7.89/3.49	YES
9.53/3.94	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.53/3.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.53/3.94	
9.53/3.94	
9.53/3.94	H-Termination with start terms of the given HASKELL could be proven:
9.53/3.94	
9.53/3.94	(0) HASKELL
9.53/3.94	(1) BR [EQUIVALENT, 0 ms]
9.53/3.94	(2) HASKELL
9.53/3.94	(3) COR [EQUIVALENT, 0 ms]
9.53/3.94	(4) HASKELL
9.53/3.94	(5) Narrow [EQUIVALENT, 19 ms]
9.53/3.94	(6) YES
9.53/3.94	
9.53/3.94	
9.53/3.94	----------------------------------------
9.53/3.94	
9.53/3.94	(0)
9.53/3.94	Obligation:
9.53/3.94	mainModule Main 
9.53/3.94	module Main where {
9.53/3.94	import qualified Prelude;
9.53/3.94	}
9.53/3.94	
9.53/3.94	----------------------------------------
9.53/3.94	
9.53/3.94	(1) BR (EQUIVALENT)
9.53/3.94	Replaced joker patterns by fresh variables and removed binding patterns.
9.53/3.94	----------------------------------------
9.53/3.94	
9.53/3.94	(2)
9.53/3.94	Obligation:
9.53/3.94	mainModule Main 
9.53/3.94	module Main where {
9.53/3.94	import qualified Prelude;
9.53/3.94	}
9.53/3.94	
9.53/3.94	----------------------------------------
9.53/3.94	
9.53/3.94	(3) COR (EQUIVALENT)
9.53/3.94	Cond Reductions:
9.53/3.94	The following Function with conditions
9.53/3.94	"min x y|x <= yx|otherwisey;
9.53/3.94	"
9.53/3.94	is transformed to
9.53/3.94	"min x y = min2 x y;
9.53/3.94	"
9.53/3.94	"min1 x y True = x;
9.53/3.94	min1 x y False = min0 x y otherwise;
9.53/3.94	"
9.53/3.94	"min0 x y True = y;
9.53/3.94	"
9.53/3.94	"min2 x y = min1 x y (x <= y);
9.53/3.94	"
9.53/3.94	The following Function with conditions
9.53/3.94	"undefined |Falseundefined;
9.53/3.94	"
9.53/3.94	is transformed to
9.53/3.94	"undefined  = undefined1;
9.53/3.94	"
9.53/3.94	"undefined0 True = undefined;
9.53/3.94	"
9.53/3.94	"undefined1  = undefined0 False;
9.53/3.94	"
9.53/3.94	
9.53/3.94	----------------------------------------
9.53/3.94	
9.53/3.94	(4)
9.53/3.94	Obligation:
9.53/3.94	mainModule Main 
9.53/3.94	module Main where {
9.53/3.94	import qualified Prelude;
9.53/3.94	}
9.53/3.94	
9.53/3.94	----------------------------------------
9.53/3.94	
9.53/3.94	(5) Narrow (EQUIVALENT)
9.53/3.94	Haskell To QDPs
9.53/3.94	
9.53/3.94	digraph dp_graph {
9.53/3.94	node [outthreshold=100, inthreshold=100];1[label="min",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.53/3.94	3[label="min vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.53/3.94	4[label="min vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.53/3.94	5[label="min2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.53/3.94	6[label="min1 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];
9.53/3.94	43 -> 7[label="",style="solid", color="burlywood", weight=3];
9.53/3.94	44[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];6 -> 44[label="",style="solid", color="burlywood", weight=9];
9.53/3.94	44 -> 8[label="",style="solid", color="burlywood", weight=3];
9.53/3.94	45[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];6 -> 45[label="",style="solid", color="burlywood", weight=9];
9.53/3.94	45 -> 9[label="",style="solid", color="burlywood", weight=3];
9.53/3.94	7[label="min1 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];
9.53/3.94	46 -> 10[label="",style="solid", color="burlywood", weight=3];
9.53/3.94	47[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 47[label="",style="solid", color="burlywood", weight=9];
9.53/3.94	47 -> 11[label="",style="solid", color="burlywood", weight=3];
9.53/3.94	48[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 48[label="",style="solid", color="burlywood", weight=9];
9.53/3.94	48 -> 12[label="",style="solid", color="burlywood", weight=3];
9.53/3.94	8[label="min1 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];
9.53/3.94	49 -> 13[label="",style="solid", color="burlywood", weight=3];
9.53/3.94	50[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 50[label="",style="solid", color="burlywood", weight=9];
