8.30/3.62	YES
10.03/4.10	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
10.03/4.10	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.03/4.10	
10.03/4.10	
10.03/4.10	H-Termination with start terms of the given HASKELL could be proven:
10.03/4.10	
10.03/4.10	(0) HASKELL
10.03/4.10	(1) BR [EQUIVALENT, 0 ms]
10.03/4.10	(2) HASKELL
10.03/4.10	(3) COR [EQUIVALENT, 0 ms]
10.03/4.10	(4) HASKELL
10.03/4.10	(5) NumRed [SOUND, 0 ms]
10.03/4.10	(6) HASKELL
10.03/4.10	(7) Narrow [EQUIVALENT, 0 ms]
10.03/4.10	(8) YES
10.03/4.10	
10.03/4.10	
10.03/4.10	----------------------------------------
10.03/4.10	
10.03/4.10	(0)
10.03/4.10	Obligation:
10.03/4.10	mainModule Main 
10.03/4.10	module Main where {
10.03/4.10	import qualified Prelude;
10.03/4.10	}
10.03/4.10	
10.03/4.10	----------------------------------------
10.03/4.10	
10.03/4.10	(1) BR (EQUIVALENT)
10.03/4.10	Replaced joker patterns by fresh variables and removed binding patterns.
10.03/4.10	----------------------------------------
10.03/4.10	
10.03/4.10	(2)
10.03/4.10	Obligation:
10.03/4.10	mainModule Main 
10.03/4.10	module Main where {
10.03/4.10	import qualified Prelude;
10.03/4.10	}
10.03/4.10	
10.03/4.10	----------------------------------------
10.03/4.10	
10.03/4.10	(3) COR (EQUIVALENT)
10.03/4.10	Cond Reductions:
10.03/4.10	The following Function with conditions
10.03/4.10	"toEnum 0 = False;
10.03/4.10	toEnum 1 = True;
10.03/4.10	"
10.03/4.10	is transformed to
10.03/4.10	"toEnum wu = toEnum3 wu;
10.03/4.10	toEnum vz = toEnum1 vz;
10.03/4.10	"
10.03/4.10	"toEnum0 True vz = True;
10.03/4.10	"
10.03/4.10	"toEnum1 vz = toEnum0 (vz == 1) vz;
10.03/4.10	"
10.03/4.10	"toEnum2 True wu = False;
10.03/4.10	toEnum2 wv ww = toEnum1 ww;
10.03/4.10	"
10.03/4.10	"toEnum3 wu = toEnum2 (wu == 0) wu;
10.03/4.10	toEnum3 wx = toEnum1 wx;
10.03/4.10	"
10.03/4.10	The following Function with conditions
10.03/4.10	"undefined |Falseundefined;
10.03/4.10	"
10.03/4.10	is transformed to
10.03/4.10	"undefined  = undefined1;
10.03/4.10	"
10.03/4.10	"undefined0 True = undefined;
10.03/4.10	"
10.03/4.10	"undefined1  = undefined0 False;
10.03/4.10	"
10.03/4.10	
10.03/4.10	----------------------------------------
10.03/4.10	
10.03/4.10	(4)
10.03/4.10	Obligation:
10.03/4.10	mainModule Main 
10.03/4.10	module Main where {
10.03/4.10	import qualified Prelude;
10.03/4.10	}
10.03/4.10	
10.03/4.10	----------------------------------------
10.03/4.10	
10.03/4.10	(5) NumRed (SOUND)
10.03/4.10	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
10.03/4.10	----------------------------------------
10.03/4.10	
10.03/4.10	(6)
10.03/4.10	Obligation:
10.03/4.10	mainModule Main 
10.03/4.10	module Main where {
10.03/4.10	import qualified Prelude;
10.03/4.10	}
10.03/4.10	
10.03/4.10	----------------------------------------
10.03/4.10	
10.03/4.10	(7) Narrow (EQUIVALENT)
10.03/4.10	Haskell To QDPs
10.03/4.10	
10.03/4.10	digraph dp_graph {
10.03/4.10	node [outthreshold=100, inthreshold=100];1[label="succ",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.03/4.10	3[label="succ wy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
10.03/4.10	4[label="toEnum . (Pos (Succ Zero) +) . fromEnum",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
10.03/4.10	5[label="toEnum ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
10.03/4.10	6[label="toEnum3 ((Pos (Succ Zero) +) . fromEnum)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
10.03/4.10	7[label="toEnum2 ((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];
10.03/4.10	8[label="toEnum2 (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];
10.03/4.10	9[label="toEnum2 (primEqInt (Pos (Succ Zero) + fromEnum wy3) (Pos Zero)) (Pos (Succ Zero) + fromEnum wy3)",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10.03/4.10	10[label="toEnum2 (primEqInt (primPlusInt (Pos (Succ Zero)) (fromEnum wy3)) (Pos Zero)) (primPlusInt (Pos (Succ Zero)) (fromEnum wy3))",fontsize=16,color="burlywood",shape="box"];33[label="wy3/False",fontsize=10,color="white",style="solid",shape="box"];10 -> 33[label="",style="solid", color="burlywood", weight=9];
