8.04/3.52	YES
9.50/3.97	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.50/3.97	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.50/3.97	
9.50/3.97	
9.50/3.97	H-Termination with start terms of the given HASKELL could be proven:
9.50/3.97	
9.50/3.97	(0) HASKELL
9.50/3.97	(1) BR [EQUIVALENT, 0 ms]
9.50/3.97	(2) HASKELL
9.50/3.97	(3) COR [EQUIVALENT, 0 ms]
9.50/3.97	(4) HASKELL
9.50/3.97	(5) Narrow [EQUIVALENT, 11 ms]
9.50/3.97	(6) YES
9.50/3.97	
9.50/3.97	
9.50/3.97	----------------------------------------
9.50/3.97	
9.50/3.97	(0)
9.50/3.97	Obligation:
9.50/3.97	mainModule Main 
9.50/3.97	module Main where {
9.50/3.97	import qualified Prelude;
9.50/3.97	}
9.50/3.97	
9.50/3.97	----------------------------------------
9.50/3.97	
9.50/3.97	(1) BR (EQUIVALENT)
9.50/3.97	Replaced joker patterns by fresh variables and removed binding patterns.
9.50/3.97	----------------------------------------
9.50/3.97	
9.50/3.97	(2)
9.50/3.97	Obligation:
9.50/3.97	mainModule Main 
9.50/3.97	module Main where {
9.50/3.97	import qualified Prelude;
9.50/3.97	}
9.50/3.97	
9.50/3.97	----------------------------------------
9.50/3.97	
9.50/3.97	(3) COR (EQUIVALENT)
9.50/3.97	Cond Reductions:
9.50/3.97	The following Function with conditions
9.50/3.97	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
9.50/3.97	"
9.50/3.97	is transformed to
9.50/3.97	"compare x y = compare3 x y;
9.50/3.97	"
9.50/3.97	"compare1 x y True = LT;
9.50/3.97	compare1 x y False = compare0 x y otherwise;
9.50/3.97	"
9.50/3.97	"compare2 x y True = EQ;
9.50/3.97	compare2 x y False = compare1 x y (x <= y);
9.50/3.97	"
9.50/3.97	"compare0 x y True = GT;
9.50/3.97	"
9.50/3.97	"compare3 x y = compare2 x y (x == y);
9.50/3.97	"
9.50/3.97	The following Function with conditions
9.50/3.97	"undefined |Falseundefined;
9.50/3.97	"
9.50/3.97	is transformed to
9.50/3.97	"undefined  = undefined1;
9.50/3.97	"
9.50/3.97	"undefined0 True = undefined;
9.50/3.97	"
9.50/3.97	"undefined1  = undefined0 False;
9.50/3.97	"
9.50/3.97	
9.50/3.97	----------------------------------------
9.50/3.97	
9.50/3.97	(4)
9.50/3.97	Obligation:
9.50/3.97	mainModule Main 
9.50/3.97	module Main where {
9.50/3.97	import qualified Prelude;
9.50/3.97	}
9.50/3.97	
9.50/3.97	----------------------------------------
9.50/3.97	
9.50/3.97	(5) Narrow (EQUIVALENT)
9.50/3.97	Haskell To QDPs
9.50/3.97	
9.50/3.97	digraph dp_graph {
9.50/3.97	node [outthreshold=100, inthreshold=100];1[label="(>)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.50/3.97	3[label="(>) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.50/3.97	4[label="(>) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.50/3.97	5[label="compare vx3 vx4 == GT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.50/3.97	6[label="compare3 vx3 vx4 == GT",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.50/3.97	7[label="compare2 vx3 vx4 (vx3 == vx4) == GT",fontsize=16,color="burlywood",shape="box"];59[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];7 -> 59[label="",style="solid", color="burlywood", weight=9];
9.50/3.97	59 -> 8[label="",style="solid", color="burlywood", weight=3];
9.50/3.97	60[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 60[label="",style="solid", color="burlywood", weight=9];
9.50/3.97	60 -> 9[label="",style="solid", color="burlywood", weight=3];
9.50/3.97	61[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 61[label="",style="solid", color="burlywood", weight=9];
9.50/3.97	61 -> 10[label="",style="solid", color="burlywood", weight=3];
9.50/3.97	8[label="compare2 LT vx4 (LT == vx4) == GT",fontsize=16,color="burlywood",shape="box"];62[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];8 -> 62[label="",style="solid", color="burlywood", weight=9];
9.50/3.97	62 -> 11[label="",style="solid", color="burlywood", weight=3];