9.53/3.94	50 -> 14[label="",style="solid", color="burlywood", weight=3];
9.53/3.94	51[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 51[label="",style="solid", color="burlywood", weight=9];
9.53/3.94	51 -> 15[label="",style="solid", color="burlywood", weight=3];
9.53/3.94	9[label="min1 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];
9.53/3.94	52 -> 16[label="",style="solid", color="burlywood", weight=3];
9.53/3.94	53[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 53[label="",style="solid", color="burlywood", weight=9];
9.53/3.94	53 -> 17[label="",style="solid", color="burlywood", weight=3];
9.53/3.94	54[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 54[label="",style="solid", color="burlywood", weight=9];
9.53/3.94	54 -> 18[label="",style="solid", color="burlywood", weight=3];
9.53/3.94	10[label="min1 LT LT (LT <= LT)",fontsize=16,color="black",shape="box"];10 -> 19[label="",style="solid", color="black", weight=3];
9.53/3.94	11[label="min1 LT EQ (LT <= EQ)",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
9.53/3.94	12[label="min1 LT GT (LT <= GT)",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
9.53/3.94	13[label="min1 EQ LT (EQ <= LT)",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
9.53/3.94	14[label="min1 EQ EQ (EQ <= EQ)",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.53/3.94	15[label="min1 EQ GT (EQ <= GT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
9.53/3.94	16[label="min1 GT LT (GT <= LT)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.53/3.94	17[label="min1 GT EQ (GT <= EQ)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
9.53/3.94	18[label="min1 GT GT (GT <= GT)",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
9.53/3.94	19[label="min1 LT LT True",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
9.53/3.94	20[label="min1 LT EQ True",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
9.53/3.94	21[label="min1 LT GT True",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
9.53/3.94	22[label="min1 EQ LT False",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
9.53/3.94	23[label="min1 EQ EQ True",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
9.53/3.94	24[label="min1 EQ GT True",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
9.53/3.94	25[label="min1 GT LT False",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
9.53/3.94	26[label="min1 GT EQ False",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
9.53/3.94	27[label="min1 GT GT True",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
9.53/3.94	28[label="LT",fontsize=16,color="green",shape="box"];29[label="LT",fontsize=16,color="green",shape="box"];30[label="LT",fontsize=16,color="green",shape="box"];31[label="min0 EQ LT otherwise",fontsize=16,color="black",shape="box"];31 -> 37[label="",style="solid", color="black", weight=3];
9.53/3.94	32[label="EQ",fontsize=16,color="green",shape="box"];33[label="EQ",fontsize=16,color="green",shape="box"];34[label="min0 GT LT otherwise",fontsize=16,color="black",shape="box"];34 -> 38[label="",style="solid", color="black", weight=3];
9.53/3.94	35[label="min0 GT EQ otherwise",fontsize=16,color="black",shape="box"];35 -> 39[label="",style="solid", color="black", weight=3];
9.53/3.94	36[label="GT",fontsize=16,color="green",shape="box"];37[label="min0 EQ LT True",fontsize=16,color="black",shape="box"];37 -> 40[label="",style="solid", color="black", weight=3];
9.53/3.94	38[label="min0 GT LT True",fontsize=16,color="black",shape="box"];38 -> 41[label="",style="solid", color="black", weight=3];
9.53/3.94	39[label="min0 GT EQ True",fontsize=16,color="black",shape="box"];39 -> 42[label="",style="solid", color="black", weight=3];
9.53/3.94	40[label="LT",fontsize=16,color="green",shape="box"];41[label="LT",fontsize=16,color="green",shape="box"];42[label="EQ",fontsize=16,color="green",shape="box"];}
9.53/3.94	
9.53/3.94	----------------------------------------
9.53/3.94	
9.53/3.94	(6)
9.53/3.94	YES
9.53/3.98	EOF