10.03/4.10	33 -> 11[label="",style="solid", color="burlywood", weight=3];
10.03/4.10	34[label="wy3/True",fontsize=10,color="white",style="solid",shape="box"];10 -> 34[label="",style="solid", color="burlywood", weight=9];
10.03/4.10	34 -> 12[label="",style="solid", color="burlywood", weight=3];
10.03/4.10	11[label="toEnum2 (primEqInt (primPlusInt (Pos (Succ Zero)) (fromEnum False)) (Pos Zero)) (primPlusInt (Pos (Succ Zero)) (fromEnum False))",fontsize=16,color="black",shape="box"];11 -> 13[label="",style="solid", color="black", weight=3];
10.03/4.10	12[label="toEnum2 (primEqInt (primPlusInt (Pos (Succ Zero)) (fromEnum True)) (Pos Zero)) (primPlusInt (Pos (Succ Zero)) (fromEnum True))",fontsize=16,color="black",shape="box"];12 -> 14[label="",style="solid", color="black", weight=3];
10.03/4.10	13[label="toEnum2 (primEqInt (primPlusInt (Pos (Succ Zero)) (Pos Zero)) (Pos Zero)) (primPlusInt (Pos (Succ Zero)) (Pos Zero))",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
10.03/4.10	14[label="toEnum2 (primEqInt (primPlusInt (Pos (Succ Zero)) (Pos (Succ Zero))) (Pos Zero)) (primPlusInt (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
10.03/4.10	15[label="toEnum2 (primEqInt (Pos (primPlusNat (Succ Zero) Zero)) (Pos Zero)) (Pos (primPlusNat (Succ Zero) Zero))",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
10.03/4.10	16[label="toEnum2 (primEqInt (Pos (primPlusNat (Succ Zero) (Succ Zero))) (Pos Zero)) (Pos (primPlusNat (Succ Zero) (Succ Zero)))",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
10.03/4.10	17[label="toEnum2 (primEqInt (Pos (Succ Zero)) (Pos Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3];
10.03/4.10	18[label="toEnum2 (primEqInt (Pos (Succ (Succ (primPlusNat Zero Zero)))) (Pos Zero)) (Pos (Succ (Succ (primPlusNat Zero Zero))))",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3];
10.03/4.10	19[label="toEnum2 False (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
10.03/4.10	20[label="toEnum2 False (Pos (Succ (Succ (primPlusNat Zero Zero))))",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
10.03/4.10	21[label="toEnum1 (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
10.03/4.10	22[label="toEnum1 (Pos (Succ (Succ (primPlusNat Zero Zero))))",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3];
10.03/4.10	23[label="toEnum0 (Pos (Succ Zero) == Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
10.03/4.10	24[label="toEnum0 (Pos (Succ (Succ (primPlusNat Zero Zero))) == Pos (Succ Zero)) (Pos (Succ (Succ (primPlusNat Zero Zero))))",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
10.03/4.10	25[label="toEnum0 (primEqInt (Pos (Succ Zero)) (Pos (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
10.03/4.10	26[label="toEnum0 (primEqInt (Pos (Succ (Succ (primPlusNat Zero Zero)))) (Pos (Succ Zero))) (Pos (Succ (Succ (primPlusNat Zero Zero))))",fontsize=16,color="black",shape="box"];26 -> 28[label="",style="solid", color="black", weight=3];
10.03/4.10	27[label="toEnum0 (primEqNat Zero Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];27 -> 29[label="",style="solid", color="black", weight=3];
10.03/4.10	28[label="toEnum0 (primEqNat (Succ (primPlusNat Zero Zero)) Zero) (Pos (Succ (Succ (primPlusNat Zero Zero))))",fontsize=16,color="black",shape="box"];28 -> 30[label="",style="solid", color="black", weight=3];
10.03/4.10	29[label="toEnum0 True (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3];
10.03/4.10	30[label="toEnum0 False (Pos (Succ (Succ (primPlusNat Zero Zero))))",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3];
10.03/4.10	31[label="True",fontsize=16,color="green",shape="box"];32[label="error []",fontsize=16,color="red",shape="box"];}
10.03/4.10	
10.03/4.10	----------------------------------------
10.03/4.10	
10.03/4.10	(8)
10.03/4.10	YES
10.08/4.15	EOF