7.80/3.59	YES
9.39/4.04	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.39/4.04	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.39/4.04	
9.39/4.04	
9.39/4.04	H-Termination with start terms of the given HASKELL could be proven:
9.39/4.04	
9.39/4.04	(0) HASKELL
9.39/4.04	(1) BR [EQUIVALENT, 0 ms]
9.39/4.04	(2) HASKELL
9.39/4.04	(3) COR [EQUIVALENT, 0 ms]
9.39/4.04	(4) HASKELL
9.39/4.04	(5) Narrow [EQUIVALENT, 0 ms]
9.39/4.04	(6) YES
9.39/4.04	
9.39/4.04	
9.39/4.04	----------------------------------------
9.39/4.04	
9.39/4.04	(0)
9.39/4.04	Obligation:
9.39/4.04	mainModule Main 
9.39/4.04	module Main where {
9.39/4.04	import qualified Prelude;
9.39/4.04	ds :: (b  ->  a)  ->  b  ->  a;
9.39/4.04	ds f x = f x;
9.39/4.04	
9.39/4.04	}
9.39/4.04	
9.39/4.04	----------------------------------------
9.39/4.04	
9.39/4.04	(1) BR (EQUIVALENT)
9.39/4.04	Replaced joker patterns by fresh variables and removed binding patterns.
9.39/4.04	----------------------------------------
9.39/4.04	
9.39/4.04	(2)
9.39/4.04	Obligation:
9.39/4.04	mainModule Main 
9.39/4.04	module Main where {
9.39/4.04	import qualified Prelude;
9.39/4.04	ds :: (a  ->  b)  ->  a  ->  b;
9.39/4.04	ds f x = f x;
9.39/4.04	
9.39/4.04	}
9.39/4.04	
9.39/4.04	----------------------------------------
9.39/4.04	
9.39/4.04	(3) COR (EQUIVALENT)
9.39/4.04	Cond Reductions:
9.39/4.04	The following Function with conditions
9.39/4.04	"undefined |Falseundefined;
9.39/4.04	"
9.39/4.04	is transformed to
9.39/4.04	"undefined  = undefined1;
9.39/4.04	"
9.39/4.04	"undefined0 True = undefined;
9.39/4.04	"
9.39/4.04	"undefined1  = undefined0 False;
9.39/4.04	"
9.39/4.04	
9.39/4.04	----------------------------------------
9.39/4.04	
9.39/4.04	(4)
9.39/4.04	Obligation:
9.39/4.04	mainModule Main 
9.39/4.04	module Main where {
9.39/4.04	import qualified Prelude;
9.39/4.04	ds :: (a  ->  b)  ->  a  ->  b;
9.39/4.04	ds f x = f x;
9.39/4.04	
9.39/4.04	}
9.39/4.04	
9.39/4.04	----------------------------------------
9.39/4.04	
9.39/4.04	(5) Narrow (EQUIVALENT)
9.39/4.04	Haskell To QDPs
9.39/4.04	
9.39/4.04	digraph dp_graph {
9.39/4.04	node [outthreshold=100, inthreshold=100];1[label="ds",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.39/4.04	3[label="ds vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.39/4.04	4[label="ds vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.39/4.04	5[label="vx3 vx4",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3];
9.39/4.04	6[label="vx4",fontsize=16,color="green",shape="box"];}
9.39/4.04	
9.39/4.04	----------------------------------------
9.39/4.04	
9.39/4.04	(6)
9.39/4.04	YES
9.62/4.09	EOF