8.33/3.62	YES
10.11/4.10	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.11/4.10	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.11/4.10	
10.11/4.10	
10.11/4.10	H-Termination with start terms of the given HASKELL could be proven:
10.11/4.10	
10.11/4.10	(0) HASKELL
10.11/4.10	(1) BR [EQUIVALENT, 0 ms]
10.11/4.10	(2) HASKELL
10.11/4.10	(3) COR [EQUIVALENT, 0 ms]
10.11/4.10	(4) HASKELL
10.11/4.10	(5) Narrow [EQUIVALENT, 5 ms]
10.11/4.10	(6) YES
10.11/4.10	
10.11/4.10	
10.11/4.10	----------------------------------------
10.11/4.10	
10.11/4.10	(0)
10.11/4.10	Obligation:
10.11/4.10	mainModule Main 
10.11/4.10	module Main where {
10.11/4.10	import qualified Prelude;
10.11/4.10	}
10.11/4.10	
10.11/4.10	----------------------------------------
10.11/4.10	
10.11/4.10	(1) BR (EQUIVALENT)
10.11/4.10	Replaced joker patterns by fresh variables and removed binding patterns.
10.11/4.10	----------------------------------------
10.11/4.10	
10.11/4.10	(2)
10.11/4.10	Obligation:
10.11/4.10	mainModule Main 
10.11/4.10	module Main where {
10.11/4.10	import qualified Prelude;
10.11/4.10	}
10.11/4.10	
10.11/4.10	----------------------------------------
10.11/4.10	
10.11/4.10	(3) COR (EQUIVALENT)
10.11/4.10	Cond Reductions:
10.11/4.10	The following Function with conditions
10.11/4.10	"compare x y|x == yEQ|x <= yLT|otherwiseGT;
10.11/4.10	"
10.11/4.10	is transformed to
10.11/4.10	"compare x y = compare3 x y;
10.11/4.10	"
10.11/4.10	"compare1 x y True = LT;
10.11/4.10	compare1 x y False = compare0 x y otherwise;
10.11/4.10	"
10.11/4.10	"compare2 x y True = EQ;
10.11/4.10	compare2 x y False = compare1 x y (x <= y);
10.11/4.10	"
10.11/4.10	"compare0 x y True = GT;
10.11/4.10	"
10.11/4.10	"compare3 x y = compare2 x y (x == y);
10.11/4.10	"
10.11/4.10	The following Function with conditions
10.11/4.10	"undefined |Falseundefined;
10.11/4.10	"
10.11/4.10	is transformed to
10.11/4.10	"undefined  = undefined1;
10.11/4.10	"
10.11/4.10	"undefined0 True = undefined;
10.11/4.10	"
10.11/4.10	"undefined1  = undefined0 False;
10.11/4.10	"
10.11/4.10	
10.11/4.10	----------------------------------------
10.11/4.10	
10.11/4.10	(4)
10.11/4.10	Obligation:
10.11/4.10	mainModule Main 
10.11/4.10	module Main where {
10.11/4.10	import qualified Prelude;
10.11/4.10	}
10.11/4.10	
10.11/4.10	----------------------------------------
10.11/4.10	
10.11/4.10	(5) Narrow (EQUIVALENT)
10.11/4.10	Haskell To QDPs
10.11/4.10	
10.11/4.10	digraph dp_graph {
10.11/4.10	node [outthreshold=100, inthreshold=100];1[label="(>=)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.11/4.10	3[label="(>=) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.11/4.10	4[label="(>=) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
10.11/4.10	5[label="compare vx3 vx4 /= LT",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
10.11/4.10	6[label="not (compare vx3 vx4 == LT)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
10.11/4.10	7[label="not (compare3 vx3 vx4 == LT)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
10.11/4.10	8[label="not (compare2 vx3 vx4 (vx3 == vx4) == LT)",fontsize=16,color="burlywood",shape="box"];34[label="vx3/False",fontsize=10,color="white",style="solid",shape="box"];8 -> 34[label="",style="solid", color="burlywood", weight=9];
10.11/4.10	34 -> 9[label="",style="solid", color="burlywood", weight=3];
10.11/4.10	35[label="vx3/True",fontsize=10,color="white",style="solid",shape="box"];8 -> 35[label="",style="solid", color="burlywood", weight=9];
10.11/4.10	35 -> 10[label="",style="solid", color="burlywood", weight=3];
10.11/4.10	9[label="not (compare2 False vx4 (False == vx4) == LT)",fontsize=16,color="burlywood",shape="box"];36[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];9 -> 36[label="",style="solid", color="burlywood", weight=9];
10.11/4.10	36 -> 11[label="",style="solid", color="burlywood", weight=3];
