7.71/3.47	YES
9.33/3.91	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
9.33/3.91	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.33/3.91	
9.33/3.91	
9.33/3.91	H-Termination with start terms of the given HASKELL could be proven:
9.33/3.91	
9.33/3.91	(0) HASKELL
9.33/3.91	(1) BR [EQUIVALENT, 0 ms]
9.33/3.91	(2) HASKELL
9.33/3.91	(3) COR [EQUIVALENT, 0 ms]
9.33/3.91	(4) HASKELL
9.33/3.91	(5) Narrow [EQUIVALENT, 25 ms]
9.33/3.91	(6) YES
9.33/3.91	
9.33/3.91	
9.33/3.91	----------------------------------------
9.33/3.91	
9.33/3.91	(0)
9.33/3.91	Obligation:
9.33/3.91	mainModule Main 
9.33/3.91	module Main where {
9.33/3.91	import qualified Prelude;
9.33/3.91	}
9.33/3.91	
9.33/3.91	----------------------------------------
9.33/3.91	
9.33/3.91	(1) BR (EQUIVALENT)
9.33/3.91	Replaced joker patterns by fresh variables and removed binding patterns.
9.33/3.91	----------------------------------------
9.33/3.91	
9.33/3.91	(2)
9.33/3.91	Obligation:
9.33/3.91	mainModule Main 
9.33/3.91	module Main where {
9.33/3.91	import qualified Prelude;
9.33/3.91	}
9.33/3.91	
9.33/3.91	----------------------------------------
9.33/3.91	
9.33/3.91	(3) COR (EQUIVALENT)
9.33/3.91	Cond Reductions:
9.33/3.91	The following Function with conditions
9.33/3.91	"max x y|x <= yy|otherwisex;
9.33/3.91	"
9.33/3.91	is transformed to
9.33/3.91	"max x y = max2 x y;
9.33/3.91	"
9.33/3.91	"max1 x y True = y;
9.33/3.91	max1 x y False = max0 x y otherwise;
9.33/3.91	"
9.33/3.91	"max0 x y True = x;
9.33/3.91	"
9.33/3.91	"max2 x y = max1 x y (x <= y);
9.33/3.91	"
9.33/3.91	The following Function with conditions
9.33/3.91	"undefined |Falseundefined;
9.33/3.91	"
9.33/3.91	is transformed to
9.33/3.91	"undefined  = undefined1;
9.33/3.91	"
9.33/3.91	"undefined0 True = undefined;
9.33/3.91	"
9.33/3.91	"undefined1  = undefined0 False;
9.33/3.91	"
9.33/3.91	
9.33/3.91	----------------------------------------
9.33/3.91	
9.33/3.91	(4)
9.33/3.91	Obligation:
9.33/3.91	mainModule Main 
9.33/3.91	module Main where {
9.33/3.91	import qualified Prelude;
9.33/3.91	}
9.33/3.91	
9.33/3.91	----------------------------------------
9.33/3.91	
9.33/3.91	(5) Narrow (EQUIVALENT)
9.33/3.91	Haskell To QDPs
9.33/3.91	
9.33/3.91	digraph dp_graph {
9.33/3.91	node [outthreshold=100, inthreshold=100];1[label="max",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.33/3.91	3[label="max vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.33/3.91	4[label="max vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.33/3.91	5[label="max2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.33/3.91	6[label="max1 vx3 vx4 (vx3 <= vx4)",fontsize=16,color="burlywood",shape="box"];43[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];6 -> 43[label="",style="solid", color="burlywood", weight=9];
9.33/3.92	43 -> 7[label="",style="solid", color="burlywood", weight=3];
9.33/3.92	44[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];6 -> 44[label="",style="solid", color="burlywood", weight=9];
9.33/3.92	44 -> 8[label="",style="solid", color="burlywood", weight=3];
9.33/3.92	45[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];6 -> 45[label="",style="solid", color="burlywood", weight=9];
9.33/3.92	45 -> 9[label="",style="solid", color="burlywood", weight=3];
9.33/3.92	7[label="max1 LT vx4 (LT <= vx4)",fontsize=16,color="burlywood",shape="box"];46[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];7 -> 46[label="",style="solid", color="burlywood", weight=9];
9.33/3.92	46 -> 10[label="",style="solid", color="burlywood", weight=3];
9.33/3.92	47[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 47[label="",style="solid", color="burlywood", weight=9];
9.33/3.92	47 -> 11[label="",style="solid", color="burlywood", weight=3];
9.33/3.92	48[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 48[label="",style="solid", color="burlywood", weight=9];
9.33/3.92	48 -> 12[label="",style="solid", color="burlywood", weight=3];
9.33/3.92	8[label="max1 EQ vx4 (EQ <= vx4)",fontsize=16,color="burlywood",shape="box"];49[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];8 -> 49[label="",style="solid", color="burlywood", weight=9];
9.33/3.92	49 -> 13[label="",style="solid", color="burlywood", weight=3];