9.50/3.97	63[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 63[label="",style="solid", color="burlywood", weight=9];
9.50/3.97	63 -> 12[label="",style="solid", color="burlywood", weight=3];
9.50/3.97	64[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 64[label="",style="solid", color="burlywood", weight=9];
9.50/3.97	64 -> 13[label="",style="solid", color="burlywood", weight=3];
9.50/3.97	9[label="compare2 EQ vx4 (EQ == vx4) == GT",fontsize=16,color="burlywood",shape="box"];65[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];9 -> 65[label="",style="solid", color="burlywood", weight=9];
9.50/3.97	65 -> 14[label="",style="solid", color="burlywood", weight=3];
9.50/3.97	66[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 66[label="",style="solid", color="burlywood", weight=9];
9.50/3.97	66 -> 15[label="",style="solid", color="burlywood", weight=3];
9.50/3.97	67[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 67[label="",style="solid", color="burlywood", weight=9];
9.50/3.97	67 -> 16[label="",style="solid", color="burlywood", weight=3];
9.50/3.97	10[label="compare2 GT vx4 (GT == vx4) == GT",fontsize=16,color="burlywood",shape="box"];68[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];10 -> 68[label="",style="solid", color="burlywood", weight=9];
9.50/3.97	68 -> 17[label="",style="solid", color="burlywood", weight=3];
9.50/3.97	69[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];10 -> 69[label="",style="solid", color="burlywood", weight=9];
9.50/3.97	69 -> 18[label="",style="solid", color="burlywood", weight=3];
9.50/3.97	70[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];10 -> 70[label="",style="solid", color="burlywood", weight=9];
9.50/3.97	70 -> 19[label="",style="solid", color="burlywood", weight=3];
9.50/3.97	11[label="compare2 LT LT (LT == LT) == GT",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
9.50/3.97	12[label="compare2 LT EQ (LT == EQ) == GT",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
9.50/3.97	13[label="compare2 LT GT (LT == GT) == GT",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
9.50/3.97	14[label="compare2 EQ LT (EQ == LT) == GT",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.50/3.97	15[label="compare2 EQ EQ (EQ == EQ) == GT",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
9.50/3.97	16[label="compare2 EQ GT (EQ == GT) == GT",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.50/3.97	17[label="compare2 GT LT (GT == LT) == GT",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
9.50/3.97	18[label="compare2 GT EQ (GT == EQ) == GT",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
9.50/3.97	19[label="compare2 GT GT (GT == GT) == GT",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
9.50/3.97	20[label="compare2 LT LT True == GT",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
9.50/3.97	21[label="compare2 LT EQ False == GT",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
9.50/3.97	22[label="compare2 LT GT False == GT",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
9.50/3.97	23[label="compare2 EQ LT False == GT",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
9.50/3.97	24[label="compare2 EQ EQ True == GT",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
9.50/3.97	25[label="compare2 EQ GT False == GT",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
9.50/3.97	26[label="compare2 GT LT False == GT",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
9.50/3.97	27[label="compare2 GT EQ False == GT",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
9.50/3.97	28[label="compare2 GT GT True == GT",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
9.50/3.97	29[label="EQ == GT",fontsize=16,color="black",shape="triangle"];29 -> 38[label="",style="solid", color="black", weight=3];
