8.26/3.52	YES
10.02/3.99	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.02/3.99	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.02/3.99	
10.02/3.99	
10.02/3.99	H-Termination with start terms of the given HASKELL could be proven:
10.02/3.99	
10.02/3.99	(0) HASKELL
10.02/3.99	(1) BR [EQUIVALENT, 0 ms]
10.02/3.99	(2) HASKELL
10.02/3.99	(3) COR [EQUIVALENT, 0 ms]
10.02/3.99	(4) HASKELL
10.02/3.99	(5) Narrow [EQUIVALENT, 0 ms]
10.02/3.99	(6) YES
10.02/3.99	
10.02/3.99	
10.02/3.99	----------------------------------------
10.02/3.99	
10.02/3.99	(0)
10.02/3.99	Obligation:
10.02/3.99	mainModule Main 
10.02/3.99	module Main where {
10.02/3.99	import qualified Prelude;
10.02/3.99	}
10.02/3.99	
10.02/3.99	----------------------------------------
10.02/3.99	
10.02/3.99	(1) BR (EQUIVALENT)
10.02/3.99	Replaced joker patterns by fresh variables and removed binding patterns.
10.02/3.99	----------------------------------------
10.02/3.99	
10.02/3.99	(2)
10.02/3.99	Obligation:
10.02/3.99	mainModule Main 
10.02/3.99	module Main where {
10.02/3.99	import qualified Prelude;
10.02/3.99	}
10.02/3.99	
10.02/3.99	----------------------------------------
10.02/3.99	
10.02/3.99	(3) COR (EQUIVALENT)
10.02/3.99	Cond Reductions:
10.02/3.99	The following Function with conditions
10.02/3.99	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
10.02/3.99	"
10.02/3.99	is transformed to
10.02/3.99	"compare x y = compare3 x y;
10.02/3.99	"
10.02/3.99	"compare0 x y True = GT;
10.02/3.99	"
10.02/3.99	"compare2 x y True = EQ;
10.02/3.99	compare2 x y False = compare1 x y (x <= y);
10.02/3.99	"
10.02/3.99	"compare1 x y True = LT;
10.02/3.99	compare1 x y False = compare0 x y otherwise;
10.02/3.99	"
10.02/3.99	"compare3 x y = compare2 x y (x == y);
10.02/3.99	"
10.02/3.99	The following Function with conditions
10.02/3.99	"undefined |Falseundefined;
10.02/3.99	"
10.02/3.99	is transformed to
10.02/3.99	"undefined  = undefined1;
10.02/3.99	"
10.02/3.99	"undefined0 True = undefined;
10.02/3.99	"
10.02/3.99	"undefined1  = undefined0 False;
10.02/3.99	"
10.02/3.99	
10.02/3.99	----------------------------------------
10.02/3.99	
10.02/3.99	(4)
10.02/3.99	Obligation:
10.02/3.99	mainModule Main 
10.02/3.99	module Main where {
10.02/3.99	import qualified Prelude;
10.02/3.99	}
10.02/3.99	
10.02/3.99	----------------------------------------
10.02/3.99	
10.02/3.99	(5) Narrow (EQUIVALENT)
10.02/3.99	Haskell To QDPs
10.02/3.99	
10.02/3.99	digraph dp_graph {
10.02/3.99	node [outthreshold=100, inthreshold=100];1[label="compare",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.02/3.99	3[label="compare vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.02/3.99	4[label="compare vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
10.02/3.99	5[label="compare3 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
10.02/3.99	6[label="compare2 vx3 vx4 (vx3 == vx4)",fontsize=16,color="burlywood",shape="box"];55[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];6 -> 55[label="",style="solid", color="burlywood", weight=9];
10.02/3.99	55 -> 7[label="",style="solid", color="burlywood", weight=3];
10.02/3.99	56[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];6 -> 56[label="",style="solid", color="burlywood", weight=9];
10.02/3.99	56 -> 8[label="",style="solid", color="burlywood", weight=3];
10.02/3.99	57[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];6 -> 57[label="",style="solid", color="burlywood", weight=9];
10.02/3.99	57 -> 9[label="",style="solid", color="burlywood", weight=3];
10.02/3.99	7[label="compare2 LT vx4 (LT == vx4)",fontsize=16,color="burlywood",shape="box"];58[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];7 -> 58[label="",style="solid", color="burlywood", weight=9];
10.02/3.99	58 -> 10[label="",style="solid", color="burlywood", weight=3];
10.02/3.99	59[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 59[label="",style="solid", color="burlywood", weight=9];
10.02/3.99	59 -> 11[label="",style="solid", color="burlywood", weight=3];
10.02/3.99	60[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 60[label="",style="solid", color="burlywood", weight=9];
10.02/3.99	60 -> 12[label="",style="solid", color="burlywood", weight=3];
10.02/3.99	8[label="compare2 EQ vx4 (EQ == vx4)",fontsize=16,color="burlywood",shape="box"];61[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];8 -> 61[label="",style="solid", color="burlywood", weight=9];
10.02/3.99	61 -> 13[label="",style="solid", color="burlywood", weight=3];
10.02/3.99	62[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 62[label="",style="solid", color="burlywood", weight=9];
10.02/3.99	62 -> 14[label="",style="solid", color="burlywood", weight=3];
10.02/3.99	63[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 63[label="",style="solid", color="burlywood", weight=9];
10.02/3.99	63 -> 15[label="",style="solid", color="burlywood", weight=3];
10.02/3.99	9[label="compare2 GT vx4 (GT == vx4)",fontsize=16,color="burlywood",shape="box"];64[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];9 -> 64[label="",style="solid", color="burlywood", weight=9];
10.02/3.99	64 -> 16[label="",style="solid", color="burlywood", weight=3];
10.02/3.99	65[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 65[label="",style="solid", color="burlywood", weight=9];
