7.42/3.77	YES
8.86/4.24	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
8.86/4.24	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.86/4.24	
8.86/4.24	
8.86/4.24	H-Termination with start terms of the given HASKELL could be proven:
8.86/4.24	
8.86/4.24	(0) HASKELL
8.86/4.24	(1) BR [EQUIVALENT, 0 ms]
8.86/4.24	(2) HASKELL
8.86/4.24	(3) COR [EQUIVALENT, 0 ms]
8.86/4.24	(4) HASKELL
8.86/4.24	(5) Narrow [EQUIVALENT, 0 ms]
8.86/4.24	(6) YES
8.86/4.24	
8.86/4.24	
8.86/4.24	----------------------------------------
8.86/4.24	
8.86/4.24	(0)
8.86/4.24	Obligation:
8.86/4.24	mainModule Main 
8.86/4.24	module Main where {
8.86/4.24	import qualified Prelude;
8.86/4.24	data Integer = Integer MyInt ;
8.86/4.24	
8.86/4.24	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
8.86/4.24	
8.86/4.24	data Main.Nat = Succ Main.Nat  | Zero ;
8.86/4.24	
8.86/4.24	fromIntegerMyInt :: Integer  ->  MyInt;
8.86/4.24	fromIntegerMyInt (Integer x) = x;
8.86/4.24	
8.86/4.24	fromIntegral = pt fromIntegerMyInt toIntegerMyInt;
8.86/4.24	
8.86/4.24	pt :: (b  ->  c)  ->  (a  ->  b)  ->  a  ->  c;
8.86/4.24	pt f g x = f (g x);
8.86/4.24	
8.86/4.24	toIntegerMyInt :: MyInt  ->  Integer;
8.86/4.24	toIntegerMyInt x = Integer x;
8.86/4.24	
8.86/4.24	}
8.86/4.24	
8.86/4.24	----------------------------------------
8.86/4.24	
8.86/4.24	(1) BR (EQUIVALENT)
8.86/4.24	Replaced joker patterns by fresh variables and removed binding patterns.
8.86/4.24	----------------------------------------
8.86/4.24	
8.86/4.24	(2)
8.86/4.24	Obligation:
8.86/4.24	mainModule Main 
8.86/4.24	module Main where {
8.86/4.24	import qualified Prelude;
8.86/4.24	data Integer = Integer MyInt ;
8.86/4.24	
8.86/4.24	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
8.86/4.24	
8.86/4.24	data Main.Nat = Succ Main.Nat  | Zero ;
8.86/4.24	
8.86/4.24	fromIntegerMyInt :: Integer  ->  MyInt;
8.86/4.24	fromIntegerMyInt (Integer x) = x;
8.86/4.24	
8.86/4.24	fromIntegral = pt fromIntegerMyInt toIntegerMyInt;
8.86/4.24	
8.86/4.24	pt :: (b  ->  a)  ->  (c  ->  b)  ->  c  ->  a;
8.86/4.24	pt f g x = f (g x);
8.86/4.24	
8.86/4.24	toIntegerMyInt :: MyInt  ->  Integer;
8.86/4.24	toIntegerMyInt x = Integer x;
8.86/4.24	
8.86/4.24	}
8.86/4.24	
8.86/4.24	----------------------------------------
8.86/4.24	
8.86/4.24	(3) COR (EQUIVALENT)
8.86/4.24	Cond Reductions:
8.86/4.24	The following Function with conditions
8.86/4.24	"undefined |Falseundefined;
8.86/4.24	"
8.86/4.24	is transformed to
8.86/4.24	"undefined  = undefined1;
8.86/4.24	"
8.86/4.24	"undefined0 True = undefined;
8.86/4.24	"
8.86/4.24	"undefined1  = undefined0 False;
8.86/4.24	"
8.86/4.24	
8.86/4.24	----------------------------------------
8.86/4.24	
8.86/4.24	(4)
8.86/4.24	Obligation:
8.86/4.24	mainModule Main 
8.86/4.24	module Main where {
8.86/4.24	import qualified Prelude;
8.86/4.24	data Integer = Integer MyInt ;
8.86/4.24	
8.86/4.24	data MyInt = Pos Main.Nat  | Neg Main.Nat ;
8.86/4.24	
8.86/4.24	data Main.Nat = Succ Main.Nat  | Zero ;
8.86/4.24	
8.86/4.24	fromIntegerMyInt :: Integer  ->  MyInt;
8.86/4.24	fromIntegerMyInt (Integer x) = x;
8.86/4.24	
8.86/4.24	fromIntegral = pt fromIntegerMyInt toIntegerMyInt;
8.86/4.24	
8.86/4.24	pt :: (a  ->  b)  ->  (c  ->  a)  ->  c  ->  b;
8.86/4.24	pt f g x = f (g x);
8.86/4.24	
8.86/4.24	toIntegerMyInt :: MyInt  ->  Integer;
8.86/4.24	toIntegerMyInt x = Integer x;
8.86/4.24	
8.86/4.24	}
8.86/4.24	
8.86/4.24	----------------------------------------
8.86/4.24	
8.86/4.24	(5) Narrow (EQUIVALENT)
8.86/4.24	Haskell To QDPs
8.86/4.24	
8.86/4.24	digraph dp_graph {
8.86/4.24	node [outthreshold=100, inthreshold=100];1[label="fromIntegral",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
8.86/4.24	3[label="fromIntegral vx3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
8.86/4.24	4[label="pt fromIntegerMyInt toIntegerMyInt vx3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
8.86/4.24	5[label="fromIntegerMyInt (toIntegerMyInt vx3)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
8.86/4.24	6[label="fromIntegerMyInt (Integer vx3)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
8.86/4.24	7[label="vx3",fontsize=16,color="green",shape="box"];}
8.86/4.24	
8.86/4.24	----------------------------------------
8.86/4.24	
8.86/4.24	(6)
8.86/4.24	YES
9.21/4.29	EOF