7.93/3.49	YES
9.51/3.93	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.51/3.93	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.51/3.93	
9.51/3.93	
9.51/3.93	H-Termination with start terms of the given HASKELL could be proven:
9.51/3.93	
9.51/3.93	(0) HASKELL
9.51/3.93	(1) BR [EQUIVALENT, 0 ms]
9.51/3.93	(2) HASKELL
9.51/3.93	(3) COR [EQUIVALENT, 0 ms]
9.51/3.93	(4) HASKELL
9.51/3.93	(5) Narrow [EQUIVALENT, 15 ms]
9.51/3.93	(6) YES
9.51/3.93	
9.51/3.93	
9.51/3.93	----------------------------------------
9.51/3.93	
9.51/3.93	(0)
9.51/3.93	Obligation:
9.51/3.93	mainModule Main 
9.51/3.93	module Main where {
9.51/3.93	import qualified Prelude;
9.51/3.93	}
9.51/3.93	
9.51/3.93	----------------------------------------
9.51/3.93	
9.51/3.93	(1) BR (EQUIVALENT)
9.51/3.93	Replaced joker patterns by fresh variables and removed binding patterns.
9.51/3.93	----------------------------------------
9.51/3.93	
9.51/3.93	(2)
9.51/3.93	Obligation:
9.51/3.93	mainModule Main 
9.51/3.93	module Main where {
9.51/3.93	import qualified Prelude;
9.51/3.93	}
9.51/3.93	
9.51/3.93	----------------------------------------
9.51/3.93	
9.51/3.93	(3) COR (EQUIVALENT)
9.51/3.93	Cond Reductions:
9.51/3.93	The following Function with conditions
9.51/3.93	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
9.51/3.93	"
9.51/3.93	is transformed to
9.51/3.93	"compare x y = compare3 x y;
9.51/3.93	"
9.51/3.93	"compare2 x y True = EQ;
9.51/3.93	compare2 x y False = compare1 x y (x <= y);
9.51/3.93	"
9.51/3.93	"compare0 x y True = GT;
9.51/3.93	"
9.51/3.93	"compare1 x y True = LT;
9.51/3.93	compare1 x y False = compare0 x y otherwise;
9.51/3.93	"
9.51/3.93	"compare3 x y = compare2 x y (x == y);
9.51/3.93	"
9.51/3.93	The following Function with conditions
9.51/3.93	"undefined |Falseundefined;
9.51/3.93	"
9.51/3.93	is transformed to
9.51/3.93	"undefined  = undefined1;
9.51/3.93	"
9.51/3.93	"undefined0 True = undefined;
9.51/3.93	"
9.51/3.93	"undefined1  = undefined0 False;
9.51/3.93	"
9.51/3.93	
9.51/3.93	----------------------------------------
9.51/3.93	
9.51/3.93	(4)
9.51/3.93	Obligation:
9.51/3.93	mainModule Main 
9.51/3.93	module Main where {
9.51/3.93	import qualified Prelude;
9.51/3.93	}
9.51/3.93	
9.51/3.93	----------------------------------------
9.51/3.93	
9.51/3.93	(5) Narrow (EQUIVALENT)
9.51/3.93	Haskell To QDPs
9.51/3.93	
9.51/3.93	digraph dp_graph {
9.51/3.93	node [outthreshold=100, inthreshold=100];1[label="(>=)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.51/3.93	3[label="(>=) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.51/3.93	4[label="(>=) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.51/3.93	5[label="compare vx3 vx4 /= LT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.51/3.93	6[label="not (compare vx3 vx4 == LT)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.51/3.93	7[label="not (compare3 vx3 vx4 == LT)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.51/3.93	8[label="not (compare2 vx3 vx4 (vx3 == vx4) == LT)",fontsize=16,color="burlywood",shape="box"];62[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];8 -> 62[label="",style="solid", color="burlywood", weight=9];
9.51/3.93	62 -> 9[label="",style="solid", color="burlywood", weight=3];
9.51/3.93	63[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 63[label="",style="solid", color="burlywood", weight=9];
9.51/3.93	63 -> 10[label="",style="solid", color="burlywood", weight=3];
9.51/3.93	64[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 64[label="",style="solid", color="burlywood", weight=9];
9.51/3.93	64 -> 11[label="",style="solid", color="burlywood", weight=3];
9.51/3.93	9[label="not (compare2 LT vx4 (LT == vx4) == LT)",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];
9.51/3.93	65 -> 12[label="",style="solid", color="burlywood", weight=3];
9.51/3.93	66[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];9 -> 66[label="",style="solid", color="burlywood", weight=9];
9.51/3.93	66 -> 13[label="",style="solid", color="burlywood", weight=3];
9.51/3.93	67[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];9 -> 67[label="",style="solid", color="burlywood", weight=9];
9.51/3.93	67 -> 14[label="",style="solid", color="burlywood", weight=3];
