175.89/153.02	MAYBE
178.22/153.66	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
178.22/153.66	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
178.22/153.66	
178.22/153.66	
178.22/153.66	H-Termination with start terms of the given HASKELL could not be shown:
178.22/153.66	
178.22/153.66	(0) HASKELL
178.22/153.66	(1) IFR [EQUIVALENT, 0 ms]
178.22/153.66	(2) HASKELL
178.22/153.66	(3) BR [EQUIVALENT, 0 ms]
178.22/153.66	(4) HASKELL
178.22/153.66	(5) COR [EQUIVALENT, 30 ms]
178.22/153.66	(6) HASKELL
178.22/153.66	(7) LetRed [EQUIVALENT, 0 ms]
178.22/153.66	(8) HASKELL
178.22/153.66	(9) NumRed [SOUND, 0 ms]
178.22/153.66	(10) HASKELL
178.22/153.66	
178.22/153.66	
178.22/153.66	----------------------------------------
178.22/153.66	
178.22/153.66	(0)
178.22/153.66	Obligation:
178.22/153.66	mainModule Main 
178.22/153.66	module Main where {
178.22/153.66	import qualified Prelude;
178.22/153.66	}
178.22/153.66	
178.22/153.66	----------------------------------------
178.22/153.66	
178.22/153.66	(1) IFR (EQUIVALENT)
178.22/153.66	If Reductions:
178.22/153.66	The following If expression
178.22/153.66	"if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero"
178.22/153.66	is transformed to
178.22/153.66	"primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y));
178.22/153.66	primDivNatS0 x y False = Zero;
178.22/153.66	"
178.22/153.66	The following If expression
178.22/153.66	"if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x"
178.22/153.66	is transformed to
178.22/153.66	"primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y);
178.22/153.66	primModNatS0 x y False = Succ x;
178.22/153.66	"
178.22/153.66	
178.22/153.66	----------------------------------------
178.22/153.66	
178.22/153.66	(2)
178.22/153.66	Obligation:
178.22/153.66	mainModule Main 
178.22/153.66	module Main where {
178.22/153.66	import qualified Prelude;
178.22/153.66	}
178.22/153.66	
178.22/153.66	----------------------------------------
178.22/153.66	
178.22/153.66	(3) BR (EQUIVALENT)
178.22/153.66	Replaced joker patterns by fresh variables and removed binding patterns.
178.22/153.66	----------------------------------------
178.22/153.66	
178.22/153.66	(4)
178.22/153.66	Obligation:
178.22/153.66	mainModule Main 
178.22/153.66	module Main where {
178.22/153.66	import qualified Prelude;
178.22/153.66	}
178.22/153.66	
178.22/153.66	----------------------------------------
178.22/153.66	
178.22/153.66	(5) COR (EQUIVALENT)
178.22/153.66	Cond Reductions:
178.22/153.66	The following Function with conditions
178.22/153.66	"absReal x|x >= 0x|otherwise`negate` x;
178.22/153.66	"
178.22/153.66	is transformed to
178.22/153.66	"absReal x = absReal2 x;
178.22/153.66	"
178.22/153.66	"absReal0 x True = `negate` x;
178.22/153.66	"
178.22/153.66	"absReal1 x True = x;
178.22/153.66	absReal1 x False = absReal0 x otherwise;
178.22/153.66	"
178.22/153.66	"absReal2 x = absReal1 x (x >= 0);
178.22/153.66	"
178.22/153.66	The following Function with conditions
178.22/153.66	"gcd' x 0 = x;
178.22/153.66	gcd' x y = gcd' y (x `rem` y);
178.22/153.66	"
178.22/153.66	is transformed to
178.22/153.66	"gcd' x xz = gcd'2 x xz;
178.22/153.66	gcd' x y = gcd'0 x y;
178.22/153.66	"
178.22/153.66	"gcd'0 x y = gcd' y (x `rem` y);
178.22/153.66	"
178.22/153.66	"gcd'1 True x xz = x;
178.22/153.66	gcd'1 yu yv yw = gcd'0 yv yw;
178.22/153.66	"
178.22/153.66	"gcd'2 x xz = gcd'1 (xz == 0) x xz;
178.22/153.66	gcd'2 yx yy = gcd'0 yx yy;
178.22/153.66	"
178.22/153.66	The following Function with conditions
178.22/153.66	"gcd 0 0 = error [];
178.22/153.66	gcd x y = gcd' (abs x) (abs y) where {
178.22/153.66	gcd' x 0 = x;
178.22/153.66	gcd' x y = gcd' y (x `rem` y);
178.22/153.66	} 
178.22/153.66	;
178.22/153.66	"
178.22/153.66	is transformed to
178.22/153.66	"gcd yz zu = gcd3 yz zu;
178.22/153.66	gcd x y = gcd0 x y;
178.22/153.66	"
178.22/153.66	"gcd0 x y = gcd' (abs x) (abs y) where {
178.22/153.66	gcd' x xz = gcd'2 x xz;
178.22/153.66	gcd' x y = gcd'0 x y;
178.22/153.66	;
178.22/153.66	gcd'0 x y = gcd' y (x `rem` y);
178.22/153.66	;
178.22/153.66	gcd'1 True x xz = x;
178.22/153.66	gcd'1 yu yv yw = gcd'0 yv yw;
178.22/153.66	;
178.22/153.66	gcd'2 x xz = gcd'1 (xz == 0) x xz;
