8.29/3.50	YES
9.73/3.91	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.73/3.91	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.73/3.91	
9.73/3.91	
9.73/3.91	H-Termination with start terms of the given HASKELL could be proven:
9.73/3.91	
9.73/3.91	(0) HASKELL
9.73/3.91	(1) BR [EQUIVALENT, 0 ms]
9.73/3.91	(2) HASKELL
9.73/3.91	(3) COR [EQUIVALENT, 0 ms]
9.73/3.91	(4) HASKELL
9.73/3.91	(5) Narrow [EQUIVALENT, 14 ms]
9.73/3.91	(6) YES
9.73/3.91	
9.73/3.91	
9.73/3.91	----------------------------------------
9.73/3.91	
9.73/3.91	(0)
9.73/3.91	Obligation:
9.73/3.91	mainModule Main 
9.73/3.91	module Main where {
9.73/3.91	import qualified Prelude;
9.73/3.91	}
9.73/3.91	
9.73/3.91	----------------------------------------
9.73/3.91	
9.73/3.91	(1) BR (EQUIVALENT)
9.73/3.91	Replaced joker patterns by fresh variables and removed binding patterns.
9.73/3.91	----------------------------------------
9.73/3.91	
9.73/3.91	(2)
9.73/3.91	Obligation:
9.73/3.91	mainModule Main 
9.73/3.91	module Main where {
9.73/3.91	import qualified Prelude;
9.73/3.91	}
9.73/3.91	
9.73/3.91	----------------------------------------
9.73/3.91	
9.73/3.91	(3) COR (EQUIVALENT)
9.73/3.91	Cond Reductions:
9.73/3.91	The following Function with conditions
9.73/3.91	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
9.73/3.91	"
9.73/3.91	is transformed to
9.73/3.91	"compare x y = compare3 x y;
9.73/3.91	"
9.73/3.91	"compare2 x y True = EQ;
9.73/3.91	compare2 x y False = compare1 x y (x <= y);
9.73/3.91	"
9.73/3.91	"compare0 x y True = GT;
9.73/3.91	"
9.73/3.91	"compare1 x y True = LT;
9.73/3.91	compare1 x y False = compare0 x y otherwise;
9.73/3.91	"
9.73/3.91	"compare3 x y = compare2 x y (x == y);
9.73/3.91	"
9.73/3.91	The following Function with conditions
9.73/3.91	"undefined |Falseundefined;
9.73/3.91	"
9.73/3.91	is transformed to
9.73/3.91	"undefined  = undefined1;
9.73/3.91	"
9.73/3.91	"undefined0 True = undefined;
9.73/3.91	"
9.73/3.91	"undefined1  = undefined0 False;
9.73/3.91	"
9.73/3.91	
9.73/3.91	----------------------------------------
9.73/3.91	
9.73/3.91	(4)
9.73/3.91	Obligation:
9.73/3.91	mainModule Main 
9.73/3.91	module Main where {
9.73/3.91	import qualified Prelude;
9.73/3.91	}
9.73/3.91	
9.73/3.91	----------------------------------------
9.73/3.91	
9.73/3.91	(5) Narrow (EQUIVALENT)
9.73/3.91	Haskell To QDPs
9.73/3.91	
9.73/3.91	digraph dp_graph {
9.73/3.91	node [outthreshold=100, inthreshold=100];1[label="(<)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.73/3.91	3[label="(<) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.73/3.91	4[label="(<) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.73/3.91	5[label="compare vx3 vx4 == LT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.73/3.91	6[label="compare3 vx3 vx4 == LT",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.73/3.91	7[label="compare2 vx3 vx4 (vx3 == vx4) == LT",fontsize=16,color="burlywood",shape="box"];31[label="vx3/False",fontsize=10,color="white",style="solid",shape="box"];7 -> 31[label="",style="solid", color="burlywood", weight=9];
9.73/3.91	31 -> 8[label="",style="solid", color="burlywood", weight=3];
9.73/3.91	32[label="vx3/True",fontsize=10,color="white",style="solid",shape="box"];7 -> 32[label="",style="solid", color="burlywood", weight=9];
9.73/3.91	32 -> 9[label="",style="solid", color="burlywood", weight=3];
9.73/3.91	8[label="compare2 False vx4 (False == vx4) == LT",fontsize=16,color="burlywood",shape="box"];33[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];8 -> 33[label="",style="solid", color="burlywood", weight=9];
9.73/3.91	33 -> 10[label="",style="solid", color="burlywood", weight=3];
9.73/3.91	34[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];8 -> 34[label="",style="solid", color="burlywood", weight=9];
9.73/3.91	34 -> 11[label="",style="solid", color="burlywood", weight=3];
9.73/3.91	9[label="compare2 True vx4 (True == vx4) == LT",fontsize=16,color="burlywood",shape="box"];35[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];9 -> 35[label="",style="solid", color="burlywood", weight=9];
9.73/3.91	35 -> 12[label="",style="solid", color="burlywood", weight=3];
9.73/3.91	36[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];9 -> 36[label="",style="solid", color="burlywood", weight=9];
9.73/3.91	36 -> 13[label="",style="solid", color="burlywood", weight=3];
9.73/3.91	10[label="compare2 False False (False == False) == LT",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
9.73/3.91	11[label="compare2 False True (False == True) == LT",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
9.73/3.91	12[label="compare2 True False (True == False) == LT",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
9.73/3.91	13[label="compare2 True True (True == True) == LT",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
9.73/3.91	14[label="compare2 False False True == LT",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
9.73/3.91	15[label="compare2 False True False == LT",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
9.73/3.91	16[label="compare2 True False False == LT",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
9.73/3.91	17[label="compare2 True True True == LT",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
9.73/3.91	18[label="EQ == LT",fontsize=16,color="black",shape="triangle"];18 -> 22[label="",style="solid", color="black", weight=3];
9.73/3.91	19[label="compare1 False True (False <= True) == LT",fontsize=16,color="black",shape="box"];19 -> 23[label="",style="solid", color="black", weight=3];
9.73/3.91	20[label="compare1 True False (True <= False) == LT",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
9.73/3.91	21 -> 18[label="",style="dashed", color="red", weight=0];
9.73/3.91	21[label="EQ == LT",fontsize=16,color="magenta"];22[label="False",fontsize=16,color="green",shape="box"];23[label="compare1 False True True == LT",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
9.73/3.91	24[label="compare1 True False False == LT",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
9.73/3.91	25[label="LT == LT",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
9.73/3.91	26[label="compare0 True False otherwise == LT",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
9.73/3.91	27[label="True",fontsize=16,color="green",shape="box"];28[label="compare0 True False True == LT",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3];
9.73/3.91	29[label="GT == LT",fontsize=16,color="black",shape="box"];29 -> 30[label="",style="solid", color="black", weight=3];
9.73/3.91	30[label="False",fontsize=16,color="green",shape="box"];}
9.73/3.91	
9.73/3.91	----------------------------------------
9.73/3.91	
9.73/3.91	(6)
9.73/3.91	YES
9.79/3.95	EOF