7.63/3.47	YES
9.38/3.95	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.38/3.95	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.38/3.95	
9.38/3.95	
9.38/3.95	H-Termination with start terms of the given HASKELL could be proven:
9.38/3.95	
9.38/3.95	(0) HASKELL
9.38/3.95	(1) BR [EQUIVALENT, 0 ms]
9.38/3.95	(2) HASKELL
9.38/3.95	(3) COR [EQUIVALENT, 0 ms]
9.38/3.95	(4) HASKELL
9.38/3.95	(5) Narrow [EQUIVALENT, 29 ms]
9.38/3.95	(6) YES
9.38/3.95	
9.38/3.95	
9.38/3.95	----------------------------------------
9.38/3.95	
9.38/3.95	(0)
9.38/3.95	Obligation:
9.38/3.95	mainModule Main 
9.38/3.95	module Main where {
9.38/3.95	import qualified Prelude;
9.38/3.95	data Integer = Integer MyInt ;
9.38/3.95	
9.38/3.95	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.38/3.95	
9.38/3.95	data Main.Nat = Succ Main.Nat  | Zero ;
9.38/3.95	
9.38/3.95	data Ratio a = CnPc a a ;
9.38/3.95	
9.38/3.95	fromIntegerMyInt :: Integer  ->  MyInt;
9.38/3.95	fromIntegerMyInt (Integer x) = x;
9.38/3.95	
9.38/3.95	fromRational (CnPc x y) = CnPc (fromIntegerMyInt x) (fromIntegerMyInt y);
9.38/3.95	
9.38/3.95	pt :: (c  ->  a)  ->  (b  ->  c)  ->  b  ->  a;
9.38/3.95	pt f g x = f (g x);
9.38/3.95	
9.38/3.95	realToFrac = pt fromRational toRational;
9.38/3.95	
9.38/3.95	toIntegerMyInt :: MyInt  ->  Integer;
9.38/3.95	toIntegerMyInt x = Integer x;
9.38/3.95	
9.38/3.95	toRational (CnPc x y) = CnPc (toIntegerMyInt x) (toIntegerMyInt y);
9.38/3.95	
9.38/3.95	}
9.38/3.95	
9.38/3.95	----------------------------------------
9.38/3.95	
9.38/3.95	(1) BR (EQUIVALENT)
9.38/3.95	Replaced joker patterns by fresh variables and removed binding patterns.
9.38/3.95	----------------------------------------
9.38/3.95	
9.38/3.95	(2)
9.38/3.95	Obligation:
9.38/3.95	mainModule Main 
9.38/3.95	module Main where {
9.38/3.95	import qualified Prelude;
9.38/3.95	data Integer = Integer MyInt ;
9.38/3.95	
9.38/3.95	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.38/3.95	
9.38/3.95	data Main.Nat = Succ Main.Nat  | Zero ;
9.38/3.95	
9.38/3.95	data Ratio a = CnPc a a ;
9.38/3.95	
9.38/3.95	fromIntegerMyInt :: Integer  ->  MyInt;
9.38/3.95	fromIntegerMyInt (Integer x) = x;
9.38/3.95	
9.38/3.95	fromRational (CnPc x y) = CnPc (fromIntegerMyInt x) (fromIntegerMyInt y);
9.38/3.95	
9.38/3.95	pt :: (b  ->  a)  ->  (c  ->  b)  ->  c  ->  a;
9.38/3.95	pt f g x = f (g x);
9.38/3.95	
9.38/3.95	realToFrac = pt fromRational toRational;
9.38/3.95	
9.38/3.95	toIntegerMyInt :: MyInt  ->  Integer;
9.38/3.95	toIntegerMyInt x = Integer x;
9.38/3.95	
9.38/3.95	toRational (CnPc x y) = CnPc (toIntegerMyInt x) (toIntegerMyInt y);
9.38/3.95	
9.38/3.95	}
9.38/3.95	
9.38/3.95	----------------------------------------
9.38/3.95	
9.38/3.95	(3) COR (EQUIVALENT)
9.38/3.95	Cond Reductions:
9.38/3.95	The following Function with conditions
9.38/3.95	"undefined |Falseundefined;
9.38/3.95	"
9.38/3.95	is transformed to
9.38/3.95	"undefined  = undefined1;
9.38/3.95	"
9.38/3.95	"undefined0 True = undefined;
9.38/3.95	"
9.38/3.95	"undefined1  = undefined0 False;
