7.96/3.56	YES
9.76/4.07	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.76/4.07	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.76/4.07	
9.76/4.07	
9.76/4.07	H-Termination with start terms of the given HASKELL could be proven:
9.76/4.07	
9.76/4.07	(0) HASKELL
9.76/4.07	(1) BR [EQUIVALENT, 0 ms]
9.76/4.07	(2) HASKELL
9.76/4.07	(3) COR [EQUIVALENT, 0 ms]
9.76/4.07	(4) HASKELL
9.76/4.07	(5) NumRed [SOUND, 0 ms]
9.76/4.07	(6) HASKELL
9.76/4.07	(7) Narrow [EQUIVALENT, 1 ms]
9.76/4.07	(8) YES
9.76/4.07	
9.76/4.07	
9.76/4.07	----------------------------------------
9.76/4.07	
9.76/4.07	(0)
9.76/4.07	Obligation:
9.76/4.07	mainModule Main 
9.76/4.07	module Main where {
9.76/4.07	import qualified Prelude;
9.76/4.07	}
9.76/4.07	
9.76/4.07	----------------------------------------
9.76/4.07	
9.76/4.07	(1) BR (EQUIVALENT)
9.76/4.07	Replaced joker patterns by fresh variables and removed binding patterns.
9.76/4.07	----------------------------------------
9.76/4.07	
9.76/4.07	(2)
9.76/4.07	Obligation:
9.76/4.07	mainModule Main 
9.76/4.07	module Main where {
9.76/4.07	import qualified Prelude;
9.76/4.07	}
9.76/4.07	
9.76/4.07	----------------------------------------
9.76/4.07	
9.76/4.07	(3) COR (EQUIVALENT)
9.76/4.07	Cond Reductions:
9.76/4.07	The following Function with conditions
9.76/4.07	"toEnum 0 = LT;
9.76/4.07	toEnum 1 = EQ;
9.76/4.07	toEnum 2 = GT;
9.76/4.07	"
9.76/4.07	is transformed to
9.76/4.07	"toEnum wy = toEnum5 wy;
9.76/4.07	toEnum wu = toEnum3 wu;
9.76/4.07	toEnum vz = toEnum1 vz;
9.76/4.07	"
9.76/4.07	"toEnum0 True vz = GT;
9.76/4.07	"
9.76/4.07	"toEnum1 vz = toEnum0 (vz == 2) vz;
9.76/4.07	"
9.76/4.07	"toEnum2 True wu = EQ;
9.76/4.07	toEnum2 wv ww = toEnum1 ww;
9.76/4.07	"
9.76/4.07	"toEnum3 wu = toEnum2 (wu == 1) wu;
9.76/4.07	toEnum3 wx = toEnum1 wx;
9.76/4.07	"
9.76/4.07	"toEnum4 True wy = LT;
9.76/4.07	toEnum4 wz xu = toEnum3 xu;
9.76/4.07	"
9.76/4.07	"toEnum5 wy = toEnum4 (wy == 0) wy;
9.76/4.07	toEnum5 xv = toEnum3 xv;
9.76/4.07	"
9.76/4.07	The following Function with conditions
9.76/4.07	"undefined |Falseundefined;
9.76/4.07	"
9.76/4.07	is transformed to
9.76/4.07	"undefined  = undefined1;
9.76/4.07	"
9.76/4.07	"undefined0 True = undefined;
9.76/4.07	"
9.76/4.07	"undefined1  = undefined0 False;
9.76/4.07	"
9.76/4.07	
9.76/4.07	----------------------------------------
9.76/4.07	
9.76/4.07	(4)
9.76/4.07	Obligation:
9.76/4.07	mainModule Main 
9.76/4.07	module Main where {
9.76/4.07	import qualified Prelude;
9.76/4.07	}
9.76/4.07	
9.76/4.07	----------------------------------------
9.76/4.07	
9.76/4.07	(5) NumRed (SOUND)
9.76/4.07	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
9.76/4.07	----------------------------------------
9.76/4.07	
9.76/4.07	(6)
9.76/4.07	Obligation:
9.76/4.07	mainModule Main 
9.76/4.07	module Main where {
9.76/4.07	import qualified Prelude;
9.76/4.07	}
9.76/4.07	
9.76/4.07	----------------------------------------
9.76/4.07	
9.76/4.07	(7) Narrow (EQUIVALENT)
9.76/4.07	Haskell To QDPs
9.76/4.07	
9.76/4.07	digraph dp_graph {
9.76/4.07	node [outthreshold=100, inthreshold=100];1[label="pred",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.76/4.07	3[label="pred xw3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
9.76/4.07	4[label="toEnum . (subtract (Pos (Succ Zero))) . fromEnum",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
9.76/4.07	5[label="toEnum ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];5 -> 6[label="",style="solid", color="black", weight=3];
9.76/4.07	6[label="toEnum5 ((subtract (Pos (Succ Zero))) . fromEnum)",fontsize=16,color="black",shape="box"];6 -> 7[label="",style="solid", color="black", weight=3];
