz;
109.42/95.84	showLitChar vxv = showLitChar2 vxv;
109.42/95.84	showLitChar c = showLitChar0 c;
109.42/95.84	"
109.42/95.84	"showLitChar0 c = showString ('\' : snd (asciiTab !! (fromEnum c)));
109.42/95.84	"
109.42/95.84	"showLitChar1 True vxv = protectEsc ('H' ==) (showString ('\' : 'S' : 'O' : []));
109.42/95.84	showLitChar1 vxw vxx = showLitChar0 vxx;
109.42/95.84	"
109.42/95.84	"showLitChar2 vxv = showLitChar1 (vxv == '\14') vxv;
109.42/95.84	showLitChar2 vxy = showLitChar0 vxy;
109.42/95.84	"
109.42/95.84	"showLitChar3 True vxz = showString ('\' : 'v' : []);
109.42/95.84	showLitChar3 vyu vyv = showLitChar2 vyv;
109.42/95.84	"
109.42/95.84	"showLitChar4 vxz = showLitChar3 (vxz == '\11') vxz;
109.42/95.84	showLitChar4 vyw = showLitChar2 vyw;
109.42/95.84	"
109.42/95.84	"showLitChar5 True vyx = showString ('\' : 't' : []);
109.42/95.84	showLitChar5 vyy vyz = showLitChar4 vyz;
109.42/95.84	"
109.42/95.84	"showLitChar6 vyx = showLitChar5 (vyx == '\9') vyx;
109.42/95.84	showLitChar6 vzu = showLitChar4 vzu;
109.42/95.84	"
109.42/95.84	"showLitChar7 True vzv = showString ('\' : 'r' : []);
109.42/95.84	showLitChar7 vzw vzx = showLitChar6 vzx;
109.42/95.84	"
109.42/95.84	"showLitChar8 vzv = showLitChar7 (vzv == '\13') vzv;
109.42/95.84	showLitChar8 vzy = showLitChar6 vzy;
109.42/95.84	"
109.42/95.84	"showLitChar9 True vzz = showString ('\' : 'n' : []);
109.42/95.84	showLitChar9 wuu wuv = showLitChar8 wuv;
109.42/95.84	"
109.42/95.84	"showLitChar10 vzz = showLitChar9 (vzz == '\10') vzz;
109.42/95.84	showLitChar10 wuw = showLitChar8 wuw;
109.42/95.84	"
109.42/95.84	"showLitChar11 True wux = showString ('\' : 'f' : []);
109.42/95.84	showLitChar11 wuy wuz = showLitChar10 wuz;
109.42/95.84	"
109.42/95.84	"showLitChar12 wux = showLitChar11 (wux == '\12') wux;
109.42/95.84	showLitChar12 wvu = showLitChar10 wvu;
109.42/95.84	"
109.42/95.84	"showLitChar13 True wvv = showString ('\' : 'b' : []);
109.42/95.84	showLitChar13 wvw wvx = showLitChar12 wvx;
109.42/95.84	"
109.42/95.84	"showLitChar14 wvv = showLitChar13 (wvv == '\8') wvv;
109.42/95.84	showLitChar14 wvy = showLitChar12 wvy;
109.42/95.84	"
109.42/95.84	"showLitChar15 True wvz = showString ('\' : 'a' : []);
109.42/95.84	showLitChar15 wwu wwv = showLitChar14 wwv;
109.42/95.84	"
109.42/95.84	"showLitChar16 wvz = showLitChar15 (wvz == '\7') wvz;
109.42/95.84	showLitChar16 www = showLitChar14 www;
109.42/95.84	"
109.42/95.84	"showLitChar17 c True = showChar c;
109.42/95.84	showLitChar17 c False = showLitChar16 c;
109.42/95.84	"
109.42/95.84	"showLitChar18 c = showLitChar17 c (c >= '\32');
109.42/95.84	showLitChar18 wwx = showLitChar16 wwx;
109.42/95.84	"
109.42/95.84	"showLitChar19 True wwy = showString ('\' : '\' : []);
109.42/95.84	showLitChar19 wwz wxu = showLitChar18 wxu;
109.42/95.84	"
109.42/95.84	"showLitChar20 wwy = showLitChar19 (wwy == '\') wwy;
109.42/95.84	showLitChar20 wxv = showLitChar18 wxv;
109.42/95.84	"
109.42/95.84	"showLitChar21 True wxw = showString ('\' : 'D' : 'E' : 'L' : []);
109.42/95.84	showLitChar21 wxx wxy = showLitChar20 wxy;
109.42/95.84	"
109.42/95.84	"showLitChar22 wxw = showLitChar21 (wxw == '\127') wxw;
109.42/95.84	showLitChar22 wxz = showLitChar20 wxz;
109.42/95.84	"
109.42/95.84	"showLitChar23 c True = (showChar '\') . protectEsc isDigit (shows (fromEnum c));
109.42/95.84	showLitChar23 c False = showLitChar22 c;
109.42/95.84	"
109.42/95.84	"showLitChar24 c = showLitChar23 c (c > '\127');
109.42/95.84	showLitChar24 wyu = showLitChar22 wyu;
109.42/95.84	"
109.42/95.84	The following Function with conditions
109.42/95.84	"cont (wy : wz)|p wy('\' : '&' : []) ++ wy : wz;
109.42/95.84	cont s = s;
109.42/95.84	"
109.42/95.84	is transformed to
109.42/95.84	"cont (wy : wz) = cont2 (wy : wz);
109.42/95.84	cont s = cont0 s;
109.42/95.84	"
109.42/95.84	"cont0 s = s;
109.42/95.84	"
109.42/95.84	"cont1 wy wz True = ('\' : '&' : []) ++ wy : wz;
109.42/95.84	cont1 wy wz False = cont0 (wy : wz);
