8.25/3.63	YES
10.06/4.15	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.06/4.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.06/4.15	
10.06/4.15	
10.06/4.15	H-Termination with start terms of the given HASKELL could be proven:
10.06/4.15	
10.06/4.15	(0) HASKELL
10.06/4.15	(1) BR [EQUIVALENT, 0 ms]
10.06/4.15	(2) HASKELL
10.06/4.15	(3) COR [EQUIVALENT, 0 ms]
10.06/4.15	(4) HASKELL
10.06/4.15	(5) NumRed [SOUND, 4 ms]
10.06/4.15	(6) HASKELL
10.06/4.15	(7) Narrow [EQUIVALENT, 0 ms]
10.06/4.15	(8) YES
10.06/4.15	
10.06/4.15	
10.06/4.15	----------------------------------------
10.06/4.15	
10.06/4.15	(0)
10.06/4.15	Obligation:
10.06/4.15	mainModule Main 
10.06/4.15	module Main where {
10.06/4.15	import qualified Prelude;
10.06/4.15	}
10.06/4.15	
10.06/4.15	----------------------------------------
10.06/4.15	
10.06/4.15	(1) BR (EQUIVALENT)
10.06/4.15	Replaced joker patterns by fresh variables and removed binding patterns.
10.06/4.15	----------------------------------------
10.06/4.15	
10.06/4.15	(2)
10.06/4.15	Obligation:
10.06/4.15	mainModule Main 
10.06/4.15	module Main where {
10.06/4.15	import qualified Prelude;
10.06/4.15	}
10.06/4.15	
10.06/4.15	----------------------------------------
10.06/4.15	
10.06/4.15	(3) COR (EQUIVALENT)
10.06/4.15	Cond Reductions:
10.06/4.15	The following Function with conditions
10.06/4.15	"toEnum 0 = False;
10.06/4.15	toEnum 1 = True;
10.06/4.15	"
10.06/4.15	is transformed to
10.06/4.15	"toEnum wu = toEnum3 wu;
10.06/4.15	toEnum vz = toEnum1 vz;
10.06/4.15	"
10.06/4.15	"toEnum0 True vz = True;
10.06/4.15	"
10.06/4.15	"toEnum1 vz = toEnum0 (vz == 1) vz;
10.06/4.15	"
10.06/4.15	"toEnum2 True wu = False;
10.06/4.15	toEnum2 wv ww = toEnum1 ww;
10.06/4.15	"
10.06/4.15	"toEnum3 wu = toEnum2 (wu == 0) wu;
10.06/4.15	toEnum3 wx = toEnum1 wx;
10.06/4.15	"
10.06/4.15	The following Function with conditions
10.06/4.15	"undefined |Falseundefined;
10.06/4.15	"
10.06/4.15	is transformed to
10.06/4.15	"undefined  = undefined1;
10.06/4.15	"
10.06/4.15	"undefined0 True = undefined;
10.06/4.15	"
10.06/4.15	"undefined1  = undefined0 False;
10.06/4.15	"
10.06/4.15	
10.06/4.15	----------------------------------------
10.06/4.15	
10.06/4.15	(4)
10.06/4.15	Obligation:
10.06/4.15	mainModule Main 
10.06/4.15	module Main where {
10.06/4.15	import qualified Prelude;
10.06/4.15	}
10.06/4.15	
10.06/4.15	----------------------------------------
10.06/4.15	
10.06/4.15	(5) NumRed (SOUND)
10.06/4.15	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
10.06/4.15	----------------------------------------
10.06/4.15	
10.06/4.15	(6)
10.06/4.15	Obligation:
10.06/4.15	mainModule Main 
10.06/4.15	module Main where {
10.06/4.15	import qualified Prelude;
10.06/4.15	}
10.06/4.15	
10.06/4.15	----------------------------------------
10.06/4.15	
10.06/4.15	(7) Narrow (EQUIVALENT)
10.06/4.15	Haskell To QDPs
10.06/4.15	
10.06/4.15	digraph dp_graph {
10.06/4.15	node [outthreshold=100, inthreshold=100];1[label="pred",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.06/4.15	3[label="pred wy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
10.06/4.15	4[label="toEnum . (subtract (Pos (Succ Zero))) . fromEnum",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
10.06/4.15	5[label="toEnum ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
10.06/4.15	6[label="toEnum3 ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
10.06/4.15	7[label="toEnum2 ((subtract (Pos (Succ Zero))) . fromEnum == Pos Zero) ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];7 -> 8[label="",style="solid", color="black", weight=3];
10.06/4.15	8[label="toEnum2 (primEqInt ((subtract (Pos (Succ Zero))) . fromEnum) (Pos Zero)) ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];8 -> 9[label="",style="solid", color="black", weight=3];
10.06/4.15	9[label="toEnum2 (primEqInt (subtract (Pos (Succ Zero)) (fromEnum wy3)) (Pos Zero)) (subtract (Pos (Succ Zero)) (fromEnum wy3))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
