7.40/3.51	YES
9.15/3.97	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.15/3.97	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.15/3.97	
9.15/3.97	
9.15/3.97	H-Termination with start terms of the given HASKELL could be proven:
9.15/3.97	
9.15/3.97	(0) HASKELL
9.15/3.97	(1) BR [EQUIVALENT, 0 ms]
9.15/3.97	(2) HASKELL
9.15/3.97	(3) COR [EQUIVALENT, 0 ms]
9.15/3.97	(4) HASKELL
9.15/3.97	(5) Narrow [EQUIVALENT, 0 ms]
9.15/3.97	(6) YES
9.15/3.97	
9.15/3.97	
9.15/3.97	----------------------------------------
9.15/3.97	
9.15/3.97	(0)
9.15/3.97	Obligation:
9.15/3.97	mainModule Main 
9.15/3.97	module Main where {
9.15/3.97	import qualified Prelude;
9.15/3.97	data Float = Float MyInt MyInt ;
9.15/3.97	
9.15/3.97	data Integer = Integer MyInt ;
9.15/3.97	
9.15/3.97	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.15/3.97	
9.15/3.97	data Main.Nat = Succ Main.Nat  | Zero ;
9.15/3.97	
9.15/3.97	fromIntegerFloat :: Integer  ->  Float;
9.15/3.97	fromIntegerFloat = primIntegerToFloat;
9.15/3.97	
9.15/3.97	fromIntegral = pt fromIntegerFloat toIntegerMyInt;
9.15/3.97	
9.15/3.97	primIntToFloat :: MyInt  ->  Float;
9.15/3.97	primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));
9.15/3.97	
9.15/3.97	primIntegerToFloat :: Integer  ->  Float;
9.15/3.97	primIntegerToFloat (Integer x) = primIntToFloat x;
9.15/3.97	
9.15/3.97	pt :: (b  ->  a)  ->  (c  ->  b)  ->  c  ->  a;
9.15/3.97	pt f g x = f (g x);
9.15/3.97	
9.15/3.97	toIntegerMyInt :: MyInt  ->  Integer;
9.21/3.97	toIntegerMyInt x = Integer x;
9.21/3.97	
9.21/3.97	}
9.21/3.97	
9.21/3.97	----------------------------------------
9.21/3.97	
9.21/3.97	(1) BR (EQUIVALENT)
9.21/3.97	Replaced joker patterns by fresh variables and removed binding patterns.
9.21/3.97	----------------------------------------
9.21/3.97	
9.21/3.97	(2)
9.21/3.97	Obligation:
9.21/3.97	mainModule Main 
9.21/3.97	module Main where {
9.21/3.97	import qualified Prelude;
9.21/3.97	data Float = Float MyInt MyInt ;
9.21/3.97	
9.21/3.97	data Integer = Integer MyInt ;
9.21/3.97	
9.21/3.97	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.21/3.97	
9.21/3.97	data Main.Nat = Succ Main.Nat  | Zero ;
9.21/3.97	
9.21/3.97	fromIntegerFloat :: Integer  ->  Float;
9.21/3.97	fromIntegerFloat = primIntegerToFloat;
9.21/3.97	
9.21/3.97	fromIntegral = pt fromIntegerFloat toIntegerMyInt;
9.21/3.97	
9.21/3.97	primIntToFloat :: MyInt  ->  Float;
9.21/3.97	primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));
9.21/3.97	
9.21/3.97	primIntegerToFloat :: Integer  ->  Float;
9.21/3.97	primIntegerToFloat (Integer x) = primIntToFloat x;
9.21/3.97	
9.21/3.97	pt :: (b  ->  a)  ->  (c  ->  b)  ->  c  ->  a;
9.21/3.97	pt f g x = f (g x);
9.21/3.97	
9.21/3.97	toIntegerMyInt :: MyInt  ->  Integer;
9.21/3.97	toIntegerMyInt x = Integer x;
9.21/3.97	
9.21/3.97	}
9.21/3.97	
9.21/3.97	----------------------------------------
9.21/3.97	
9.21/3.97	(3) COR (EQUIVALENT)
9.21/3.97	Cond Reductions:
9.21/3.97	The following Function with conditions
9.21/3.97	"undefined |Falseundefined;
9.21/3.97	"
9.21/3.97	is transformed to
9.21/3.97	"undefined  = undefined1;
9.21/3.97	"
9.21/3.97	"undefined0 True = undefined;
9.21/3.97	"
9.21/3.97	"undefined1  = undefined0 False;
9.21/3.97	"
9.21/3.97	
9.21/3.97	----------------------------------------
9.21/3.97	
9.21/3.97	(4)
9.21/3.97	Obligation:
9.21/3.97	mainModule Main 
9.21/3.97	module Main where {
9.21/3.97	import qualified Prelude;
9.21/3.97	data Float = Float MyInt MyInt ;
9.21/3.97	
9.21/3.97	data Integer = Integer MyInt ;
9.21/3.97	
9.21/3.97	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.21/3.97	
9.21/3.97	data Main.Nat = Succ Main.Nat  | Zero ;
9.21/3.97	
9.21/3.97	fromIntegerFloat :: Integer  ->  Float;
9.21/3.97	fromIntegerFloat = primIntegerToFloat;
9.21/3.97	
9.21/3.97	fromIntegral = pt fromIntegerFloat toIntegerMyInt;
9.21/3.97	
9.21/3.97	primIntToFloat :: MyInt  ->  Float;
9.21/3.97	primIntToFloat x = Float x (Main.Pos (Main.Succ Main.Zero));
9.21/3.97	
9.21/3.97	primIntegerToFloat :: Integer  ->  Float;
9.21/3.97	primIntegerToFloat (Integer x) = primIntToFloat x;
9.21/3.97	
9.21/3.97	pt :: (c  ->  b)  ->  (a  ->  c)  ->  a  ->  b;
9.21/3.97	pt f g x = f (g x);
9.21/3.97	
9.21/3.97	toIntegerMyInt :: MyInt  ->  Integer;
9.21/3.97	toIntegerMyInt x = Integer x;
9.21/3.97	
9.21/3.97	}
9.21/3.97	
9.21/3.97	----------------------------------------
9.21/3.97	
9.21/3.97	(5) Narrow (EQUIVALENT)
9.21/3.97	Haskell To QDPs
9.21/3.97	
9.21/3.97	digraph dp_graph {
9.21/3.97	node [outthreshold=100, inthreshold=100];1[label="fromIntegral",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.21/3.97	3[label="fromIntegral vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.21/3.97	4[label="pt fromIntegerFloat toIntegerMyInt vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.21/3.97	5[label="fromIntegerFloat (toIntegerMyInt vx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.21/3.97	6[label="primIntegerToFloat (toIntegerMyInt vx3)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.21/3.97	7[label="primIntegerToFloat (Integer vx3)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.21/3.97	8[label="primIntToFloat vx3",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.21/3.97	9[label="Float vx3 (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];}
9.21/3.97	
9.21/3.97	----------------------------------------
9.21/3.97	
9.21/3.97	(6)
9.21/3.97	YES
9.21/4.02	EOF