7.56/3.52	YES
9.24/3.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.24/3.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.24/3.98	
9.24/3.98	
9.24/3.98	H-Termination with start terms of the given HASKELL could be proven:
9.24/3.98	
9.24/3.98	(0) HASKELL
9.24/3.98	(1) BR [EQUIVALENT, 0 ms]
9.24/3.98	(2) HASKELL
9.24/3.98	(3) COR [EQUIVALENT, 0 ms]
9.24/3.98	(4) HASKELL
9.24/3.98	(5) Narrow [EQUIVALENT, 0 ms]
9.24/3.98	(6) YES
9.24/3.98	
9.24/3.98	
9.24/3.98	----------------------------------------
9.24/3.98	
9.24/3.98	(0)
9.24/3.98	Obligation:
9.24/3.98	mainModule Main 
9.24/3.98	module Main where {
9.24/3.98	import qualified Prelude;
9.24/3.98	data Integer = Integer MyInt ;
9.24/3.98	
9.24/3.98	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.24/3.98	
9.24/3.98	data Main.Nat = Succ Main.Nat  | Zero ;
9.24/3.98	
9.24/3.98	data Ratio a = CnPc a a ;
9.24/3.98	
9.24/3.98	toIntegerMyInt :: MyInt  ->  Integer;
9.24/3.98	toIntegerMyInt x = Integer x;
9.24/3.98	
9.24/3.98	toRationalRatio :: Ratio MyInt  ->  Ratio Integer;
9.24/3.98	toRationalRatio (CnPc x y) = CnPc (toIntegerMyInt x) (toIntegerMyInt y);
9.24/3.98	
9.24/3.98	}
9.24/3.98	
9.24/3.98	----------------------------------------
9.24/3.98	
9.24/3.98	(1) BR (EQUIVALENT)
9.24/3.98	Replaced joker patterns by fresh variables and removed binding patterns.
9.24/3.98	----------------------------------------
9.24/3.98	
9.24/3.98	(2)
9.24/3.98	Obligation:
9.24/3.98	mainModule Main 
9.24/3.98	module Main where {
9.24/3.98	import qualified Prelude;
9.24/3.98	data Integer = Integer MyInt ;
9.24/3.98	
9.24/3.98	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.24/3.98	
9.24/3.98	data Main.Nat = Succ Main.Nat  | Zero ;
9.24/3.98	
9.24/3.98	data Ratio a = CnPc a a ;
9.24/3.98	
9.24/3.98	toIntegerMyInt :: MyInt  ->  Integer;
9.24/3.98	toIntegerMyInt x = Integer x;
9.24/3.98	
9.24/3.98	toRationalRatio :: Ratio MyInt  ->  Ratio Integer;
9.24/3.98	toRationalRatio (CnPc x y) = CnPc (toIntegerMyInt x) (toIntegerMyInt y);
9.24/3.98	
9.24/3.98	}
9.24/3.98	
9.24/3.98	----------------------------------------
9.24/3.98	
9.24/3.98	(3) COR (EQUIVALENT)
9.24/3.98	Cond Reductions:
9.24/3.98	The following Function with conditions
9.24/3.98	"undefined |Falseundefined;
9.24/3.98	"
9.24/3.98	is transformed to
9.24/3.98	"undefined  = undefined1;
9.24/3.98	"
9.24/3.98	"undefined0 True = undefined;
9.24/3.98	"
9.24/3.98	"undefined1  = undefined0 False;
9.24/3.98	"
9.24/3.98	
9.24/3.98	----------------------------------------
9.24/3.98	
9.24/3.98	(4)
9.24/3.98	Obligation:
9.24/3.98	mainModule Main 
9.24/3.98	module Main where {
9.24/3.98	import qualified Prelude;
9.24/3.98	data Integer = Integer MyInt ;
9.24/3.98	
9.24/3.98	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.24/3.98	
9.24/3.98	data Main.Nat = Succ Main.Nat  | Zero ;
9.24/3.98	
9.24/3.98	data Ratio a = CnPc a a ;
9.24/3.98	
9.24/3.98	toIntegerMyInt :: MyInt  ->  Integer;
9.24/3.98	toIntegerMyInt x = Integer x;
9.24/3.98	
9.24/3.98	toRationalRatio :: Ratio MyInt  ->  Ratio Integer;
9.24/3.98	toRationalRatio (CnPc x y) = CnPc (toIntegerMyInt x) (toIntegerMyInt y);
9.24/3.98	
9.24/3.98	}
9.24/3.98	
9.24/3.98	----------------------------------------
9.24/3.98	
9.24/3.98	(5) Narrow (EQUIVALENT)
9.24/3.98	Haskell To QDPs
9.24/3.98	
9.24/3.98	digraph dp_graph {
9.24/3.98	node [outthreshold=100, inthreshold=100];1[label="toRationalRatio",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.24/3.98	3[label="toRationalRatio vx3",fontsize=16,color="burlywood",shape="triangle"];10[label="vx3/CnPc vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];3 -> 10[label="",style="solid", color="burlywood", weight=9];
9.24/3.98	10 -> 4[label="",style="solid", color="burlywood", weight=3];
9.24/3.98	4[label="toRationalRatio (CnPc vx30 vx31)",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.24/3.98	5[label="CnPc (toIntegerMyInt vx30) (toIntegerMyInt vx31)",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3];
9.24/3.98	5 -> 7[label="",style="dashed", color="green", weight=3];
9.24/3.98	6[label="toIntegerMyInt vx30",fontsize=16,color="black",shape="triangle"];6 -> 8[label="",style="solid", color="black", weight=3];
9.24/3.98	7 -> 6[label="",style="dashed", color="red", weight=0];
9.24/3.98	7[label="toIntegerMyInt vx31",fontsize=16,color="magenta"];7 -> 9[label="",style="dashed", color="magenta", weight=3];
9.24/3.98	8[label="Integer vx30",fontsize=16,color="green",shape="box"];9[label="vx31",fontsize=16,color="green",shape="box"];}
9.24/3.98	
9.24/3.98	----------------------------------------
9.24/3.98	
9.24/3.98	(6)
9.24/3.98	YES
9.33/6.83	EOF