10.06/4.15	10[label="toEnum2 (primEqInt (flip (-) (Pos (Succ Zero)) (fromEnum wy3)) (Pos Zero)) (flip (-) (Pos (Succ Zero)) (fromEnum wy3))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
10.06/4.15	11[label="toEnum2 (primEqInt ((-) fromEnum wy3 Pos (Succ Zero)) (Pos Zero)) ((-) fromEnum wy3 Pos (Succ Zero))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
10.06/4.15	12[label="toEnum2 (primEqInt (primMinusInt (fromEnum wy3) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum wy3) (Pos (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];30[label="wy3/False",fontsize=10,color="white",style="solid",shape="box"];12 -> 30[label="",style="solid", color="burlywood", weight=9];
10.06/4.15	30 -> 13[label="",style="solid", color="burlywood", weight=3];
10.06/4.15	31[label="wy3/True",fontsize=10,color="white",style="solid",shape="box"];12 -> 31[label="",style="solid", color="burlywood", weight=9];
10.06/4.15	31 -> 14[label="",style="solid", color="burlywood", weight=3];
10.06/4.15	13[label="toEnum2 (primEqInt (primMinusInt (fromEnum False) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum False) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
10.06/4.15	14[label="toEnum2 (primEqInt (primMinusInt (fromEnum True) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum True) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
10.06/4.15	15[label="toEnum2 (primEqInt (primMinusInt (Pos Zero) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (Pos Zero) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];15 -> 17[label="",style="solid", color="black", weight=3];
10.06/4.15	16[label="toEnum2 (primEqInt (primMinusInt (Pos (Succ Zero)) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];16 -> 18[label="",style="solid", color="black", weight=3];
10.06/4.15	17[label="toEnum2 (primEqInt (primMinusNat Zero (Succ Zero)) (Pos Zero)) (primMinusNat Zero (Succ Zero))",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3];
10.06/4.15	18[label="toEnum2 (primEqInt (primMinusNat (Succ Zero) (Succ Zero)) (Pos Zero)) (primMinusNat (Succ Zero) (Succ Zero))",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3];
10.06/4.15	19[label="toEnum2 (primEqInt (Neg (Succ Zero)) (Pos Zero)) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];19 -> 21[label="",style="solid", color="black", weight=3];
10.06/4.15	20[label="toEnum2 (primEqInt (primMinusNat Zero Zero) (Pos Zero)) (primMinusNat Zero Zero)",fontsize=16,color="black",shape="box"];20 -> 22[label="",style="solid", color="black", weight=3];
10.06/4.15	21[label="toEnum2 False (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];21 -> 23[label="",style="solid", color="black", weight=3];
10.06/4.15	22[label="toEnum2 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero)",fontsize=16,color="black",shape="box"];22 -> 24[label="",style="solid", color="black", weight=3];
10.06/4.15	23[label="toEnum1 (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];23 -> 25[label="",style="solid", color="black", weight=3];
10.06/4.15	24[label="toEnum2 True (Pos Zero)",fontsize=16,color="black",shape="box"];24 -> 26[label="",style="solid", color="black", weight=3];
10.06/4.15	25[label="toEnum0 (Neg (Succ Zero) == Pos (Succ Zero)) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];25 -> 27[label="",style="solid", color="black", weight=3];
10.06/4.15	26[label="False",fontsize=16,color="green",shape="box"];27[label="toEnum0 (primEqInt (Neg (Succ Zero)) (Pos (Succ Zero))) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];27 -> 28[label="",style="solid", color="black", weight=3];
10.06/4.15	28[label="toEnum0 False (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];28 -> 29[label="",style="solid", color="black", weight=3];
10.06/4.15	29[label="error []",fontsize=16,color="red",shape="box"];}
10.06/4.15	
10.06/4.15	----------------------------------------
10.06/4.15	
10.06/4.15	(8)
10.06/4.15	YES
10.25/6.13	EOF