7.90/3.56	YES
9.45/4.04	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.45/4.04	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.45/4.04	
9.45/4.04	
9.45/4.04	H-Termination with start terms of the given HASKELL could be proven:
9.45/4.04	
9.45/4.04	(0) HASKELL
9.45/4.04	(1) BR [EQUIVALENT, 0 ms]
9.45/4.04	(2) HASKELL
9.45/4.04	(3) COR [EQUIVALENT, 0 ms]
9.45/4.04	(4) HASKELL
9.45/4.04	(5) Narrow [EQUIVALENT, 11 ms]
9.45/4.04	(6) YES
9.45/4.04	
9.45/4.04	
9.45/4.04	----------------------------------------
9.45/4.04	
9.45/4.04	(0)
9.45/4.04	Obligation:
9.45/4.04	mainModule Main 
9.45/4.04	module Main where {
9.45/4.04	import qualified Prelude;
9.45/4.04	}
9.45/4.04	
9.45/4.04	----------------------------------------
9.45/4.04	
9.45/4.04	(1) BR (EQUIVALENT)
9.45/4.04	Replaced joker patterns by fresh variables and removed binding patterns.
9.45/4.04	----------------------------------------
9.45/4.04	
9.45/4.04	(2)
9.45/4.04	Obligation:
9.45/4.04	mainModule Main 
9.45/4.04	module Main where {
9.45/4.04	import qualified Prelude;
9.45/4.04	}
9.45/4.04	
9.45/4.04	----------------------------------------
9.45/4.04	
9.45/4.04	(3) COR (EQUIVALENT)
9.45/4.04	Cond Reductions:
9.45/4.04	The following Function with conditions
9.45/4.04	"min x y|x <= yx|otherwisey;
9.45/4.04	"
9.45/4.04	is transformed to
9.45/4.04	"min x y = min2 x y;
9.45/4.04	"
9.45/4.04	"min0 x y True = y;
9.45/4.04	"
9.45/4.04	"min1 x y True = x;
9.45/4.04	min1 x y False = min0 x y otherwise;
9.45/4.04	"
9.45/4.04	"min2 x y = min1 x y (x <= y);
9.45/4.04	"
9.45/4.04	The following Function with conditions
9.45/4.04	"undefined |Falseundefined;
9.45/4.04	"
9.45/4.04	is transformed to
9.45/4.04	"undefined  = undefined1;
9.45/4.04	"
9.45/4.04	"undefined0 True = undefined;
9.45/4.04	"
9.45/4.04	"undefined1  = undefined0 False;
9.45/4.04	"
9.45/4.04	
9.45/4.04	----------------------------------------
9.45/4.04	
9.45/4.04	(4)
9.45/4.04	Obligation:
9.45/4.04	mainModule Main 
9.45/4.04	module Main where {
9.45/4.04	import qualified Prelude;
9.45/4.04	}
9.45/4.04	
9.45/4.04	----------------------------------------
9.45/4.04	
9.45/4.04	(5) Narrow (EQUIVALENT)
9.45/4.04	Haskell To QDPs
9.45/4.04	
9.45/4.04	digraph dp_graph {
9.45/4.04	node [outthreshold=100, inthreshold=100];1[label="min",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.45/4.04	3[label="min vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.45/4.04	4[label="min vx3 vx4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.45/4.04	5[label="min2 vx3 vx4",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.45/4.04	6[label="min1 vx3 vx4 (vx3 <= vx4)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.45/4.04	7[label="min1 vx3 vx4 (compare vx3 vx4 /= GT)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.45/4.04	8[label="min1 vx3 vx4 (not (compare vx3 vx4 == GT))",fontsize=16,color="burlywood",shape="box"];15[label="vx3/()",fontsize=10,color="white",style="solid",shape="box"];8 -> 15[label="",style="solid", color="burlywood", weight=9];
9.45/4.04	15 -> 9[label="",style="solid", color="burlywood", weight=3];
9.45/4.04	9[label="min1 () vx4 (not (compare () vx4 == GT))",fontsize=16,color="burlywood",shape="box"];16[label="vx4/()",fontsize=10,color="white",style="solid",shape="box"];9 -> 16[label="",style="solid", color="burlywood", weight=9];
9.45/4.04	16 -> 10[label="",style="solid", color="burlywood", weight=3];
9.45/4.04	10[label="min1 () () (not (compare () () == GT))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
9.45/4.04	11[label="min1 () () (not (EQ == GT))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
9.45/4.04	12[label="min1 () () (not False)",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
9.45/4.04	13[label="min1 () () True",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
9.45/4.04	14[label="()",fontsize=16,color="green",shape="box"];}
9.45/4.04	
9.45/4.04	----------------------------------------
9.45/4.04	
9.45/4.04	(6)
9.45/4.04	YES
9.75/4.09	EOF