7.53/3.46	YES
9.47/3.99	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.47/3.99	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.47/3.99	
9.47/3.99	
9.47/3.99	H-Termination with start terms of the given HASKELL could be proven:
9.47/3.99	
9.47/3.99	(0) HASKELL
9.47/3.99	(1) BR [EQUIVALENT, 0 ms]
9.47/3.99	(2) HASKELL
9.47/3.99	(3) COR [EQUIVALENT, 0 ms]
9.47/3.99	(4) HASKELL
9.47/3.99	(5) NumRed [SOUND, 0 ms]
9.47/3.99	(6) HASKELL
9.47/3.99	(7) Narrow [EQUIVALENT, 14 ms]
9.47/3.99	(8) YES
9.47/3.99	
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(0)
9.47/3.99	Obligation:
9.47/3.99	mainModule Main 
9.47/3.99	module Main where {
9.47/3.99	import qualified Prelude;
9.47/3.99	}
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(1) BR (EQUIVALENT)
9.47/3.99	Replaced joker patterns by fresh variables and removed binding patterns.
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(2)
9.47/3.99	Obligation:
9.47/3.99	mainModule Main 
9.47/3.99	module Main where {
9.47/3.99	import qualified Prelude;
9.47/3.99	}
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(3) COR (EQUIVALENT)
9.47/3.99	Cond Reductions:
9.47/3.99	The following Function with conditions
9.47/3.99	"toEnum 0 = ();
9.47/3.99	"
9.47/3.99	is transformed to
9.47/3.99	"toEnum vz = toEnum1 vz;
9.47/3.99	"
9.47/3.99	"toEnum0 True vz = ();
9.47/3.99	"
9.47/3.99	"toEnum1 vz = toEnum0 (vz == 0) vz;
9.47/3.99	"
9.47/3.99	The following Function with conditions
9.47/3.99	"undefined |Falseundefined;
9.47/3.99	"
9.47/3.99	is transformed to
9.47/3.99	"undefined  = undefined1;
9.47/3.99	"
9.47/3.99	"undefined0 True = undefined;
9.47/3.99	"
9.47/3.99	"undefined1  = undefined0 False;
9.47/3.99	"
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(4)
9.47/3.99	Obligation:
9.47/3.99	mainModule Main 
9.47/3.99	module Main where {
9.47/3.99	import qualified Prelude;
9.47/3.99	}
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(5) NumRed (SOUND)
9.47/3.99	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(6)
9.47/3.99	Obligation:
9.47/3.99	mainModule Main 
9.47/3.99	module Main where {
9.47/3.99	import qualified Prelude;
9.47/3.99	}
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(7) Narrow (EQUIVALENT)
9.47/3.99	Haskell To QDPs
9.47/3.99	
9.47/3.99	digraph dp_graph {
9.47/3.99	node [outthreshold=100, inthreshold=100];1[label="toEnum",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.47/3.99	3[label="toEnum wu3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.47/3.99	4[label="toEnum1 wu3",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.47/3.99	5[label="toEnum0 (wu3 == Pos Zero) wu3",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.47/3.99	6[label="toEnum0 (primEqInt wu3 (Pos Zero)) wu3",fontsize=16,color="burlywood",shape="box"];21[label="wu3/Pos wu30",fontsize=10,color="white",style="solid",shape="box"];6 -> 21[label="",style="solid", color="burlywood", weight=9];
9.47/3.99	21 -> 7[label="",style="solid", color="burlywood", weight=3];
9.47/3.99	22[label="wu3/Neg wu30",fontsize=10,color="white",style="solid",shape="box"];6 -> 22[label="",style="solid", color="burlywood", weight=9];
9.47/3.99	22 -> 8[label="",style="solid", color="burlywood", weight=3];
9.47/3.99	7[label="toEnum0 (primEqInt (Pos wu30) (Pos Zero)) (Pos wu30)",fontsize=16,color="burlywood",shape="box"];23[label="wu30/Succ wu300",fontsize=10,color="white",style="solid",shape="box"];7 -> 23[label="",style="solid", color="burlywood", weight=9];
9.47/3.99	23 -> 9[label="",style="solid", color="burlywood", weight=3];
9.47/3.99	24[label="wu30/Zero",fontsize=10,color="white",style="solid",shape="box"];7 -> 24[label="",style="solid", color="burlywood", weight=9];
9.47/3.99	24 -> 10[label="",style="solid", color="burlywood", weight=3];
9.47/3.99	8[label="toEnum0 (primEqInt (Neg wu30) (Pos Zero)) (Neg wu30)",fontsize=16,color="burlywood",shape="box"];25[label="wu30/Succ wu300",fontsize=10,color="white",style="solid",shape="box"];8 -> 25[label="",style="solid", color="burlywood", weight=9];
9.47/3.99	25 -> 11[label="",style="solid", color="burlywood", weight=3];
9.47/3.99	26[label="wu30/Zero",fontsize=10,color="white",style="solid",shape="box"];8 -> 26[label="",style="solid", color="burlywood", weight=9];
9.47/3.99	26 -> 12[label="",style="solid", color="burlywood", weight=3];
9.47/3.99	9[label="toEnum0 (primEqInt (Pos (Succ wu300)) (Pos Zero)) (Pos (Succ wu300))",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
9.47/3.99	10[label="toEnum0 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero)",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
9.47/3.99	11[label="toEnum0 (primEqInt (Neg (Succ wu300)) (Pos Zero)) (Neg (Succ wu300))",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
9.47/3.99	12[label="toEnum0 (primEqInt (Neg Zero) (Pos Zero)) (Neg Zero)",fontsize=16,color="black",shape="box"];12 -> 16[label="",style="solid", color="black", weight=3];
9.47/3.99	13[label="toEnum0 False (Pos (Succ wu300))",fontsize=16,color="black",shape="box"];13 -> 17[label="",style="solid", color="black", weight=3];
9.47/3.99	14[label="toEnum0 True (Pos Zero)",fontsize=16,color="black",shape="box"];14 -> 18[label="",style="solid", color="black", weight=3];
9.47/3.99	15[label="toEnum0 False (Neg (Succ wu300))",fontsize=16,color="black",shape="box"];15 -> 19[label="",style="solid", color="black", weight=3];
9.47/3.99	16[label="toEnum0 True (Neg Zero)",fontsize=16,color="black",shape="box"];16 -> 20[label="",style="solid", color="black", weight=3];
9.47/3.99	17[label="error []",fontsize=16,color="red",shape="box"];18[label="()",fontsize=16,color="green",shape="box"];19[label="error []",fontsize=16,color="red",shape="box"];20[label="()",fontsize=16,color="green",shape="box"];}
9.47/3.99	
9.47/3.99	----------------------------------------
9.47/3.99	
9.47/3.99	(8)
9.47/3.99	YES
9.71/4.03	EOF