10.11/4.10	37[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];9 -> 37[label="",style="solid", color="burlywood", weight=9];
10.11/4.10	37 -> 12[label="",style="solid", color="burlywood", weight=3];
10.11/4.10	10[label="not (compare2 True vx4 (True == vx4) == LT)",fontsize=16,color="burlywood",shape="box"];38[label="vx4/False",fontsize=10,color="white",style="solid",shape="box"];10 -> 38[label="",style="solid", color="burlywood", weight=9];
10.11/4.10	38 -> 13[label="",style="solid", color="burlywood", weight=3];
10.11/4.10	39[label="vx4/True",fontsize=10,color="white",style="solid",shape="box"];10 -> 39[label="",style="solid", color="burlywood", weight=9];
10.11/4.10	39 -> 14[label="",style="solid", color="burlywood", weight=3];
10.11/4.10	11[label="not (compare2 False False (False == False) == LT)",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
10.11/4.10	12[label="not (compare2 False True (False == True) == LT)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
10.11/4.10	13[label="not (compare2 True False (True == False) == LT)",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
10.11/4.10	14[label="not (compare2 True True (True == True) == LT)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
10.11/4.10	15[label="not (compare2 False False True == LT)",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
10.11/4.10	16[label="not (compare2 False True False == LT)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
10.11/4.10	17[label="not (compare2 True False False == LT)",fontsize=16,color="black",shape="box"];17 -> 21[label="",style="solid", color="black", weight=3];
10.11/4.10	18[label="not (compare2 True True True == LT)",fontsize=16,color="black",shape="box"];18 -> 22[label="",style="solid", color="black", weight=3];
10.11/4.10	19[label="not (EQ == LT)",fontsize=16,color="black",shape="triangle"];19 -> 23[label="",style="solid", color="black", weight=3];
10.11/4.10	20[label="not (compare1 False True (False <= True) == LT)",fontsize=16,color="black",shape="box"];20 -> 24[label="",style="solid", color="black", weight=3];
10.11/4.10	21[label="not (compare1 True False (True <= False) == LT)",fontsize=16,color="black",shape="box"];21 -> 25[label="",style="solid", color="black", weight=3];
10.11/4.10	22 -> 19[label="",style="dashed", color="red", weight=0];
10.11/4.10	22[label="not (EQ == LT)",fontsize=16,color="magenta"];23[label="not False",fontsize=16,color="black",shape="triangle"];23 -> 26[label="",style="solid", color="black", weight=3];
10.11/4.10	24[label="not (compare1 False True True == LT)",fontsize=16,color="black",shape="box"];24 -> 27[label="",style="solid", color="black", weight=3];
10.11/4.10	25[label="not (compare1 True False False == LT)",fontsize=16,color="black",shape="box"];25 -> 28[label="",style="solid", color="black", weight=3];
10.11/4.10	26[label="True",fontsize=16,color="green",shape="box"];27[label="not (LT == LT)",fontsize=16,color="black",shape="box"];27 -> 29[label="",style="solid", color="black", weight=3];
10.11/4.10	28[label="not (compare0 True False otherwise == LT)",fontsize=16,color="black",shape="box"];28 -> 30[label="",style="solid", color="black", weight=3];
10.11/4.10	29[label="not True",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3];
10.11/4.10	30[label="not (compare0 True False True == LT)",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3];
10.11/4.10	31[label="False",fontsize=16,color="green",shape="box"];32[label="not (GT == LT)",fontsize=16,color="black",shape="box"];32 -> 33[label="",style="solid", color="black", weight=3];
10.11/4.10	33 -> 23[label="",style="dashed", color="red", weight=0];
10.11/4.10	33[label="not False",fontsize=16,color="magenta"];}
10.11/4.10	
10.11/4.10	----------------------------------------
10.11/4.10	
10.11/4.10	(6)
10.11/4.10	YES
10.17/4.14	EOF