7.78/3.54	YES
9.25/3.99	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.25/3.99	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.25/3.99	
9.25/3.99	
9.25/3.99	H-Termination with start terms of the given HASKELL could be proven:
9.25/3.99	
9.25/3.99	(0) HASKELL
9.25/3.99	(1) BR [EQUIVALENT, 0 ms]
9.25/3.99	(2) HASKELL
9.25/3.99	(3) COR [EQUIVALENT, 0 ms]
9.25/3.99	(4) HASKELL
9.25/3.99	(5) Narrow [EQUIVALENT, 20 ms]
9.25/3.99	(6) YES
9.25/3.99	
9.25/3.99	
9.25/3.99	----------------------------------------
9.25/3.99	
9.25/3.99	(0)
9.25/3.99	Obligation:
9.25/3.99	mainModule Main 
9.25/3.99	module Main where {
9.25/3.99	import qualified Prelude;
9.25/3.99	}
9.25/3.99	
9.25/3.99	----------------------------------------
9.25/3.99	
9.25/3.99	(1) BR (EQUIVALENT)
9.25/3.99	Replaced joker patterns by fresh variables and removed binding patterns.
9.25/3.99	----------------------------------------
9.25/3.99	
9.25/3.99	(2)
9.25/3.99	Obligation:
9.25/3.99	mainModule Main 
9.25/3.99	module Main where {
9.25/3.99	import qualified Prelude;
9.25/3.99	}
9.25/3.99	
9.25/3.99	----------------------------------------
9.25/3.99	
9.25/3.99	(3) COR (EQUIVALENT)
9.25/3.99	Cond Reductions:
9.25/3.99	The following Function with conditions
9.25/3.99	"lookup k [] = Nothing;
9.25/3.99	lookup k ((x,y) : xys)|k == xJust y|otherwiselookup k xys;
9.25/3.99	"
9.25/3.99	is transformed to
9.25/3.99	"lookup k [] = lookup3 k [];
9.25/3.99	lookup k ((x,y) : xys) = lookup2 k ((x,y) : xys);
9.25/3.99	"
9.25/3.99	"lookup1 k x y xys True = Just y;
9.25/3.99	lookup1 k x y xys False = lookup0 k x y xys otherwise;
9.25/3.99	"
9.25/3.99	"lookup0 k x y xys True = lookup k xys;
9.25/3.99	"
9.25/3.99	"lookup2 k ((x,y) : xys) = lookup1 k x y xys (k == x);
9.25/3.99	"
9.25/3.99	"lookup3 k [] = Nothing;
9.25/3.99	lookup3 wu wv = lookup2 wu wv;
9.25/3.99	"
9.25/3.99	The following Function with conditions
9.25/3.99	"undefined |Falseundefined;
9.25/3.99	"
9.25/3.99	is transformed to
9.25/3.99	"undefined  = undefined1;
9.25/3.99	"
9.25/3.99	"undefined0 True = undefined;
9.25/3.99	"
9.25/3.99	"undefined1  = undefined0 False;
9.25/3.99	"
9.25/3.99	
9.25/3.99	----------------------------------------
9.25/3.99	
9.25/3.99	(4)
9.25/3.99	Obligation:
9.25/3.99	mainModule Main 
9.25/3.99	module Main where {
9.25/3.99	import qualified Prelude;
9.25/3.99	}
9.25/3.99	
9.25/3.99	----------------------------------------
9.25/3.99	
9.25/3.99	(5) Narrow (EQUIVALENT)
9.25/3.99	Haskell To QDPs
9.25/3.99	
9.25/3.99	digraph dp_graph {
9.25/3.99	node [outthreshold=100, inthreshold=100];1[label="lookup",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.25/3.99	3[label="lookup ww3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.25/3.99	4[label="lookup ww3 ww4",fontsize=16,color="burlywood",shape="triangle"];16[label="ww4/ww40 : ww41",fontsize=10,color="white",style="solid",shape="box"];4 -> 16[label="",style="solid", color="burlywood", weight=9];
9.25/3.99	16 -> 5[label="",style="solid", color="burlywood", weight=3];
9.25/3.99	17[label="ww4/[]",fontsize=10,color="white",style="solid",shape="box"];4 -> 17[label="",style="solid", color="burlywood", weight=9];
9.25/3.99	17 -> 6[label="",style="solid", color="burlywood", weight=3];
9.25/3.99	5[label="lookup ww3 (ww40 : ww41)",fontsize=16,color="burlywood",shape="box"];18[label="ww40/(ww400,ww401)",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
9.25/3.99	18 -> 7[label="",style="solid", color="burlywood", weight=3];
9.25/3.99	6[label="lookup ww3 []",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
9.25/3.99	7[label="lookup ww3 ((ww400,ww401) : ww41)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
9.25/3.99	8[label="lookup3 ww3 []",fontsize=16,color="black",shape="box"];8 -> 10[label="",style="solid", color="black", weight=3];
9.25/3.99	9[label="lookup2 ww3 ((ww400,ww401) : ww41)",fontsize=16,color="black",shape="box"];9 -> 11[label="",style="solid", color="black", weight=3];
9.25/3.99	10[label="Nothing",fontsize=16,color="green",shape="box"];11[label="lookup1 ww3 ww400 ww401 ww41 (ww3 == ww400)",fontsize=16,color="burlywood",shape="box"];19[label="ww3/()",fontsize=10,color="white",style="solid",shape="box"];11 -> 19[label="",style="solid", color="burlywood", weight=9];
9.25/3.99	19 -> 12[label="",style="solid", color="burlywood", weight=3];
9.25/3.99	12[label="lookup1 () ww400 ww401 ww41 (() == ww400)",fontsize=16,color="burlywood",shape="box"];20[label="ww400/()",fontsize=10,color="white",style="solid",shape="box"];12 -> 20[label="",style="solid", color="burlywood", weight=9];
9.25/3.99	20 -> 13[label="",style="solid", color="burlywood", weight=3];
9.25/3.99	13[label="lookup1 () () ww401 ww41 (() == ())",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
9.25/3.99	14[label="lookup1 () () ww401 ww41 True",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
9.25/3.99	15[label="Just ww401",fontsize=16,color="green",shape="box"];}
9.25/3.99	
9.25/3.99	----------------------------------------
9.25/3.99	
9.25/3.99	(6)
9.25/3.99	YES
9.37/4.04	EOF