9.76/4.07	7[label="toEnum4 ((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];
9.76/4.07	8[label="toEnum4 (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];
9.76/4.07	9[label="toEnum4 (primEqInt (subtract (Pos (Succ Zero)) (fromEnum xw3)) (Pos Zero)) (subtract (Pos (Succ Zero)) (fromEnum xw3))",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
9.76/4.07	10[label="toEnum4 (primEqInt (flip (-) (Pos (Succ Zero)) (fromEnum xw3)) (Pos Zero)) (flip (-) (Pos (Succ Zero)) (fromEnum xw3))",fontsize=16,color="black",shape="box"];10 -> 11[label="",style="solid", color="black", weight=3];
9.76/4.07	11[label="toEnum4 (primEqInt ((-) fromEnum xw3 Pos (Succ Zero)) (Pos Zero)) ((-) fromEnum xw3 Pos (Succ Zero))",fontsize=16,color="black",shape="box"];11 -> 12[label="",style="solid", color="black", weight=3];
9.76/4.07	12[label="toEnum4 (primEqInt (primMinusInt (fromEnum xw3) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum xw3) (Pos (Succ Zero)))",fontsize=16,color="burlywood",shape="box"];46[label="xw3/LT",fontsize=10,color="white",style="solid",shape="box"];12 -> 46[label="",style="solid", color="burlywood", weight=9];
9.76/4.07	46 -> 13[label="",style="solid", color="burlywood", weight=3];
9.76/4.07	47[label="xw3/EQ",fontsize=10,color="white",style="solid",shape="box"];12 -> 47[label="",style="solid", color="burlywood", weight=9];
9.76/4.07	47 -> 14[label="",style="solid", color="burlywood", weight=3];
9.76/4.07	48[label="xw3/GT",fontsize=10,color="white",style="solid",shape="box"];12 -> 48[label="",style="solid", color="burlywood", weight=9];
9.76/4.07	48 -> 15[label="",style="solid", color="burlywood", weight=3];
9.76/4.07	13[label="toEnum4 (primEqInt (primMinusInt (fromEnum LT) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum LT) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];13 -> 16[label="",style="solid", color="black", weight=3];
9.76/4.07	14[label="toEnum4 (primEqInt (primMinusInt (fromEnum EQ) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum EQ) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];14 -> 17[label="",style="solid", color="black", weight=3];
9.76/4.07	15[label="toEnum4 (primEqInt (primMinusInt (fromEnum GT) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (fromEnum GT) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];15 -> 18[label="",style="solid", color="black", weight=3];
9.76/4.07	16[label="toEnum4 (primEqInt (primMinusInt (Pos Zero) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (Pos Zero) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];16 -> 19[label="",style="solid", color="black", weight=3];
9.76/4.07	17[label="toEnum4 (primEqInt (primMinusInt (Pos (Succ Zero)) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (Pos (Succ Zero)) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];17 -> 20[label="",style="solid", color="black", weight=3];
9.76/4.07	18[label="toEnum4 (primEqInt (primMinusInt (Pos (Succ (Succ Zero))) (Pos (Succ Zero))) (Pos Zero)) (primMinusInt (Pos (Succ (Succ Zero))) (Pos (Succ Zero)))",fontsize=16,color="black",shape="box"];18 -> 21[label="",style="solid", color="black", weight=3];
9.76/4.07	19[label="toEnum4 (primEqInt (primMinusNat Zero (Succ Zero)) (Pos Zero)) (primMinusNat Zero (Succ Zero))",fontsize=16,color="black",shape="box"];19 -> 22[label="",style="solid", color="black", weight=3];
9.76/4.07	20[label="toEnum4 (primEqInt (primMinusNat (Succ Zero) (Succ Zero)) (Pos Zero)) (primMinusNat (Succ Zero) (Succ Zero))",fontsize=16,color="black",shape="box"];20 -> 23[label="",style="solid", color="black", weight=3];
