7.73/3.52	YES
9.36/3.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.36/3.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.36/3.98	
9.36/3.98	
9.36/3.98	H-Termination with start terms of the given HASKELL could be proven:
9.36/3.98	
9.36/3.98	(0) HASKELL
9.36/3.98	(1) BR [EQUIVALENT, 0 ms]
9.36/3.98	(2) HASKELL
9.36/3.98	(3) COR [EQUIVALENT, 0 ms]
9.36/3.98	(4) HASKELL
9.36/3.98	(5) Narrow [EQUIVALENT, 0 ms]
9.36/3.98	(6) YES
9.36/3.98	
9.36/3.98	
9.36/3.98	----------------------------------------
9.36/3.98	
9.36/3.98	(0)
9.36/3.98	Obligation:
9.36/3.98	mainModule Main 
9.36/3.98	module Main where {
9.36/3.98	import qualified Prelude;
9.36/3.98	data Float = Float MyInt MyInt ;
9.36/3.98	
9.36/3.98	data Integer = Integer MyInt ;
9.36/3.98	
9.36/3.98	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.36/3.98	
9.36/3.98	data Main.Nat = Succ Main.Nat  | Zero ;
9.36/3.98	
9.36/3.98	data Ratio a = CnPc a a ;
9.36/3.98	
9.36/3.98	fromRationalFloat :: Ratio Integer  ->  Float;
9.36/3.98	fromRationalFloat = primRationalToFloat;
9.36/3.98	
9.36/3.98	primRationalToFloat :: Ratio Integer  ->  Float;
9.36/3.98	primRationalToFloat = rationalToFloat;
9.36/3.98	
9.36/3.98	pt :: (b  ->  a)  ->  (c  ->  b)  ->  c  ->  a;
9.36/3.98	pt f g x = f (g x);
9.36/3.98	
9.36/3.98	rationalToFloat :: Ratio Integer  ->  Float;
9.36/3.98	rationalToFloat (CnPc (Integer x) (Integer y)) = Float x y;
9.36/3.98	
9.36/3.98	realToFrac = pt fromRationalFloat toRational;
9.36/3.99	
9.36/3.99	toIntegerMyInt :: MyInt  ->  Integer;
9.36/3.99	toIntegerMyInt x = Integer x;
9.36/3.99	
9.36/3.99	toRational (CnPc x y) = CnPc (toIntegerMyInt x) (toIntegerMyInt y);
9.36/3.99	
9.36/3.99	}
9.36/3.99	
9.36/3.99	----------------------------------------
9.36/3.99	
9.36/3.99	(1) BR (EQUIVALENT)
9.36/3.99	Replaced joker patterns by fresh variables and removed binding patterns.
9.36/3.99	----------------------------------------
9.36/3.99	
9.36/3.99	(2)
9.36/3.99	Obligation:
9.36/3.99	mainModule Main 
9.36/3.99	module Main where {
9.36/3.99	import qualified Prelude;
9.36/3.99	data Float = Float MyInt MyInt ;
9.36/3.99	
9.36/3.99	data Integer = Integer MyInt ;
9.36/3.99	
9.36/3.99	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.36/3.99	
9.36/3.99	data Main.Nat = Succ Main.Nat  | Zero ;
9.36/3.99	
9.36/3.99	data Ratio a = CnPc a a ;
9.36/3.99	
9.36/3.99	fromRationalFloat :: Ratio Integer  ->  Float;
9.36/3.99	fromRationalFloat = primRationalToFloat;
9.36/3.99	
9.36/3.99	primRationalToFloat :: Ratio Integer  ->  Float;
9.36/3.99	primRationalToFloat = rationalToFloat;
9.36/3.99	
9.36/3.99	pt :: (b  ->  a)  ->  (c  ->  b)  ->  c  ->  a;
9.36/3.99	pt f g x = f (g x);
9.36/3.99	
9.36/3.99	rationalToFloat :: Ratio Integer  ->  Float;
9.36/3.99	rationalToFloat (CnPc (Integer x) (Integer y)) = Float x y;
9.36/3.99	
9.36/3.99	realToFrac = pt fromRationalFloat toRational;
9.36/3.99	
9.36/3.99	toIntegerMyInt :: MyInt  ->  Integer;
9.36/3.99	toIntegerMyInt x = Integer x;
9.36/3.99	
9.36/3.99	toRational (CnPc x y) = CnPc (toIntegerMyInt x) (toIntegerMyInt y);
9.36/3.99	
9.36/3.99	}
9.36/3.99	
9.36/3.99	----------------------------------------
9.36/3.99	
9.36/3.99	(3) COR (EQUIVALENT)
9.36/3.99	Cond Reductions:
9.36/3.99	The following Function with conditions
9.36/3.99	"undefined |Falseundefined;
9.36/3.99	"
9.36/3.99	is transformed to
9.36/3.99	"undefined  = undefined1;
9.36/3.99	"
9.36/3.99	"undefined0 True = undefined;
9.36/3.99	"
9.36/3.99	"undefined1  = undefined0 False;
9.36/3.99	"
9.36/3.99	
9.36/3.99	----------------------------------------
9.36/3.99	
9.36/3.99	(4)
9.36/3.99	Obligation:
9.36/3.99	mainModule Main 
9.36/3.99	module Main where {
9.36/3.99	import qualified Prelude;
9.36/3.99	data Float = Float MyInt MyInt ;
9.36/3.99	
9.36/3.99	data Integer = Integer MyInt ;
9.36/3.99	
9.36/3.99	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.36/3.99	
9.36/3.99	data Main.Nat = Succ Main.Nat  | Zero ;
9.36/3.99	
9.36/3.99	data Ratio a = CnPc a a ;
9.36/3.99	
9.36/3.99	fromRationalFloat :: Ratio Integer  ->  Float;
9.36/3.99	fromRationalFloat = primRationalToFloat;
9.36/3.99	
9.36/3.99	primRationalToFloat :: Ratio Integer  ->  Float;
9.36/3.99	primRationalToFloat = rationalToFloat;
9.36/3.99	
9.36/3.99	pt :: (a  ->  b)  ->  (c  ->  a)  ->  c  ->  b;
9.36/3.99	pt f g x = f (g x);
9.36/3.99	
9.36/3.99	rationalToFloat :: Ratio Integer  ->  Float;
9.36/3.99	rationalToFloat (CnPc (Integer x) (Integer y)) = Float x y;
9.36/3.99	
9.36/3.99	realToFrac = pt fromRationalFloat toRational;
9.36/3.99	
9.36/3.99	toIntegerMyInt :: MyInt  ->  Integer;
9.36/3.99	toIntegerMyInt x = Integer x;
9.36/3.99	
9.36/3.99	toRational (CnPc x y) = CnPc (toIntegerMyInt x) (toIntegerMyInt y);
9.36/3.99	
9.36/3.99	}
9.36/3.99	
9.36/3.99	----------------------------------------
9.36/3.99	
9.36/3.99	(5) Narrow (EQUIVALENT)
9.36/3.99	Haskell To QDPs
9.36/3.99	
9.36/3.99	digraph dp_graph {
9.36/3.99	node [outthreshold=100, inthreshold=100];1[label="realToFrac",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.36/3.99	3[label="realToFrac vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.36/3.99	4[label="pt fromRationalFloat toRational vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.36/3.99	5[label="fromRationalFloat (toRational vx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.36/3.99	6[label="primRationalToFloat (toRational vx3)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.36/3.99	7[label="rationalToFloat (toRational vx3)",fontsize=16,color="burlywood",shape="box"];13[label="vx3/CnPc vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];7 -> 13[label="",style="solid", color="burlywood", weight=9];
9.36/3.99	13 -> 8[label="",style="solid", color="burlywood", weight=3];
9.36/3.99	8[label="rationalToFloat (toRational (CnPc vx30 vx31))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.36/3.99	9[label="rationalToFloat (CnPc (toIntegerMyInt vx30) (toIntegerMyInt vx31))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
9.36/3.99	10[label="rationalToFloat (CnPc (Integer vx30) (toIntegerMyInt vx31))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
9.36/3.99	11[label="rationalToFloat (CnPc (Integer vx30) (Integer vx31))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
9.36/3.99	12[label="Float vx30 vx31",fontsize=16,color="green",shape="box"];}
9.36/3.99	
9.36/3.99	----------------------------------------
9.36/3.99	
9.36/3.99	(6)
9.36/3.99	YES
9.36/4.03	EOF