9.51/3.93	10[label="not (compare2 EQ vx4 (EQ == vx4) == LT)",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];
9.51/3.93	68 -> 15[label="",style="solid", color="burlywood", weight=3];
9.51/3.93	69[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];10 -> 69[label="",style="solid", color="burlywood", weight=9];
9.51/3.93	69 -> 16[label="",style="solid", color="burlywood", weight=3];
9.51/3.93	70[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];10 -> 70[label="",style="solid", color="burlywood", weight=9];
9.51/3.93	70 -> 17[label="",style="solid", color="burlywood", weight=3];
9.51/3.93	11[label="not (compare2 GT vx4 (GT == vx4) == LT)",fontsize=16,color="burlywood",shape="box"];71[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];11 -> 71[label="",style="solid", color="burlywood", weight=9];
9.51/3.93	71 -> 18[label="",style="solid", color="burlywood", weight=3];
9.51/3.93	72[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];11 -> 72[label="",style="solid", color="burlywood", weight=9];
9.51/3.93	72 -> 19[label="",style="solid", color="burlywood", weight=3];
9.51/3.93	73[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];11 -> 73[label="",style="solid", color="burlywood", weight=9];
9.51/3.93	73 -> 20[label="",style="solid", color="burlywood", weight=3];
9.51/3.93	12[label="not (compare2 LT LT (LT == LT) == LT)",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
9.51/3.93	13[label="not (compare2 LT EQ (LT == EQ) == LT)",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
9.51/3.93	14[label="not (compare2 LT GT (LT == GT) == LT)",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.51/3.93	15[label="not (compare2 EQ LT (EQ == LT) == LT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
9.51/3.93	16[label="not (compare2 EQ EQ (EQ == EQ) == LT)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.51/3.93	17[label="not (compare2 EQ GT (EQ == GT) == LT)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
9.51/3.93	18[label="not (compare2 GT LT (GT == LT) == LT)",fontsize=16,color="black",shape="box"];18 -> 27[label="",style="solid", color="black", weight=3];
9.51/3.93	19[label="not (compare2 GT EQ (GT == EQ) == LT)",fontsize=16,color="black",shape="box"];19 -> 28[label="",style="solid", color="black", weight=3];
9.51/3.93	20[label="not (compare2 GT GT (GT == GT) == LT)",fontsize=16,color="black",shape="box"];20 -> 29[label="",style="solid", color="black", weight=3];
9.51/3.93	21[label="not (compare2 LT LT True == LT)",fontsize=16,color="black",shape="box"];21 -> 30[label="",style="solid", color="black", weight=3];
9.51/3.93	22[label="not (compare2 LT EQ False == LT)",fontsize=16,color="black",shape="box"];22 -> 31[label="",style="solid", color="black", weight=3];
9.51/3.93	23[label="not (compare2 LT GT False == LT)",fontsize=16,color="black",shape="box"];23 -> 32[label="",style="solid", color="black", weight=3];
9.51/3.93	24[label="not (compare2 EQ LT False == LT)",fontsize=16,color="black",shape="box"];24 -> 33[label="",style="solid", color="black", weight=3];
9.51/3.93	25[label="not (compare2 EQ EQ True == LT)",fontsize=16,color="black",shape="box"];25 -> 34[label="",style="solid", color="black", weight=3];
9.51/3.93	26[label="not (compare2 EQ GT False == LT)",fontsize=16,color="black",shape="box"];26 -> 35[label="",style="solid", color="black", weight=3];
9.51/3.93	27[label="not (compare2 GT LT False == LT)",fontsize=16,color="black",shape="box"];27 -> 36[label="",style="solid", color="black", weight=3];
9.51/3.93	28[label="not (compare2 GT EQ False == LT)",fontsize=16,color="black",shape="box"];28 -> 37[label="",style="solid", color="black", weight=3];
9.51/3.93	29[label="not (compare2 GT GT True == LT)",fontsize=16,color="black",shape="box"];29 -> 38[label="",style="solid", color="black", weight=3];
9.51/3.93	30[label="not (EQ == LT)",fontsize=16,color="black",shape="triangle"];30 -> 39[label="",style="solid", color="black", weight=3];
9.51/3.93	31[label="not (compare1 LT EQ (LT <= EQ) == LT)",fontsize=16,color="black",shape="box"];31 -> 40[label="",style="solid", color="black", weight=3];
