7.78/3.55	YES
9.67/4.04	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.67/4.04	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.67/4.04	
9.67/4.04	
9.67/4.04	H-Termination with start terms of the given HASKELL could be proven:
9.67/4.04	
9.67/4.04	(0) HASKELL
9.67/4.04	(1) BR [EQUIVALENT, 0 ms]
9.67/4.04	(2) HASKELL
9.67/4.04	(3) COR [EQUIVALENT, 0 ms]
9.67/4.04	(4) HASKELL
9.67/4.04	(5) NumRed [SOUND, 0 ms]
9.67/4.04	(6) HASKELL
9.67/4.04	(7) Narrow [EQUIVALENT, 19 ms]
9.67/4.04	(8) YES
9.67/4.04	
9.67/4.04	
9.67/4.04	----------------------------------------
9.67/4.04	
9.67/4.04	(0)
9.67/4.04	Obligation:
9.67/4.04	mainModule Main 
9.67/4.04	module Main where {
9.67/4.04	import qualified Prelude;
9.67/4.04	}
9.67/4.04	
9.67/4.04	----------------------------------------
9.67/4.04	
9.67/4.04	(1) BR (EQUIVALENT)
9.67/4.04	Replaced joker patterns by fresh variables and removed binding patterns.
9.67/4.04	----------------------------------------
9.67/4.04	
9.67/4.04	(2)
9.67/4.04	Obligation:
9.67/4.04	mainModule Main 
9.67/4.04	module Main where {
9.67/4.04	import qualified Prelude;
9.67/4.04	}
9.67/4.04	
9.67/4.04	----------------------------------------
9.67/4.04	
9.67/4.04	(3) COR (EQUIVALENT)
9.67/4.04	Cond Reductions:
9.67/4.04	The following Function with conditions
9.67/4.04	"undefined |Falseundefined;
9.67/4.04	"
9.67/4.04	is transformed to
9.67/4.04	"undefined  = undefined1;
9.67/4.04	"
9.67/4.04	"undefined0 True = undefined;
9.67/4.04	"
9.67/4.04	"undefined1  = undefined0 False;
9.67/4.04	"
9.67/4.04	
9.67/4.04	----------------------------------------
9.67/4.04	
9.67/4.04	(4)
9.67/4.04	Obligation:
9.67/4.04	mainModule Main 
9.67/4.04	module Main where {
9.67/4.04	import qualified Prelude;
9.67/4.04	}
9.67/4.04	
9.67/4.04	----------------------------------------
9.67/4.04	
9.67/4.04	(5) NumRed (SOUND)
9.67/4.04	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
9.67/4.04	----------------------------------------
9.67/4.04	
9.67/4.04	(6)
9.67/4.04	Obligation:
9.67/4.04	mainModule Main 
9.67/4.04	module Main where {
9.67/4.04	import qualified Prelude;
9.67/4.04	}
9.67/4.04	
9.67/4.04	----------------------------------------
9.67/4.04	
9.67/4.04	(7) Narrow (EQUIVALENT)
9.67/4.04	Haskell To QDPs
9.67/4.04	
9.67/4.04	digraph dp_graph {
9.67/4.04	node [outthreshold=100, inthreshold=100];1[label="index",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.67/4.04	3[label="index vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.67/4.04	4[label="index vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];10[label="vx3/(vx30,vx31)",fontsize=10,color="white",style="solid",shape="box"];4 -> 10[label="",style="solid", color="burlywood", weight=9];
9.67/4.04	10 -> 5[label="",style="solid", color="burlywood", weight=3];
9.67/4.04	5[label="index (vx30,vx31) vx4",fontsize=16,color="burlywood",shape="box"];11[label="vx30/()",fontsize=10,color="white",style="solid",shape="box"];5 -> 11[label="",style="solid", color="burlywood", weight=9];
9.67/4.04	11 -> 6[label="",style="solid", color="burlywood", weight=3];
9.67/4.04	6[label="index ((),vx31) vx4",fontsize=16,color="burlywood",shape="box"];12[label="vx31/()",fontsize=10,color="white",style="solid",shape="box"];6 -> 12[label="",style="solid", color="burlywood", weight=9];
9.67/4.04	12 -> 7[label="",style="solid", color="burlywood", weight=3];
9.67/4.04	7[label="index ((),()) vx4",fontsize=16,color="burlywood",shape="box"];13[label="vx4/()",fontsize=10,color="white",style="solid",shape="box"];7 -> 13[label="",style="solid", color="burlywood", weight=9];
9.67/4.04	13 -> 8[label="",style="solid", color="burlywood", weight=3];
9.67/4.04	8[label="index ((),()) ()",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.67/4.04	9[label="Pos Zero",fontsize=16,color="green",shape="box"];}
9.67/4.04	
9.67/4.04	----------------------------------------
9.67/4.04	
9.67/4.04	(8)
9.67/4.04	YES
9.67/4.08	EOF