10.02/3.99	65 -> 17[label="",style="solid", color="burlywood", weight=3];
10.02/3.99	66[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 66[label="",style="solid", color="burlywood", weight=9];
10.02/3.99	66 -> 18[label="",style="solid", color="burlywood", weight=3];
10.02/3.99	10[label="compare2 LT LT (LT == LT)",fontsize=16,color="black",shape="box"];10 -> 19[label="",style="solid", color="black", weight=3];
10.02/3.99	11[label="compare2 LT EQ (LT == EQ)",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
10.02/3.99	12[label="compare2 LT GT (LT == GT)",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
10.02/3.99	13[label="compare2 EQ LT (EQ == LT)",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
10.02/3.99	14[label="compare2 EQ EQ (EQ == EQ)",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
10.02/3.99	15[label="compare2 EQ GT (EQ == GT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
10.02/3.99	16[label="compare2 GT LT (GT == LT)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
10.02/3.99	17[label="compare2 GT EQ (GT == EQ)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
10.02/3.99	18[label="compare2 GT GT (GT == GT)",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
10.02/3.99	19[label="compare2 LT LT True",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
10.02/3.99	20[label="compare2 LT EQ False",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
10.02/3.99	21[label="compare2 LT GT False",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
10.02/3.99	22[label="compare2 EQ LT False",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
10.02/3.99	23[label="compare2 EQ EQ True",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
10.02/3.99	24[label="compare2 EQ GT False",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
10.02/3.99	25[label="compare2 GT LT False",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
10.02/3.99	26[label="compare2 GT EQ False",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
10.02/3.99	27[label="compare2 GT GT True",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
10.02/3.99	28[label="EQ",fontsize=16,color="green",shape="box"];29[label="compare1 LT EQ (LT <= EQ)",fontsize=16,color="black",shape="box"];29 -> 37[label="",style="solid", color="black", weight=3];
10.02/3.99	30[label="compare1 LT GT (LT <= GT)",fontsize=16,color="black",shape="box"];30 -> 38[label="",style="solid", color="black", weight=3];
10.02/3.99	31[label="compare1 EQ LT (EQ <= LT)",fontsize=16,color="black",shape="box"];31 -> 39[label="",style="solid", color="black", weight=3];
10.02/3.99	32[label="EQ",fontsize=16,color="green",shape="box"];33[label="compare1 EQ GT (EQ <= GT)",fontsize=16,color="black",shape="box"];33 -> 40[label="",style="solid", color="black", weight=3];
10.02/3.99	34[label="compare1 GT LT (GT <= LT)",fontsize=16,color="black",shape="box"];34 -> 41[label="",style="solid", color="black", weight=3];
10.02/3.99	35[label="compare1 GT EQ (GT <= EQ)",fontsize=16,color="black",shape="box"];35 -> 42[label="",style="solid", color="black", weight=3];
10.02/3.99	36[label="EQ",fontsize=16,color="green",shape="box"];37[label="compare1 LT EQ True",fontsize=16,color="black",shape="box"];37 -> 43[label="",style="solid", color="black", weight=3];
10.02/3.99	38[label="compare1 LT GT True",fontsize=16,color="black",shape="box"];38 -> 44[label="",style="solid", color="black", weight=3];
10.02/3.99	39[label="compare1 EQ LT False",fontsize=16,color="black",shape="box"];39 -> 45[label="",style="solid", color="black", weight=3];
10.02/3.99	40[label="compare1 EQ GT True",fontsize=16,color="black",shape="box"];40 -> 46[label="",style="solid", color="black", weight=3];
10.02/3.99	41[label="compare1 GT LT False",fontsize=16,color="black",shape="box"];41 -> 47[label="",style="solid", color="black", weight=3];
10.02/3.99	42[label="compare1 GT EQ False",fontsize=16,color="black",shape="box"];42 -> 48[label="",style="solid", color="black", weight=3];
10.02/3.99	43[label="LT",fontsize=16,color="green",shape="box"];44[label="LT",fontsize=16,color="green",shape="box"];45[label="compare0 EQ LT otherwise",fontsize=16,color="black",shape="box"];45 -> 49[label="",style="solid", color="black", weight=3];
10.02/3.99	46[label="LT",fontsize=16,color="green",shape="box"];47[label="compare0 GT LT otherwise",fontsize=16,color="black",shape="box"];47 -> 50[label="",style="solid", color="black", weight=3];
10.02/3.99	48[label="compare0 GT EQ otherwise",fontsize=16,color="black",shape="box"];48 -> 51[label="",style="solid", color="black", weight=3];
10.02/3.99	49[label="compare0 EQ LT True",fontsize=16,color="black",shape="box"];49 -> 52[label="",style="solid", color="black", weight=3];
10.02/3.99	50[label="compare0 GT LT True",fontsize=16,color="black",shape="box"];50 -> 53[label="",style="solid", color="black", weight=3];
10.02/3.99	51[label="compare0 GT EQ True",fontsize=16,color="black",shape="box"];51 -> 54[label="",style="solid", color="black", weight=3];
10.02/3.99	52[label="GT",fontsize=16,color="green",shape="box"];53[label="GT",fontsize=16,color="green",shape="box"];54[label="GT",fontsize=16,color="green",shape="box"];}
10.02/3.99	
10.02/3.99	----------------------------------------
10.02/3.99	
10.02/3.99	(6)
10.02/3.99	YES
10.18/4.05	EOF