9.51/3.93	32[label="not (compare1 LT GT (LT <= GT) == LT)",fontsize=16,color="black",shape="box"];32 -> 41[label="",style="solid", color="black", weight=3];
9.51/3.93	33[label="not (compare1 EQ LT (EQ <= LT) == LT)",fontsize=16,color="black",shape="box"];33 -> 42[label="",style="solid", color="black", weight=3];
9.51/3.93	34 -> 30[label="",style="dashed", color="red", weight=0];
9.51/3.93	34[label="not (EQ == LT)",fontsize=16,color="magenta"];35[label="not (compare1 EQ GT (EQ <= GT) == LT)",fontsize=16,color="black",shape="box"];35 -> 43[label="",style="solid", color="black", weight=3];
9.51/3.93	36[label="not (compare1 GT LT (GT <= LT) == LT)",fontsize=16,color="black",shape="box"];36 -> 44[label="",style="solid", color="black", weight=3];
9.51/3.93	37[label="not (compare1 GT EQ (GT <= EQ) == LT)",fontsize=16,color="black",shape="box"];37 -> 45[label="",style="solid", color="black", weight=3];
9.51/3.93	38 -> 30[label="",style="dashed", color="red", weight=0];
9.51/3.93	38[label="not (EQ == LT)",fontsize=16,color="magenta"];39[label="not False",fontsize=16,color="black",shape="triangle"];39 -> 46[label="",style="solid", color="black", weight=3];
9.51/3.93	40[label="not (compare1 LT EQ True == LT)",fontsize=16,color="black",shape="box"];40 -> 47[label="",style="solid", color="black", weight=3];
9.51/3.93	41[label="not (compare1 LT GT True == LT)",fontsize=16,color="black",shape="box"];41 -> 48[label="",style="solid", color="black", weight=3];
9.51/3.93	42[label="not (compare1 EQ LT False == LT)",fontsize=16,color="black",shape="box"];42 -> 49[label="",style="solid", color="black", weight=3];
9.51/3.93	43[label="not (compare1 EQ GT True == LT)",fontsize=16,color="black",shape="box"];43 -> 50[label="",style="solid", color="black", weight=3];
9.51/3.93	44[label="not (compare1 GT LT False == LT)",fontsize=16,color="black",shape="box"];44 -> 51[label="",style="solid", color="black", weight=3];
9.51/3.93	45[label="not (compare1 GT EQ False == LT)",fontsize=16,color="black",shape="box"];45 -> 52[label="",style="solid", color="black", weight=3];
9.51/3.93	46[label="True",fontsize=16,color="green",shape="box"];47[label="not (LT == LT)",fontsize=16,color="black",shape="triangle"];47 -> 53[label="",style="solid", color="black", weight=3];
9.51/3.93	48 -> 47[label="",style="dashed", color="red", weight=0];
9.51/3.93	48[label="not (LT == LT)",fontsize=16,color="magenta"];49[label="not (compare0 EQ LT otherwise == LT)",fontsize=16,color="black",shape="box"];49 -> 54[label="",style="solid", color="black", weight=3];
9.51/3.93	50 -> 47[label="",style="dashed", color="red", weight=0];
9.51/3.93	50[label="not (LT == LT)",fontsize=16,color="magenta"];51[label="not (compare0 GT LT otherwise == LT)",fontsize=16,color="black",shape="box"];51 -> 55[label="",style="solid", color="black", weight=3];
9.51/3.93	52[label="not (compare0 GT EQ otherwise == LT)",fontsize=16,color="black",shape="box"];52 -> 56[label="",style="solid", color="black", weight=3];
9.51/3.93	53[label="not True",fontsize=16,color="black",shape="box"];53 -> 57[label="",style="solid", color="black", weight=3];
9.51/3.93	54[label="not (compare0 EQ LT True == LT)",fontsize=16,color="black",shape="box"];54 -> 58[label="",style="solid", color="black", weight=3];
9.51/3.93	55[label="not (compare0 GT LT True == LT)",fontsize=16,color="black",shape="box"];55 -> 59[label="",style="solid", color="black", weight=3];
9.51/3.93	56[label="not (compare0 GT EQ True == LT)",fontsize=16,color="black",shape="box"];56 -> 60[label="",style="solid", color="black", weight=3];
9.51/3.93	57[label="False",fontsize=16,color="green",shape="box"];58[label="not (GT == LT)",fontsize=16,color="black",shape="triangle"];58 -> 61[label="",style="solid", color="black", weight=3];
9.51/3.93	59 -> 58[label="",style="dashed", color="red", weight=0];
9.51/3.93	59[label="not (GT == LT)",fontsize=16,color="magenta"];60 -> 58[label="",style="dashed", color="red", weight=0];
9.51/3.93	60[label="not (GT == LT)",fontsize=16,color="magenta"];61 -> 39[label="",style="dashed", color="red", weight=0];
9.51/3.93	61[label="not False",fontsize=16,color="magenta"];}
9.51/3.93	
9.51/3.93	----------------------------------------
9.51/3.93	
9.51/3.93	(6)
9.51/3.93	YES
9.57/3.97	EOF