7.87/4.32	YES
9.27/4.79	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.27/4.79	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.27/4.79	
9.27/4.79	
9.27/4.79	H-Termination with start terms of the given HASKELL could be proven:
9.27/4.79	
9.27/4.79	(0) HASKELL
9.27/4.79	(1) BR [EQUIVALENT, 0 ms]
9.27/4.79	(2) HASKELL
9.27/4.79	(3) COR [EQUIVALENT, 0 ms]
9.27/4.79	(4) HASKELL
9.27/4.79	(5) Narrow [EQUIVALENT, 20 ms]
9.27/4.79	(6) YES
9.27/4.79	
9.27/4.79	
9.27/4.79	----------------------------------------
9.27/4.79	
9.27/4.79	(0)
9.27/4.79	Obligation:
9.27/4.79	mainModule Main 
9.27/4.79	module Main where {
9.27/4.79	import qualified Prelude;
9.27/4.79	data Integer = Integer MyInt ;
9.27/4.79	
9.27/4.79	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.27/4.79	
9.27/4.79	data Main.Nat = Succ Main.Nat  | Zero ;
9.27/4.79	
9.27/4.79	data Ratio a = CnPc a a ;
9.27/4.79	
9.27/4.79	fromIntMyInt :: MyInt  ->  MyInt;
9.27/4.79	fromIntMyInt x = x;
9.27/4.79	
9.27/4.79	fromIntegerMyInt :: Integer  ->  MyInt;
9.27/4.79	fromIntegerMyInt (Integer x) = x;
9.27/4.79	
9.27/4.79	fromIntegerRatio :: Integer  ->  Ratio MyInt;
9.27/4.79	fromIntegerRatio x = CnPc (fromIntegerMyInt x) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero)));
9.27/4.79	
9.27/4.79	fromIntegral = pt fromIntegerRatio toIntegerMyInt;
9.27/4.79	
9.27/4.79	pt :: (a  ->  c)  ->  (b  ->  a)  ->  b  ->  c;
9.27/4.79	pt f g x = f (g x);
9.27/4.79	
9.27/4.79	toIntegerMyInt :: MyInt  ->  Integer;
9.27/4.79	toIntegerMyInt x = Integer x;
9.27/4.79	
9.27/4.79	}
9.27/4.79	
9.27/4.79	----------------------------------------
9.27/4.79	
9.27/4.79	(1) BR (EQUIVALENT)
9.27/4.79	Replaced joker patterns by fresh variables and removed binding patterns.
9.27/4.79	----------------------------------------
9.27/4.79	
9.27/4.79	(2)
9.27/4.79	Obligation:
9.27/4.79	mainModule Main 
9.27/4.79	module Main where {
9.27/4.79	import qualified Prelude;
9.27/4.79	data Integer = Integer MyInt ;
9.27/4.79	
9.27/4.79	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.27/4.79	
9.27/4.79	data Main.Nat = Succ Main.Nat  | Zero ;
9.27/4.79	
9.27/4.79	data Ratio a = CnPc a a ;
9.27/4.79	
9.27/4.79	fromIntMyInt :: MyInt  ->  MyInt;
9.27/4.79	fromIntMyInt x = x;
9.27/4.79	
9.27/4.79	fromIntegerMyInt :: Integer  ->  MyInt;
9.27/4.79	fromIntegerMyInt (Integer x) = x;
9.27/4.79	
9.27/4.79	fromIntegerRatio :: Integer  ->  Ratio MyInt;
9.27/4.79	fromIntegerRatio x = CnPc (fromIntegerMyInt x) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero)));
9.27/4.79	
9.27/4.79	fromIntegral = pt fromIntegerRatio toIntegerMyInt;
9.27/4.79	
9.27/4.79	pt :: (c  ->  b)  ->  (a  ->  c)  ->  a  ->  b;
9.27/4.79	pt f g x = f (g x);
9.27/4.79	
9.27/4.79	toIntegerMyInt :: MyInt  ->  Integer;
9.27/4.79	toIntegerMyInt x = Integer x;
9.27/4.79	
9.27/4.79	}
9.27/4.79	
9.27/4.79	----------------------------------------