9.33/3.92	50[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 50[label="",style="solid", color="burlywood", weight=9];
9.33/3.92	50 -> 14[label="",style="solid", color="burlywood", weight=3];
9.33/3.92	51[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 51[label="",style="solid", color="burlywood", weight=9];
9.33/3.92	51 -> 15[label="",style="solid", color="burlywood", weight=3];
9.33/3.92	9[label="max1 GT vx4 (GT <= vx4)",fontsize=16,color="burlywood",shape="box"];52[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];9 -> 52[label="",style="solid", color="burlywood", weight=9];
9.33/3.92	52 -> 16[label="",style="solid", color="burlywood", weight=3];
9.33/3.92	53[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 53[label="",style="solid", color="burlywood", weight=9];
9.33/3.92	53 -> 17[label="",style="solid", color="burlywood", weight=3];
9.33/3.92	54[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 54[label="",style="solid", color="burlywood", weight=9];
9.33/3.92	54 -> 18[label="",style="solid", color="burlywood", weight=3];
9.33/3.92	10[label="max1 LT LT (LT <= LT)",fontsize=16,color="black",shape="box"];10 -> 19[label="",style="solid", color="black", weight=3];
9.33/3.92	11[label="max1 LT EQ (LT <= EQ)",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
9.33/3.92	12[label="max1 LT GT (LT <= GT)",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
9.33/3.92	13[label="max1 EQ LT (EQ <= LT)",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
9.33/3.92	14[label="max1 EQ EQ (EQ <= EQ)",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.33/3.92	15[label="max1 EQ GT (EQ <= GT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
9.33/3.92	16[label="max1 GT LT (GT <= LT)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.33/3.92	17[label="max1 GT EQ (GT <= EQ)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
9.33/3.92	18[label="max1 GT GT (GT <= GT)",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
9.33/3.92	19[label="max1 LT LT True",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
9.33/3.92	20[label="max1 LT EQ True",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
9.33/3.92	21[label="max1 LT GT True",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
9.33/3.92	22[label="max1 EQ LT False",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
9.33/3.92	23[label="max1 EQ EQ True",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
9.33/3.92	24[label="max1 EQ GT True",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
9.33/3.92	25[label="max1 GT LT False",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
9.33/3.92	26[label="max1 GT EQ False",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
9.33/3.92	27[label="max1 GT GT True",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
9.33/3.92	28[label="LT",fontsize=16,color="green",shape="box"];29[label="EQ",fontsize=16,color="green",shape="box"];30[label="GT",fontsize=16,color="green",shape="box"];31[label="max0 EQ LT otherwise",fontsize=16,color="black",shape="box"];31 -> 37[label="",style="solid", color="black", weight=3];
9.33/3.92	32[label="EQ",fontsize=16,color="green",shape="box"];33[label="GT",fontsize=16,color="green",shape="box"];34[label="max0 GT LT otherwise",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3];
9.33/3.92	35[label="max0 GT EQ otherwise",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3];
9.33/3.92	36[label="GT",fontsize=16,color="green",shape="box"];37[label="max0 EQ LT True",fontsize=16,color="black",shape="box"];37 -> 40[label="",style="solid", color="black", weight=3];
9.33/3.92	38[label="max0 GT LT True",fontsize=16,color="black",shape="box"];38 -> 41[label="",style="solid", color="black", weight=3];
9.33/3.92	39[label="max0 GT EQ True",fontsize=16,color="black",shape="box"];39 -> 42[label="",style="solid", color="black", weight=3];
9.33/3.92	40[label="EQ",fontsize=16,color="green",shape="box"];41[label="GT",fontsize=16,color="green",shape="box"];42[label="GT",fontsize=16,color="green",shape="box"];}
9.33/3.92	
9.33/3.92	----------------------------------------
9.33/3.92	
9.33/3.92	(6)
9.33/3.92	YES
9.39/6.33	EOF