8.14/3.50	YES
9.61/3.96	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.61/3.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.61/3.96	
9.61/3.96	
9.61/3.96	H-Termination with start terms of the given HASKELL could be proven:
9.61/3.96	
9.61/3.96	(0) HASKELL
9.61/3.96	(1) BR [EQUIVALENT, 0 ms]
9.61/3.96	(2) HASKELL
9.61/3.96	(3) COR [EQUIVALENT, 0 ms]
9.61/3.96	(4) HASKELL
9.61/3.96	(5) Narrow [EQUIVALENT, 20 ms]
9.61/3.96	(6) YES
9.61/3.96	
9.61/3.96	
9.61/3.96	----------------------------------------
9.61/3.96	
9.61/3.96	(0)
9.61/3.96	Obligation:
9.61/3.96	mainModule Main 
9.61/3.96	module Main where {
9.61/3.96	import qualified Prelude;
9.61/3.96	}
9.61/3.96	
9.61/3.96	----------------------------------------
9.61/3.96	
9.61/3.96	(1) BR (EQUIVALENT)
9.61/3.96	Replaced joker patterns by fresh variables and removed binding patterns.
9.61/3.96	----------------------------------------
9.61/3.96	
9.61/3.96	(2)
9.61/3.96	Obligation:
9.61/3.96	mainModule Main 
9.61/3.96	module Main where {
9.61/3.96	import qualified Prelude;
9.61/3.96	}
9.61/3.96	
9.61/3.96	----------------------------------------
9.61/3.96	
9.61/3.96	(3) COR (EQUIVALENT)
9.61/3.96	Cond Reductions:
9.61/3.96	The following Function with conditions
9.61/3.96	"undefined |Falseundefined;
9.61/3.96	"
9.61/3.96	is transformed to
9.61/3.96	"undefined  = undefined1;
9.61/3.96	"
9.61/3.96	"undefined0 True = undefined;
9.61/3.96	"
9.61/3.96	"undefined1  = undefined0 False;
9.61/3.96	"
9.61/3.96	
9.61/3.96	----------------------------------------
9.61/3.96	
9.61/3.96	(4)
9.61/3.96	Obligation:
9.61/3.96	mainModule Main 
9.61/3.96	module Main where {
9.61/3.96	import qualified Prelude;
9.61/3.96	}
9.61/3.96	
9.61/3.96	----------------------------------------
9.61/3.96	
9.61/3.96	(5) Narrow (EQUIVALENT)
9.61/3.96	Haskell To QDPs
9.61/3.96	
9.61/3.96	digraph dp_graph {
9.61/3.96	node [outthreshold=100, inthreshold=100];1[label="(/=)",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.61/3.96	3[label="(/=) vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.61/3.96	4[label="(/=) vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.61/3.96	5[label="not (vx3 == vx4)",fontsize=16,color="burlywood",shape="box"];29[label="vx3/LT",fontsize=10,color="white",style="solid",shape="box"];5 -> 29[label="",style="solid", color="burlywood", weight=9];
9.61/3.96	29 -> 6[label="",style="solid", color="burlywood", weight=3];
9.61/3.96	30[label="vx3/EQ",fontsize=10,color="white",style="solid",shape="box"];5 -> 30[label="",style="solid", color="burlywood", weight=9];
9.61/3.96	30 -> 7[label="",style="solid", color="burlywood", weight=3];
9.61/3.96	31[label="vx3/GT",fontsize=10,color="white",style="solid",shape="box"];5 -> 31[label="",style="solid", color="burlywood", weight=9];
9.61/3.96	31 -> 8[label="",style="solid", color="burlywood", weight=3];
9.61/3.96	6[label="not (LT == vx4)",fontsize=16,color="burlywood",shape="box"];32[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];6 -> 32[label="",style="solid", color="burlywood", weight=9];
9.61/3.96	32 -> 9[label="",style="solid", color="burlywood", weight=3];
9.61/3.96	33[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];6 -> 33[label="",style="solid", color="burlywood", weight=9];
9.61/3.96	33 -> 10[label="",style="solid", color="burlywood", weight=3];
9.61/3.96	34[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];6 -> 34[label="",style="solid", color="burlywood", weight=9];
9.61/3.96	34 -> 11[label="",style="solid", color="burlywood", weight=3];
9.61/3.96	7[label="not (EQ == vx4)",fontsize=16,color="burlywood",shape="box"];35[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];7 -> 35[label="",style="solid", color="burlywood", weight=9];
