7.56/3.41	YES
8.84/3.88	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
8.84/3.88	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
8.84/3.88	
8.84/3.88	
8.84/3.88	H-Termination with start terms of the given HASKELL could be proven:
8.84/3.88	
8.84/3.88	(0) HASKELL
8.84/3.88	(1) BR [EQUIVALENT, 0 ms]
8.84/3.88	(2) HASKELL
8.84/3.88	(3) COR [EQUIVALENT, 0 ms]
8.84/3.88	(4) HASKELL
8.84/3.88	(5) Narrow [EQUIVALENT, 0 ms]
8.84/3.88	(6) YES
8.84/3.88	
8.84/3.88	
8.84/3.88	----------------------------------------
8.84/3.88	
8.84/3.88	(0)
8.84/3.88	Obligation:
8.84/3.88	mainModule Main 
8.84/3.88	module Main where {
8.84/3.88	import qualified Prelude;
8.84/3.88	data Tup2 a b = Tup2 a b ;
8.84/3.88	
8.84/3.88	fst :: Tup2 b a  ->  b;
8.84/3.88	fst (Tup2 x vw) = x;
8.84/3.88	
8.84/3.88	snd :: Tup2 a b  ->  b;
8.84/3.88	snd (Tup2 vv y) = y;
8.84/3.88	
8.84/3.88	uncurry :: (b  ->  a  ->  c)  ->  Tup2 b a  ->  c;
8.84/3.88	uncurry f p = f (fst p) (snd p);
8.84/3.88	
8.84/3.88	}
8.84/3.88	
8.84/3.88	----------------------------------------
8.84/3.88	
8.84/3.88	(1) BR (EQUIVALENT)
8.84/3.88	Replaced joker patterns by fresh variables and removed binding patterns.
8.84/3.88	----------------------------------------
8.84/3.88	
8.84/3.88	(2)
8.84/3.88	Obligation:
8.84/3.88	mainModule Main 
8.84/3.88	module Main where {
8.84/3.88	import qualified Prelude;
8.84/3.88	data Tup2 b a = Tup2 b a ;
8.84/3.88	
8.84/3.88	fst :: Tup2 a b  ->  a;
8.84/3.88	fst (Tup2 x vw) = x;
8.84/3.88	
8.84/3.88	snd :: Tup2 b a  ->  a;
8.84/3.88	snd (Tup2 vv y) = y;
8.84/3.88	
8.84/3.88	uncurry :: (b  ->  c  ->  a)  ->  Tup2 b c  ->  a;
8.84/3.88	uncurry f p = f (fst p) (snd p);
8.84/3.88	
8.84/3.88	}
8.84/3.88	
8.84/3.88	----------------------------------------
8.84/3.88	
8.84/3.88	(3) COR (EQUIVALENT)
8.84/3.88	Cond Reductions:
8.84/3.88	The following Function with conditions
8.84/3.88	"undefined |Falseundefined;
8.84/3.88	"
8.84/3.88	is transformed to
8.84/3.88	"undefined  = undefined1;
8.84/3.88	"
8.84/3.88	"undefined0 True = undefined;
8.84/3.88	"
8.84/3.88	"undefined1  = undefined0 False;
8.84/3.88	"
8.84/3.88	
8.84/3.88	----------------------------------------
8.84/3.88	
8.84/3.88	(4)
8.84/3.88	Obligation:
8.84/3.88	mainModule Main 
8.84/3.88	module Main where {
8.84/3.88	import qualified Prelude;
8.84/3.88	data Tup2 b a = Tup2 b a ;
8.84/3.88	
8.84/3.88	fst :: Tup2 b a  ->  b;
8.84/3.88	fst (Tup2 x vw) = x;
8.84/3.88	
8.84/3.88	snd :: Tup2 b a  ->  a;
8.84/3.88	snd (Tup2 vv y) = y;
8.84/3.88	
8.84/3.88	uncurry :: (a  ->  c  ->  b)  ->  Tup2 a c  ->  b;
8.84/3.88	uncurry f p = f (fst p) (snd p);
8.84/3.88	
8.84/3.88	}
8.84/3.88	
8.84/3.88	----------------------------------------
8.84/3.88	
8.84/3.88	(5) Narrow (EQUIVALENT)
8.84/3.88	Haskell To QDPs
8.84/3.88	
8.84/3.88	digraph dp_graph {
8.84/3.88	node [outthreshold=100, inthreshold=100];1[label="uncurry",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
8.84/3.88	3[label="uncurry vz3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
8.84/3.88	4[label="uncurry vz3 vz4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
8.84/3.88	5[label="vz3 (fst vz4) (snd vz4)",fontsize=16,color="green",shape="box"];5 -> 6[label="",style="dashed", color="green", weight=3];
8.84/3.88	5 -> 7[label="",style="dashed", color="green", weight=3];
8.84/3.88	6[label="fst vz4",fontsize=16,color="burlywood",shape="box"];12[label="vz4/Tup2 vz40 vz41",fontsize=10,color="white",style="solid",shape="box"];6 -> 12[label="",style="solid", color="burlywood", weight=9];
8.84/3.88	12 -> 8[label="",style="solid", color="burlywood", weight=3];
8.84/3.88	7[label="snd vz4",fontsize=16,color="burlywood",shape="box"];13[label="vz4/Tup2 vz40 vz41",fontsize=10,color="white",style="solid",shape="box"];7 -> 13[label="",style="solid", color="burlywood", weight=9];
8.84/3.88	13 -> 9[label="",style="solid", color="burlywood", weight=3];
8.84/3.88	8[label="fst (Tup2 vz40 vz41)",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
8.84/3.88	9[label="snd (Tup2 vz40 vz41)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
8.84/3.88	10[label="vz40",fontsize=16,color="green",shape="box"];11[label="vz41",fontsize=16,color="green",shape="box"];}
8.84/3.88	
8.84/3.88	----------------------------------------
8.84/3.88	
8.84/3.88	(6)
8.84/3.88	YES
9.21/3.93	EOF