9.27/4.79	
9.27/4.79	(3) COR (EQUIVALENT)
9.27/4.79	Cond Reductions:
9.27/4.79	The following Function with conditions
9.27/4.79	"undefined |Falseundefined;
9.27/4.79	"
9.27/4.79	is transformed to
9.27/4.79	"undefined  = undefined1;
9.27/4.79	"
9.27/4.79	"undefined0 True = undefined;
9.27/4.79	"
9.27/4.79	"undefined1  = undefined0 False;
9.27/4.79	"
9.27/4.79	
9.27/4.79	----------------------------------------
9.27/4.79	
9.27/4.79	(4)
9.27/4.79	Obligation:
9.27/4.79	mainModule Main 
9.27/4.79	module Main where {
9.27/4.79	import qualified Prelude;
9.27/4.79	data Integer = Integer MyInt ;
9.27/4.79	
9.27/4.79	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.27/4.79	
9.27/4.79	data Main.Nat = Succ Main.Nat  | Zero ;
9.27/4.79	
9.27/4.79	data Ratio a = CnPc a a ;
9.27/4.79	
9.27/4.79	fromIntMyInt :: MyInt  ->  MyInt;
9.27/4.79	fromIntMyInt x = x;
9.27/4.79	
9.27/4.79	fromIntegerMyInt :: Integer  ->  MyInt;
9.27/4.79	fromIntegerMyInt (Integer x) = x;
9.27/4.79	
9.27/4.79	fromIntegerRatio :: Integer  ->  Ratio MyInt;
9.27/4.79	fromIntegerRatio x = CnPc (fromIntegerMyInt x) (fromIntMyInt (Main.Pos (Main.Succ Main.Zero)));
9.27/4.79	
9.27/4.79	fromIntegral = pt fromIntegerRatio toIntegerMyInt;
9.27/4.79	
9.27/4.79	pt :: (a  ->  b)  ->  (c  ->  a)  ->  c  ->  b;
9.27/4.79	pt f g x = f (g x);
9.27/4.79	
9.27/4.79	toIntegerMyInt :: MyInt  ->  Integer;
9.27/4.79	toIntegerMyInt x = Integer x;
9.27/4.79	
9.27/4.79	}
9.27/4.79	
9.27/4.79	----------------------------------------
9.27/4.79	
9.27/4.79	(5) Narrow (EQUIVALENT)
9.27/4.79	Haskell To QDPs
9.27/4.79	
9.27/4.79	digraph dp_graph {
9.27/4.79	node [outthreshold=100, inthreshold=100];1[label="fromIntegral",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.27/4.79	3[label="fromIntegral vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.27/4.79	4[label="pt fromIntegerRatio toIntegerMyInt vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.27/4.79	5[label="fromIntegerRatio (toIntegerMyInt vx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.27/4.79	6[label="CnPc (fromIntegerMyInt (toIntegerMyInt vx3)) (fromIntMyInt (Pos (Succ Zero)))",fontsize=16,color="green",shape="box"];6 -> 7[label="",style="dashed", color="green", weight=3];
9.27/4.79	6 -> 8[label="",style="dashed", color="green", weight=3];
9.27/4.79	7[label="fromIntegerMyInt (toIntegerMyInt vx3)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
9.27/4.79	8[label="fromIntMyInt (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9.27/4.79	9[label="fromIntegerMyInt (Integer vx3)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
9.27/4.79	10[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];11[label="vx3",fontsize=16,color="green",shape="box"];}
9.27/4.79	
9.27/4.79	----------------------------------------
9.27/4.79	
9.27/4.79	(6)
9.27/4.79	YES
9.57/4.87	EOF