9.61/3.96	35 -> 12[label="",style="solid", color="burlywood", weight=3];
9.61/3.96	36[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];7 -> 36[label="",style="solid", color="burlywood", weight=9];
9.61/3.96	36 -> 13[label="",style="solid", color="burlywood", weight=3];
9.61/3.96	37[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];7 -> 37[label="",style="solid", color="burlywood", weight=9];
9.61/3.96	37 -> 14[label="",style="solid", color="burlywood", weight=3];
9.61/3.96	8[label="not (GT == vx4)",fontsize=16,color="burlywood",shape="box"];38[label="vx4/LT",fontsize=10,color="white",style="solid",shape="box"];8 -> 38[label="",style="solid", color="burlywood", weight=9];
9.61/3.96	38 -> 15[label="",style="solid", color="burlywood", weight=3];
9.61/3.96	39[label="vx4/EQ",fontsize=10,color="white",style="solid",shape="box"];8 -> 39[label="",style="solid", color="burlywood", weight=9];
9.61/3.96	39 -> 16[label="",style="solid", color="burlywood", weight=3];
9.61/3.96	40[label="vx4/GT",fontsize=10,color="white",style="solid",shape="box"];8 -> 40[label="",style="solid", color="burlywood", weight=9];
9.61/3.96	40 -> 17[label="",style="solid", color="burlywood", weight=3];
9.61/3.96	9[label="not (LT == LT)",fontsize=16,color="black",shape="box"];9 -> 18[label="",style="solid", color="black", weight=3];
9.61/3.96	10[label="not (LT == EQ)",fontsize=16,color="black",shape="box"];10 -> 19[label="",style="solid", color="black", weight=3];
9.61/3.96	11[label="not (LT == GT)",fontsize=16,color="black",shape="box"];11 -> 20[label="",style="solid", color="black", weight=3];
9.61/3.96	12[label="not (EQ == LT)",fontsize=16,color="black",shape="box"];12 -> 21[label="",style="solid", color="black", weight=3];
9.61/3.96	13[label="not (EQ == EQ)",fontsize=16,color="black",shape="box"];13 -> 22[label="",style="solid", color="black", weight=3];
9.61/3.96	14[label="not (EQ == GT)",fontsize=16,color="black",shape="box"];14 -> 23[label="",style="solid", color="black", weight=3];
9.61/3.96	15[label="not (GT == LT)",fontsize=16,color="black",shape="box"];15 -> 24[label="",style="solid", color="black", weight=3];
9.61/3.96	16[label="not (GT == EQ)",fontsize=16,color="black",shape="box"];16 -> 25[label="",style="solid", color="black", weight=3];
9.61/3.96	17[label="not (GT == GT)",fontsize=16,color="black",shape="box"];17 -> 26[label="",style="solid", color="black", weight=3];
9.61/3.96	18[label="not True",fontsize=16,color="black",shape="triangle"];18 -> 27[label="",style="solid", color="black", weight=3];
9.61/3.96	19[label="not False",fontsize=16,color="black",shape="triangle"];19 -> 28[label="",style="solid", color="black", weight=3];
9.61/3.96	20 -> 19[label="",style="dashed", color="red", weight=0];
9.61/3.96	20[label="not False",fontsize=16,color="magenta"];21 -> 19[label="",style="dashed", color="red", weight=0];
9.61/3.96	21[label="not False",fontsize=16,color="magenta"];22 -> 18[label="",style="dashed", color="red", weight=0];
9.61/3.96	22[label="not True",fontsize=16,color="magenta"];23 -> 19[label="",style="dashed", color="red", weight=0];
9.61/3.96	23[label="not False",fontsize=16,color="magenta"];24 -> 19[label="",style="dashed", color="red", weight=0];
9.61/3.96	24[label="not False",fontsize=16,color="magenta"];25 -> 19[label="",style="dashed", color="red", weight=0];
9.61/3.96	25[label="not False",fontsize=16,color="magenta"];26 -> 18[label="",style="dashed", color="red", weight=0];
9.61/3.96	26[label="not True",fontsize=16,color="magenta"];27[label="False",fontsize=16,color="green",shape="box"];28[label="True",fontsize=16,color="green",shape="box"];}
9.61/3.96	
9.61/3.96	----------------------------------------
9.61/3.96	
9.61/3.96	(6)
9.61/3.96	YES
9.61/4.00	EOF