7.62/3.44	YES
9.25/3.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.25/3.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.25/3.89	
9.25/3.89	
9.25/3.89	H-Termination with start terms of the given HASKELL could be proven:
9.25/3.89	
9.25/3.89	(0) HASKELL
9.25/3.89	(1) BR [EQUIVALENT, 0 ms]
9.25/3.89	(2) HASKELL
9.25/3.89	(3) COR [EQUIVALENT, 0 ms]
9.25/3.89	(4) HASKELL
9.25/3.89	(5) Narrow [EQUIVALENT, 0 ms]
9.25/3.89	(6) YES
9.25/3.89	
9.25/3.89	
9.25/3.89	----------------------------------------
9.25/3.89	
9.25/3.89	(0)
9.25/3.89	Obligation:
9.25/3.89	mainModule Main 
9.25/3.89	module Main where {
9.25/3.89	import qualified Prelude;
9.25/3.89	data Float = Float MyInt MyInt ;
9.25/3.89	
9.25/3.89	data Integer = Integer MyInt ;
9.25/3.89	
9.25/3.89	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.25/3.89	
9.25/3.89	data Main.Nat = Succ Main.Nat  | Zero ;
9.25/3.89	
9.25/3.89	data Ratio a = CnPc a a ;
9.25/3.89	
9.25/3.89	fromRationalFloat :: Ratio Integer  ->  Float;
9.25/3.89	fromRationalFloat = primRationalToFloat;
9.25/3.89	
9.25/3.89	primRationalToFloat :: Ratio Integer  ->  Float;
9.25/3.89	primRationalToFloat = rationalToFloat;
9.25/3.89	
9.25/3.89	rationalToFloat :: Ratio Integer  ->  Float;
9.25/3.89	rationalToFloat (CnPc (Integer x) (Integer y)) = Float x y;
9.25/3.89	
9.25/3.89	}
9.25/3.89	
9.25/3.89	----------------------------------------
9.25/3.89	
9.25/3.89	(1) BR (EQUIVALENT)
9.25/3.89	Replaced joker patterns by fresh variables and removed binding patterns.
9.25/3.89	----------------------------------------
9.25/3.89	
9.25/3.89	(2)
9.25/3.89	Obligation:
9.25/3.89	mainModule Main 
9.25/3.89	module Main where {
9.25/3.89	import qualified Prelude;
9.25/3.89	data Float = Float MyInt MyInt ;
9.25/3.89	
9.25/3.89	data Integer = Integer MyInt ;
9.25/3.89	
9.25/3.89	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.25/3.89	
9.25/3.89	data Main.Nat = Succ Main.Nat  | Zero ;
9.25/3.89	
9.25/3.89	data Ratio a = CnPc a a ;
9.25/3.89	
9.25/3.89	fromRationalFloat :: Ratio Integer  ->  Float;
9.25/3.89	fromRationalFloat = primRationalToFloat;
9.25/3.89	
9.25/3.89	primRationalToFloat :: Ratio Integer  ->  Float;
9.25/3.89	primRationalToFloat = rationalToFloat;
9.25/3.89	
9.25/3.89	rationalToFloat :: Ratio Integer  ->  Float;
9.25/3.89	rationalToFloat (CnPc (Integer x) (Integer y)) = Float x y;
9.25/3.89	
9.25/3.89	}
9.25/3.89	
9.25/3.89	----------------------------------------
9.25/3.89	
9.25/3.89	(3) COR (EQUIVALENT)
9.25/3.89	Cond Reductions:
9.25/3.89	The following Function with conditions
9.25/3.89	"undefined |Falseundefined;
9.25/3.89	"
9.25/3.89	is transformed to
9.25/3.89	"undefined  = undefined1;
9.25/3.89	"
9.25/3.89	"undefined0 True = undefined;
9.25/3.89	"
9.25/3.89	"undefined1  = undefined0 False;
9.25/3.89	"
9.25/3.89	
9.25/3.89	----------------------------------------
9.25/3.89	
9.25/3.89	(4)
9.25/3.89	Obligation:
9.25/3.89	mainModule Main 
9.25/3.89	module Main where {
9.25/3.89	import qualified Prelude;
9.25/3.89	data Float = Float MyInt MyInt ;
9.25/3.89	
9.25/3.89	data Integer = Integer MyInt ;
9.25/3.89	
9.25/3.89	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.25/3.89	
9.25/3.89	data Main.Nat = Succ Main.Nat  | Zero ;
9.25/3.89	
9.25/3.89	data Ratio a = CnPc a a ;
9.25/3.89	
9.25/3.89	fromRationalFloat :: Ratio Integer  ->  Float;
9.25/3.89	fromRationalFloat = primRationalToFloat;
9.25/3.89	
9.25/3.89	primRationalToFloat :: Ratio Integer  ->  Float;
9.25/3.89	primRationalToFloat = rationalToFloat;
9.25/3.89	
9.25/3.89	rationalToFloat :: Ratio Integer  ->  Float;
9.25/3.89	rationalToFloat (CnPc (Integer x) (Integer y)) = Float x y;
9.25/3.89	
9.25/3.89	}
9.25/3.89	
9.25/3.89	----------------------------------------
9.25/3.89	
9.25/3.89	(5) Narrow (EQUIVALENT)
9.25/3.89	Haskell To QDPs
9.25/3.89	
9.25/3.89	digraph dp_graph {
9.25/3.89	node [outthreshold=100, inthreshold=100];1[label="fromRationalFloat",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.25/3.89	3[label="fromRationalFloat vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.25/3.89	4[label="primRationalToFloat vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.25/3.89	5[label="rationalToFloat vx3",fontsize=16,color="burlywood",shape="box"];10[label="vx3/CnPc vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];5 -> 10[label="",style="solid", color="burlywood", weight=9];
9.25/3.89	10 -> 6[label="",style="solid", color="burlywood", weight=3];
9.25/3.89	6[label="rationalToFloat (CnPc vx30 vx31)",fontsize=16,color="burlywood",shape="box"];11[label="vx30/Integer vx300",fontsize=10,color="white",style="solid",shape="box"];6 -> 11[label="",style="solid", color="burlywood", weight=9];
9.25/3.89	11 -> 7[label="",style="solid", color="burlywood", weight=3];
9.25/3.89	7[label="rationalToFloat (CnPc (Integer vx300) vx31)",fontsize=16,color="burlywood",shape="box"];12[label="vx31/Integer vx310",fontsize=10,color="white",style="solid",shape="box"];7 -> 12[label="",style="solid", color="burlywood", weight=9];
9.25/3.89	12 -> 8[label="",style="solid", color="burlywood", weight=3];
9.25/3.89	8[label="rationalToFloat (CnPc (Integer vx300) (Integer vx310))",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.25/3.89	9[label="Float vx300 vx310",fontsize=16,color="green",shape="box"];}
9.25/3.89	
9.25/3.89	----------------------------------------
9.25/3.89	
9.25/3.89	(6)
9.25/3.89	YES
9.25/3.92	EOF