109.42/95.84	"
109.42/95.84	"cont2 (wy : wz) = cont1 wy wz (p wy);
109.42/95.84	cont2 wyw = cont0 wyw;
109.42/95.84	"
109.42/95.84	The following Function with conditions
109.42/95.84	"undefined |Falseundefined;
109.42/95.84	"
109.42/95.84	is transformed to
109.42/95.84	"undefined  = undefined1;
109.42/95.84	"
109.42/95.84	"undefined0 True = undefined;
109.42/95.84	"
109.42/95.84	"undefined1  = undefined0 False;
109.42/95.84	"
109.42/95.84	
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(8)
109.42/95.84	Obligation:
109.42/95.84	mainModule Main 
109.42/95.84	module Main where {
109.42/95.84	import qualified Prelude;
109.42/95.84	}
109.42/95.84	
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(9) LetRed (EQUIVALENT)
109.42/95.84	Let/Where Reductions:
109.42/95.84	The bindings of the following Let/Where expression
109.42/95.84	"(showChar '"') . showl cs where {
109.42/95.84	showl [] = showl3 [];
109.42/95.84	showl (zv : cs) = showl2 (zv : cs);
109.42/95.84	showl (c : cs) = showl0 (c : cs);
109.42/95.84	;
109.42/95.84	showl0 (c : cs) = (showLitChar c) . showl cs;
109.42/95.84	;
109.42/95.84	showl1 True (zv : cs) = (showString ('\' : '"' : [])) . showl cs;
109.42/95.84	showl1 zw zx = showl0 zx;
109.42/95.84	;
109.42/95.84	showl2 (zv : cs) = showl1 (zv == '"') (zv : cs);
109.42/95.84	showl2 zy = showl0 zy;
109.42/95.84	;
109.42/95.84	showl3 [] = showChar '"';
109.42/95.84	showl3 vuu = showl2 vuu;
109.42/95.84	} 
109.42/95.84	"
109.42/95.84	are unpacked to the following functions on top level
109.42/95.84	"showListShowl1 True (zv : cs) = (showString ('\' : '"' : [])) . showListShowl cs;
109.42/95.84	showListShowl1 zw zx = showListShowl0 zx;
109.42/95.84	"
109.42/95.84	"showListShowl [] = showListShowl3 [];
109.42/95.84	showListShowl (zv : cs) = showListShowl2 (zv : cs);
109.42/95.84	showListShowl (c : cs) = showListShowl0 (c : cs);
109.42/95.84	"
109.42/95.84	"showListShowl3 [] = showChar '"';
109.42/95.84	showListShowl3 vuu = showListShowl2 vuu;
109.42/95.84	"
109.42/95.84	"showListShowl2 (zv : cs) = showListShowl1 (zv == '"') (zv : cs);
109.42/95.84	showListShowl2 zy = showListShowl0 zy;
109.42/95.84	"
109.42/95.84	"showListShowl0 (c : cs) = (showLitChar c) . showListShowl cs;
109.42/95.84	"
109.42/95.84	The bindings of the following Let/Where expression
109.42/95.84	"f . cont where {
109.42/95.84	cont (wy : wz) = cont2 (wy : wz);
109.42/95.84	cont s = cont0 s;
109.42/95.84	;
109.42/95.84	cont0 s = s;
109.42/95.84	;
109.42/95.84	cont1 wy wz True = ('\' : '&' : []) ++ wy : wz;
109.42/95.84	cont1 wy wz False = cont0 (wy : wz);
109.42/95.84	;
109.42/95.84	cont2 (wy : wz) = cont1 wy wz (p wy);
109.42/95.84	cont2 wyw = cont0 wyw;
109.42/95.84	} 
109.42/95.84	"
109.42/95.84	are unpacked to the following functions on top level
109.42/95.84	"protectEscCont2 wyx (wy : wz) = protectEscCont1 wyx wy wz (wyx wy);
109.42/95.84	protectEscCont2 wyx wyw = protectEscCont0 wyx wyw;
109.42/95.84	"
109.42/95.84	"protectEscCont wyx (wy : wz) = protectEscCont2 wyx (wy : wz);
109.42/95.84	protectEscCont wyx s = protectEscCont0 wyx s;
109.42/95.84	"
109.42/95.84	"protectEscCont0 wyx s = s;
109.42/95.84	"
109.42/95.84	"protectEscCont1 wyx wy wz True = ('\' : '&' : []) ++ wy : wz;
109.42/95.84	protectEscCont1 wyx wy wz False = protectEscCont0 wyx (wy : wz);
109.42/95.84	"
109.42/95.84	
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(10)
109.42/95.84	Obligation:
109.42/95.84	mainModule Main 
109.42/95.84	module Main where {
109.42/95.84	import qualified Prelude;
109.42/95.84	}
109.42/95.84	
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(11) NumRed (SOUND)
109.42/95.84	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
109.42/95.84	----------------------------------------
109.42/95.84	
109.42/95.84	(12)
109.42/95.84	Obligation:
109.42/95.84	mainModule Main 
109.42/95.84	module Main where {
109.42/95.84	import qualified Prelude;
109.42/95.84	}
109.69/95.90	EOF