7.26/3.41	YES
8.94/3.87	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
8.94/3.87	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.94/3.87	
8.94/3.87	
8.94/3.87	H-Termination with start terms of the given HASKELL could be proven:
8.94/3.87	
8.94/3.87	(0) HASKELL
8.94/3.87	(1) BR [EQUIVALENT, 0 ms]
8.94/3.87	(2) HASKELL
8.94/3.87	(3) COR [EQUIVALENT, 0 ms]
8.94/3.87	(4) HASKELL
8.94/3.87	(5) Narrow [EQUIVALENT, 0 ms]
8.94/3.87	(6) YES
8.94/3.87	
8.94/3.87	
8.94/3.87	----------------------------------------
8.94/3.87	
8.94/3.87	(0)
8.94/3.87	Obligation:
8.94/3.87	mainModule Main 
8.94/3.87	module Main where {
8.94/3.87	import qualified Prelude;
8.94/3.87	data Tup2 b a = Tup2 b a ;
8.94/3.87	
8.94/3.87	fst :: Tup2 a b  ->  a;
8.94/3.87	fst (Tup2 x vv) = x;
8.94/3.87	
8.94/3.87	}
8.94/3.87	
8.94/3.87	----------------------------------------
8.94/3.87	
8.94/3.87	(1) BR (EQUIVALENT)
8.94/3.87	Replaced joker patterns by fresh variables and removed binding patterns.
8.94/3.87	----------------------------------------
8.94/3.87	
8.94/3.87	(2)
8.94/3.87	Obligation:
8.94/3.87	mainModule Main 
8.94/3.87	module Main where {
8.94/3.87	import qualified Prelude;
8.94/3.87	data Tup2 a b = Tup2 a b ;
8.94/3.87	
8.94/3.87	fst :: Tup2 b a  ->  b;
8.94/3.87	fst (Tup2 x vv) = x;
8.94/3.87	
8.94/3.87	}
8.94/3.87	
8.94/3.87	----------------------------------------
8.94/3.87	
8.94/3.87	(3) COR (EQUIVALENT)
8.94/3.87	Cond Reductions:
8.94/3.87	The following Function with conditions
8.94/3.87	"undefined |Falseundefined;
8.94/3.87	"
8.94/3.87	is transformed to
8.94/3.87	"undefined  = undefined1;
8.94/3.87	"
8.94/3.87	"undefined0 True = undefined;
8.94/3.87	"
8.94/3.87	"undefined1  = undefined0 False;
8.94/3.87	"
8.94/3.87	
8.94/3.87	----------------------------------------
8.94/3.87	
8.94/3.87	(4)
8.94/3.87	Obligation:
8.94/3.87	mainModule Main 
8.94/3.87	module Main where {
8.94/3.87	import qualified Prelude;
8.94/3.87	data Tup2 a b = Tup2 a b ;
8.94/3.87	
8.94/3.87	fst :: Tup2 b a  ->  b;
8.94/3.87	fst (Tup2 x vv) = x;
8.94/3.87	
8.94/3.87	}
8.94/3.87	
8.94/3.87	----------------------------------------
8.94/3.87	
8.94/3.87	(5) Narrow (EQUIVALENT)
8.94/3.87	Haskell To QDPs
8.94/3.87	
8.94/3.87	digraph dp_graph {
8.94/3.87	node [outthreshold=100, inthreshold=100];1[label="fst",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
8.94/3.87	3[label="fst vy3",fontsize=16,color="burlywood",shape="triangle"];6[label="vy3/Tup2 vy30 vy31",fontsize=10,color="white",style="solid",shape="box"];3 -> 6[label="",style="solid", color="burlywood", weight=9];
8.94/3.87	6 -> 4[label="",style="solid", color="burlywood", weight=3];
8.94/3.87	4[label="fst (Tup2 vy30 vy31)",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
8.94/3.87	5[label="vy30",fontsize=16,color="green",shape="box"];}
8.94/3.87	
8.94/3.87	----------------------------------------
8.94/3.87	
8.94/3.87	(6)
8.94/3.87	YES
9.03/3.92	EOF