9.50/3.97	30[label="compare1 LT EQ (LT <= EQ) == GT",fontsize=16,color="black",shape="box"];30 -> 39[label="",style="solid", color="black", weight=3];
9.50/3.97	31[label="compare1 LT GT (LT <= GT) == GT",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
9.50/3.97	32[label="compare1 EQ LT (EQ <= LT) == GT",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
9.50/3.97	33 -> 29[label="",style="dashed", color="red", weight=0];
9.50/3.97	33[label="EQ == GT",fontsize=16,color="magenta"];34[label="compare1 EQ GT (EQ <= GT) == GT",fontsize=16,color="black",shape="box"];34 -> 42[label="",style="solid", color="black", weight=3];
9.50/3.97	35[label="compare1 GT LT (GT <= LT) == GT",fontsize=16,color="black",shape="box"];35 -> 43[label="",style="solid", color="black", weight=3];
9.50/3.97	36[label="compare1 GT EQ (GT <= EQ) == GT",fontsize=16,color="black",shape="box"];36 -> 44[label="",style="solid", color="black", weight=3];
9.50/3.97	37 -> 29[label="",style="dashed", color="red", weight=0];
9.50/3.97	37[label="EQ == GT",fontsize=16,color="magenta"];38[label="False",fontsize=16,color="green",shape="box"];39[label="compare1 LT EQ True == GT",fontsize=16,color="black",shape="box"];39 -> 45[label="",style="solid", color="black", weight=3];
9.50/3.97	40[label="compare1 LT GT True == GT",fontsize=16,color="black",shape="box"];40 -> 46[label="",style="solid", color="black", weight=3];
9.50/3.97	41[label="compare1 EQ LT False == GT",fontsize=16,color="black",shape="box"];41 -> 47[label="",style="solid", color="black", weight=3];
9.50/3.97	42[label="compare1 EQ GT True == GT",fontsize=16,color="black",shape="box"];42 -> 48[label="",style="solid", color="black", weight=3];
9.50/3.97	43[label="compare1 GT LT False == GT",fontsize=16,color="black",shape="box"];43 -> 49[label="",style="solid", color="black", weight=3];
9.50/3.97	44[label="compare1 GT EQ False == GT",fontsize=16,color="black",shape="box"];44 -> 50[label="",style="solid", color="black", weight=3];
9.50/3.97	45[label="LT == GT",fontsize=16,color="black",shape="triangle"];45 -> 51[label="",style="solid", color="black", weight=3];
9.50/3.97	46 -> 45[label="",style="dashed", color="red", weight=0];
9.50/3.97	46[label="LT == GT",fontsize=16,color="magenta"];47[label="compare0 EQ LT otherwise == GT",fontsize=16,color="black",shape="box"];47 -> 52[label="",style="solid", color="black", weight=3];
9.50/3.97	48 -> 45[label="",style="dashed", color="red", weight=0];
9.50/3.97	48[label="LT == GT",fontsize=16,color="magenta"];49[label="compare0 GT LT otherwise == GT",fontsize=16,color="black",shape="box"];49 -> 53[label="",style="solid", color="black", weight=3];
9.50/3.97	50[label="compare0 GT EQ otherwise == GT",fontsize=16,color="black",shape="box"];50 -> 54[label="",style="solid", color="black", weight=3];
9.50/3.97	51[label="False",fontsize=16,color="green",shape="box"];52[label="compare0 EQ LT True == GT",fontsize=16,color="black",shape="box"];52 -> 55[label="",style="solid", color="black", weight=3];
9.50/3.97	53[label="compare0 GT LT True == GT",fontsize=16,color="black",shape="box"];53 -> 56[label="",style="solid", color="black", weight=3];
9.50/3.97	54[label="compare0 GT EQ True == GT",fontsize=16,color="black",shape="box"];54 -> 57[label="",style="solid", color="black", weight=3];
9.50/3.97	55[label="GT == GT",fontsize=16,color="black",shape="triangle"];55 -> 58[label="",style="solid", color="black", weight=3];
9.50/3.97	56 -> 55[label="",style="dashed", color="red", weight=0];
9.50/3.97	56[label="GT == GT",fontsize=16,color="magenta"];57 -> 55[label="",style="dashed", color="red", weight=0];
9.50/3.97	57[label="GT == GT",fontsize=16,color="magenta"];58[label="True",fontsize=16,color="green",shape="box"];}
9.50/3.97	
9.50/3.97	----------------------------------------
9.50/3.97	
9.50/3.97	(6)
9.50/3.97	YES
9.68/4.05	EOF