7.85/3.52	YES
9.73/4.05	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.73/4.05	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.73/4.05	
9.73/4.05	
9.73/4.05	H-Termination with start terms of the given HASKELL could be proven:
9.73/4.05	
9.73/4.05	(0) HASKELL
9.73/4.05	(1) BR [EQUIVALENT, 0 ms]
9.73/4.05	(2) HASKELL
9.73/4.05	(3) COR [EQUIVALENT, 0 ms]
9.73/4.05	(4) HASKELL
9.73/4.05	(5) NumRed [SOUND, 0 ms]
9.73/4.05	(6) HASKELL
9.73/4.05	(7) Narrow [EQUIVALENT, 5 ms]
9.73/4.05	(8) YES
9.73/4.05	
9.73/4.05	
9.73/4.05	----------------------------------------
9.73/4.05	
9.73/4.05	(0)
9.73/4.05	Obligation:
9.73/4.05	mainModule Main 
9.73/4.05	module Main where {
9.73/4.05	import qualified Prelude;
9.73/4.05	}
9.73/4.05	
9.73/4.05	----------------------------------------
9.73/4.05	
9.73/4.05	(1) BR (EQUIVALENT)
9.73/4.05	Replaced joker patterns by fresh variables and removed binding patterns.
9.73/4.05	----------------------------------------
9.73/4.05	
9.73/4.05	(2)
9.73/4.05	Obligation:
9.73/4.05	mainModule Main 
9.73/4.05	module Main where {
9.73/4.05	import qualified Prelude;
9.73/4.05	}
9.73/4.05	
9.73/4.05	----------------------------------------
9.73/4.05	
9.73/4.05	(3) COR (EQUIVALENT)
9.73/4.05	Cond Reductions:
9.73/4.05	The following Function with conditions
9.73/4.05	"toEnum 0 = ();
9.73/4.05	"
9.73/4.05	is transformed to
9.73/4.05	"toEnum vz = toEnum1 vz;
9.73/4.05	"
9.73/4.05	"toEnum0 True vz = ();
9.73/4.05	"
9.73/4.05	"toEnum1 vz = toEnum0 (vz == 0) vz;
9.73/4.05	"
9.73/4.05	The following Function with conditions
9.73/4.05	"undefined |Falseundefined;
9.73/4.05	"
9.73/4.05	is transformed to
9.73/4.05	"undefined  = undefined1;
9.73/4.05	"
9.73/4.05	"undefined0 True = undefined;
9.73/4.05	"
9.73/4.05	"undefined1  = undefined0 False;
9.73/4.05	"
9.73/4.05	
9.73/4.05	----------------------------------------
9.73/4.05	
9.73/4.05	(4)
9.73/4.05	Obligation:
9.73/4.05	mainModule Main 
9.73/4.05	module Main where {
9.73/4.05	import qualified Prelude;
9.73/4.05	}
9.73/4.05	
9.73/4.05	----------------------------------------
9.73/4.05	
9.73/4.05	(5) NumRed (SOUND)
9.73/4.05	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
9.73/4.05	----------------------------------------
9.73/4.05	
9.73/4.05	(6)
9.73/4.05	Obligation:
9.73/4.05	mainModule Main 
9.73/4.05	module Main where {
9.73/4.05	import qualified Prelude;
9.73/4.05	}
9.73/4.05	
9.73/4.05	----------------------------------------
9.73/4.05	
9.73/4.05	(7) Narrow (EQUIVALENT)
9.73/4.05	Haskell To QDPs
9.73/4.05	
9.73/4.05	digraph dp_graph {
9.73/4.05	node [outthreshold=100, inthreshold=100];1[label="succ",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.73/4.05	3[label="succ wu3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.73/4.05	4[label="toEnum . (Pos (Succ Zero) +) . fromEnum",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.73/4.05	5[label="toEnum ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.73/4.05	6[label="toEnum1 ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.73/4.05	7[label="toEnum0 ((Pos (Succ Zero) +) . fromEnum == Pos Zero) ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
9.73/4.05	8[label="toEnum0 (primEqInt ((Pos (Succ Zero) +) . fromEnum) (Pos Zero)) ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
9.73/4.05	9[label="toEnum0 (primEqInt (Pos (Succ Zero) + fromEnum wu3) (Pos Zero)) (Pos (Succ Zero) + fromEnum wu3)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
9.73/4.05	10[label="toEnum0 (primEqInt (primPlusInt (Pos (Succ Zero)) (fromEnum wu3)) (Pos Zero)) (primPlusInt (Pos (Succ Zero)) (fromEnum wu3))",fontsize=16,color="burlywood",shape="box"];17[label="wu3/()",fontsize=10,color="white",style="solid",shape="box"];10 -> 17[label="",style="solid", color="burlywood", weight=9];
9.73/4.05	17 -> 11[label="",style="solid", color="burlywood", weight=3];
9.73/4.05	11[label="toEnum0 (primEqInt (primPlusInt (Pos (Succ Zero)) (fromEnum ())) (Pos Zero)) (primPlusInt (Pos (Succ Zero)) (fromEnum ()))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
9.73/4.05	12[label="toEnum0 (primEqInt (primPlusInt (Pos (Succ Zero)) (Pos Zero)) (Pos Zero)) (primPlusInt (Pos (Succ Zero)) (Pos Zero))",fontsize=16,color="black",shape="box"];12 -> 13[label="",style="solid", color="black", weight=3];
9.73/4.05	13[label="toEnum0 (primEqInt (Pos (primPlusNat (Succ Zero) Zero)) (Pos Zero)) (Pos (primPlusNat (Succ Zero) Zero))",fontsize=16,color="black",shape="box"];13 -> 14[label="",style="solid", color="black", weight=3];
9.73/4.05	14[label="toEnum0 (primEqInt (Pos (Succ Zero)) (Pos Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];14 -> 15[label="",style="solid", color="black", weight=3];
9.73/4.05	15[label="toEnum0 False (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];15 -> 16[label="",style="solid", color="black", weight=3];
9.73/4.05	16[label="error []",fontsize=16,color="red",shape="box"];}
9.73/4.05	
9.73/4.05	----------------------------------------
9.73/4.05	
9.73/4.05	(8)
9.73/4.05	YES
9.73/4.09	EOF