9.38/3.95	"
9.38/3.95	
9.38/3.95	----------------------------------------
9.38/3.95	
9.38/3.95	(4)
9.38/3.95	Obligation:
9.38/3.95	mainModule Main 
9.38/3.95	module Main where {
9.38/3.95	import qualified Prelude;
9.38/3.95	data Integer = Integer MyInt ;
9.38/3.95	
9.38/3.95	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
9.38/3.95	
9.38/3.95	data Main.Nat = Succ Main.Nat  | Zero ;
9.38/3.95	
9.38/3.95	data Ratio a = CnPc a a ;
9.38/3.95	
9.38/3.95	fromIntegerMyInt :: Integer  ->  MyInt;
9.38/3.95	fromIntegerMyInt (Integer x) = x;
9.38/3.95	
9.38/3.95	fromRational (CnPc x y) = CnPc (fromIntegerMyInt x) (fromIntegerMyInt y);
9.38/3.95	
9.38/3.95	pt :: (a  ->  b)  ->  (c  ->  a)  ->  c  ->  b;
9.38/3.95	pt f g x = f (g x);
9.38/3.95	
9.38/3.95	realToFrac = pt fromRational toRational;
9.38/3.95	
9.38/3.95	toIntegerMyInt :: MyInt  ->  Integer;
9.38/3.95	toIntegerMyInt x = Integer x;
9.38/3.95	
9.38/3.95	toRational (CnPc x y) = CnPc (toIntegerMyInt x) (toIntegerMyInt y);
9.38/3.95	
9.38/3.95	}
9.38/3.95	
9.38/3.95	----------------------------------------
9.38/3.95	
9.38/3.95	(5) Narrow (EQUIVALENT)
9.38/3.95	Haskell To QDPs
9.38/3.95	
9.38/3.95	digraph dp_graph {
9.38/3.95	node [outthreshold=100, inthreshold=100];1[label="realToFrac",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.38/3.95	3[label="realToFrac vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.38/3.95	4[label="pt fromRational toRational vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.38/3.95	5[label="fromRational (toRational vx3)",fontsize=16,color="burlywood",shape="box"];14[label="vx3/CnPc vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];5 -> 14[label="",style="solid", color="burlywood", weight=9];
9.38/3.95	14 -> 6[label="",style="solid", color="burlywood", weight=3];
9.38/3.95	6[label="fromRational (toRational (CnPc vx30 vx31))",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.38/3.95	7[label="fromRational (CnPc (toIntegerMyInt vx30) (toIntegerMyInt vx31))",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.38/3.95	8[label="CnPc (fromIntegerMyInt (toIntegerMyInt vx30)) (fromIntegerMyInt (toIntegerMyInt vx31))",fontsize=16,color="green",shape="box"];8 -> 9[label="",style="dashed", color="green", weight=3];
9.38/3.95	8 -> 10[label="",style="dashed", color="green", weight=3];
9.38/3.95	9[label="fromIntegerMyInt (toIntegerMyInt vx30)",fontsize=16,color="black",shape="triangle"];9 -> 11[label="",style="solid", color="black", weight=3];
9.38/3.95	10 -> 9[label="",style="dashed", color="red", weight=0];
9.38/3.95	10[label="fromIntegerMyInt (toIntegerMyInt vx31)",fontsize=16,color="magenta"];10 -> 12[label="",style="dashed", color="magenta", weight=3];
9.38/3.95	11[label="fromIntegerMyInt (Integer vx30)",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
9.38/3.95	12[label="vx31",fontsize=16,color="green",shape="box"];13[label="vx30",fontsize=16,color="green",shape="box"];}
9.38/3.95	
9.38/3.95	----------------------------------------
9.38/3.95	
9.38/3.95	(6)
9.38/3.95	YES
9.58/3.98	EOF