178.22/153.66	gcd'2 yx yy = gcd'0 yx yy;
178.22/153.66	} 
178.22/153.66	;
178.22/153.66	"
178.22/153.66	"gcd1 True yz zu = error [];
178.22/153.66	gcd1 zv zw zx = gcd0 zw zx;
178.22/153.66	"
178.22/153.66	"gcd2 True yz zu = gcd1 (zu == 0) yz zu;
178.22/153.66	gcd2 zy zz vuu = gcd0 zz vuu;
178.22/153.66	"
178.22/153.66	"gcd3 yz zu = gcd2 (yz == 0) yz zu;
178.22/153.66	gcd3 vuv vuw = gcd0 vuv vuw;
178.22/153.66	"
178.22/153.66	The following Function with conditions
178.22/153.66	"undefined |Falseundefined;
178.22/153.66	"
178.22/153.66	is transformed to
178.22/153.66	"undefined  = undefined1;
178.22/153.66	"
178.22/153.66	"undefined0 True = undefined;
178.22/153.66	"
178.22/153.66	"undefined1  = undefined0 False;
178.22/153.66	"
178.22/153.66	The following Function with conditions
178.22/153.66	"reduce x y|y == 0error []|otherwisex `quot` d :% (y `quot` d) where {
178.22/153.66	d  = gcd x y;
178.22/153.66	} 
178.22/153.66	;
178.22/153.66	"
178.22/153.66	is transformed to
178.22/153.66	"reduce x y = reduce2 x y;
178.22/153.66	"
178.22/153.66	"reduce2 x y = reduce1 x y (y == 0) where {
178.22/153.66	d  = gcd x y;
178.22/153.66	;
178.22/153.66	reduce0 x y True = x `quot` d :% (y `quot` d);
178.22/153.66	;
178.22/153.66	reduce1 x y True = error [];
178.22/153.66	reduce1 x y False = reduce0 x y otherwise;
178.22/153.66	} 
178.22/153.66	;
178.22/153.66	"
178.22/153.66	
178.22/153.66	----------------------------------------
178.22/153.66	
178.22/153.66	(6)
178.22/153.66	Obligation:
178.22/153.66	mainModule Main 
178.22/153.66	module Main where {
178.22/153.66	import qualified Prelude;
178.22/153.66	}
178.22/153.66	
178.22/153.66	----------------------------------------
178.22/153.66	
178.22/153.66	(7) LetRed (EQUIVALENT)
178.22/153.66	Let/Where Reductions:
178.22/153.66	The bindings of the following Let/Where expression
178.22/153.66	"gcd' (abs x) (abs y) where {
178.22/153.66	gcd' x xz = gcd'2 x xz;
178.22/153.66	gcd' x y = gcd'0 x y;
178.22/153.66	;
178.22/153.66	gcd'0 x y = gcd' y (x `rem` y);
178.22/153.66	;
178.22/153.66	gcd'1 True x xz = x;
178.22/153.66	gcd'1 yu yv yw = gcd'0 yv yw;
178.22/153.66	;
178.22/153.66	gcd'2 x xz = gcd'1 (xz == 0) x xz;
178.22/153.66	gcd'2 yx yy = gcd'0 yx yy;
178.22/153.66	} 
178.22/153.66	"
178.22/153.66	are unpacked to the following functions on top level
178.22/153.66	"gcd0Gcd'2 x xz = gcd0Gcd'1 (xz == 0) x xz;
178.22/153.66	gcd0Gcd'2 yx yy = gcd0Gcd'0 yx yy;
178.22/153.66	"
178.22/153.66	"gcd0Gcd'0 x y = gcd0Gcd' y (x `rem` y);
178.22/153.66	"
178.22/153.66	"gcd0Gcd'1 True x xz = x;
178.22/153.66	gcd0Gcd'1 yu yv yw = gcd0Gcd'0 yv yw;
178.22/153.66	"
178.22/153.66	"gcd0Gcd' x xz = gcd0Gcd'2 x xz;
178.22/153.66	gcd0Gcd' x y = gcd0Gcd'0 x y;
178.22/153.66	"
178.22/153.66	The bindings of the following Let/Where expression
178.22/153.66	"reduce1 x y (y == 0) where {
178.22/153.66	d  = gcd x y;
178.22/153.66	;
178.22/153.66	reduce0 x y True = x `quot` d :% (y `quot` d);
178.22/153.66	;
178.22/153.66	reduce1 x y True = error [];
178.22/153.66	reduce1 x y False = reduce0 x y otherwise;
178.22/153.66	} 
178.22/153.66	"
178.22/153.66	are unpacked to the following functions on top level
178.22/153.66	"reduce2D vux vuy = gcd vux vuy;
178.22/153.66	"
178.22/153.66	"reduce2Reduce1 vux vuy x y True = error [];
178.22/153.66	reduce2Reduce1 vux vuy x y False = reduce2Reduce0 vux vuy x y otherwise;
178.22/153.66	"
178.22/153.66	"reduce2Reduce0 vux vuy x y True = x `quot` reduce2D vux vuy :% (y `quot` reduce2D vux vuy);
178.22/153.66	"
178.22/153.66	
178.22/153.66	----------------------------------------
178.22/153.66	
178.22/153.66	(8)
178.22/153.66	Obligation:
178.22/153.66	mainModule Main 
178.22/153.66	module Main where {
178.22/153.66	import qualified Prelude;
178.22/153.66	}
178.22/153.66	
178.22/153.66	----------------------------------------
178.22/153.66	
178.22/153.66	(9) NumRed (SOUND)
178.22/153.66	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
178.22/153.66	----------------------------------------
178.22/153.66	
178.22/153.66	(10)
178.22/153.66	Obligation:
178.22/153.66	mainModule Main 
178.22/153.66	module Main where {
178.22/153.66	import qualified Prelude;
178.22/153.66	}
178.26/153.70	EOF