7.91/3.54	YES
9.39/3.97	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.39/3.97	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.39/3.97	
9.39/3.97	
9.39/3.97	H-Termination with start terms of the given HASKELL could be proven:
9.39/3.97	
9.39/3.97	(0) HASKELL
9.39/3.97	(1) BR [EQUIVALENT, 0 ms]
9.39/3.97	(2) HASKELL
9.39/3.97	(3) COR [EQUIVALENT, 0 ms]
9.39/3.97	(4) HASKELL
9.39/3.97	(5) Narrow [EQUIVALENT, 20 ms]
9.39/3.97	(6) YES
9.39/3.97	
9.39/3.97	
9.39/3.97	----------------------------------------
9.39/3.97	
9.39/3.97	(0)
9.39/3.97	Obligation:
9.39/3.97	mainModule Main 
9.39/3.97	module Main where {
9.39/3.97	import qualified Prelude;
9.39/3.97	}
9.39/3.97	
9.39/3.97	----------------------------------------
9.39/3.97	
9.39/3.97	(1) BR (EQUIVALENT)
9.39/3.97	Replaced joker patterns by fresh variables and removed binding patterns.
9.39/3.97	----------------------------------------
9.39/3.97	
9.39/3.97	(2)
9.39/3.97	Obligation:
9.39/3.97	mainModule Main 
9.39/3.97	module Main where {
9.39/3.97	import qualified Prelude;
9.39/3.97	}
9.39/3.97	
9.39/3.97	----------------------------------------
9.39/3.97	
9.39/3.97	(3) COR (EQUIVALENT)
9.39/3.97	Cond Reductions:
9.39/3.97	The following Function with conditions
9.39/3.97	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
9.39/3.97	"
9.39/3.97	is transformed to
9.39/3.97	"compare x y = compare3 x y;
9.39/3.97	"
9.39/3.97	"compare0 x y True = GT;
9.39/3.97	"
9.39/3.97	"compare1 x y True = LT;
9.39/3.97	compare1 x y False = compare0 x y otherwise;
9.39/3.97	"
9.39/3.97	"compare2 x y True = EQ;
9.39/3.97	compare2 x y False = compare1 x y (x <= y);
9.39/3.97	"
9.39/3.97	"compare3 x y = compare2 x y (x == y);
9.39/3.97	"
9.39/3.97	The following Function with conditions
9.39/3.97	"undefined |Falseundefined;
9.39/3.97	"
9.39/3.97	is transformed to
9.39/3.97	"undefined  = undefined1;
9.39/3.97	"
9.39/3.97	"undefined0 True = undefined;
9.39/3.97	"
9.39/3.97	"undefined1  = undefined0 False;
9.39/3.97	"
9.39/3.97	
9.39/3.97	----------------------------------------
9.39/3.97	
9.39/3.97	(4)
9.39/3.97	Obligation:
9.39/3.97	mainModule Main 
9.39/3.97	module Main where {
9.39/3.97	import qualified Prelude;
9.39/3.97	}
9.39/3.97	
9.39/3.97	----------------------------------------
9.39/3.97	
9.39/3.97	(5) Narrow (EQUIVALENT)
9.39/3.97	Haskell To QDPs
9.39/3.97	
9.39/3.97	digraph dp_graph {
9.39/3.97	node [outthreshold=100, inthreshold=100];1[label="compare",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.39/3.97	3[label="compare vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.39/3.97	4[label="compare vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.39/3.97	5[label="compare3 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.39/3.97	6[label="compare2 vx3 vx4 (vx3 == vx4)",fontsize=16,color="burlywood",shape="box"];27[label="vx3/False",fontsize=10,color="white",style="solid",shape="box"];6 -> 27[label="",style="solid", color="burlywood", weight=9];
9.39/3.97	27 -> 7[label="",style="solid", color="burlywood", weight=3];
9.39/3.97	28[label="vx3/True",fontsize=10,color="white",style="solid",shape="box"];6 -> 28[label="",style="solid", color="burlywood", weight=9];
9.39/3.97	28 -> 8[label="",style="solid", color="burlywood", weight=3];
9.39/3.97	7[label="compare2 False vx4 (False == vx4)",fontsize=16,color="burlywood",shape="box"];29[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];7 -> 29[label="",style="solid", color="burlywood", weight=9];
9.39/3.97	29 -> 9[label="",style="solid", color="burlywood", weight=3];
9.39/3.97	30[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];7 -> 30[label="",style="solid", color="burlywood", weight=9];
9.39/3.97	30 -> 10[label="",style="solid", color="burlywood", weight=3];
9.39/3.97	8[label="compare2 True vx4 (True == vx4)",fontsize=16,color="burlywood",shape="box"];31[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];8 -> 31[label="",style="solid", color="burlywood", weight=9];
9.39/3.97	31 -> 11[label="",style="solid", color="burlywood", weight=3];
9.39/3.97	32[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];8 -> 32[label="",style="solid", color="burlywood", weight=9];
9.39/3.97	32 -> 12[label="",style="solid", color="burlywood", weight=3];
9.39/3.97	9[label="compare2 False False (False == False)",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
9.39/3.97	10[label="compare2 False True (False == True)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
9.39/3.97	11[label="compare2 True False (True == False)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
9.39/3.97	12[label="compare2 True True (True == True)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
9.39/3.97	13[label="compare2 False False True",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
9.39/3.97	14[label="compare2 False True False",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
9.39/3.97	15[label="compare2 True False False",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
9.39/3.97	16[label="compare2 True True True",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
9.39/3.97	17[label="EQ",fontsize=16,color="green",shape="box"];18[label="compare1 False True (False <= True)",fontsize=16,color="black",shape="box"];18 -> 21[label="",style="solid", color="black", weight=3];
9.39/3.97	19[label="compare1 True False (True <= False)",fontsize=16,color="black",shape="box"];19 -> 22[label="",style="solid", color="black", weight=3];
9.39/3.97	20[label="EQ",fontsize=16,color="green",shape="box"];21[label="compare1 False True True",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
9.39/3.97	22[label="compare1 True False False",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3];
9.39/3.97	23[label="LT",fontsize=16,color="green",shape="box"];24[label="compare0 True False otherwise",fontsize=16,color="black",shape="box"];24 -> 25[label="",style="solid", color="black", weight=3];
9.39/3.97	25[label="compare0 True False True",fontsize=16,color="black",shape="box"];25 -> 26[label="",style="solid", color="black", weight=3];
9.39/3.97	26[label="GT",fontsize=16,color="green",shape="box"];}
9.39/3.97	
9.39/3.97	----------------------------------------
9.39/3.97	
9.39/3.97	(6)
9.39/3.97	YES
9.63/4.02	EOF