9.76/4.07	21[label="toEnum4 (primEqInt (primMinusNat (Succ (Succ Zero)) (Succ Zero)) (Pos Zero)) (primMinusNat (Succ (Succ Zero)) (Succ Zero))",fontsize=16,color="black",shape="box"];21 -> 24[label="",style="solid", color="black", weight=3];
9.76/4.07	22[label="toEnum4 (primEqInt (Neg (Succ Zero)) (Pos Zero)) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];22 -> 25[label="",style="solid", color="black", weight=3];
9.76/4.07	23[label="toEnum4 (primEqInt (primMinusNat Zero Zero) (Pos Zero)) (primMinusNat Zero Zero)",fontsize=16,color="black",shape="box"];23 -> 26[label="",style="solid", color="black", weight=3];
9.76/4.07	24[label="toEnum4 (primEqInt (primMinusNat (Succ Zero) Zero) (Pos Zero)) (primMinusNat (Succ Zero) Zero)",fontsize=16,color="black",shape="box"];24 -> 27[label="",style="solid", color="black", weight=3];
9.76/4.07	25[label="toEnum4 False (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];25 -> 28[label="",style="solid", color="black", weight=3];
9.76/4.07	26[label="toEnum4 (primEqInt (Pos Zero) (Pos Zero)) (Pos Zero)",fontsize=16,color="black",shape="box"];26 -> 29[label="",style="solid", color="black", weight=3];
9.76/4.07	27[label="toEnum4 (primEqInt (Pos (Succ Zero)) (Pos Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];27 -> 30[label="",style="solid", color="black", weight=3];
9.76/4.07	28[label="toEnum3 (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];28 -> 31[label="",style="solid", color="black", weight=3];
9.76/4.07	29[label="toEnum4 True (Pos Zero)",fontsize=16,color="black",shape="box"];29 -> 32[label="",style="solid", color="black", weight=3];
9.76/4.07	30[label="toEnum4 False (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];30 -> 33[label="",style="solid", color="black", weight=3];
9.76/4.07	31[label="toEnum2 (Neg (Succ Zero) == Pos (Succ Zero)) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];31 -> 34[label="",style="solid", color="black", weight=3];
9.76/4.07	32[label="LT",fontsize=16,color="green",shape="box"];33[label="toEnum3 (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];33 -> 35[label="",style="solid", color="black", weight=3];
9.76/4.07	34[label="toEnum2 (primEqInt (Neg (Succ Zero)) (Pos (Succ Zero))) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];34 -> 36[label="",style="solid", color="black", weight=3];
9.76/4.07	35[label="toEnum2 (Pos (Succ Zero) == Pos (Succ Zero)) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];35 -> 37[label="",style="solid", color="black", weight=3];
9.76/4.07	36[label="toEnum2 False (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];36 -> 38[label="",style="solid", color="black", weight=3];
9.76/4.07	37[label="toEnum2 (primEqInt (Pos (Succ Zero)) (Pos (Succ Zero))) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];37 -> 39[label="",style="solid", color="black", weight=3];
9.76/4.07	38[label="toEnum1 (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];38 -> 40[label="",style="solid", color="black", weight=3];
9.76/4.07	39[label="toEnum2 (primEqNat Zero Zero) (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];39 -> 41[label="",style="solid", color="black", weight=3];
9.76/4.07	40[label="toEnum0 (Neg (Succ Zero) == Pos (Succ (Succ Zero))) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];40 -> 42[label="",style="solid", color="black", weight=3];
9.76/4.07	41[label="toEnum2 True (Pos (Succ Zero))",fontsize=16,color="black",shape="box"];41 -> 43[label="",style="solid", color="black", weight=3];
9.76/4.07	42[label="toEnum0 (primEqInt (Neg (Succ Zero)) (Pos (Succ (Succ Zero)))) (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];42 -> 44[label="",style="solid", color="black", weight=3];
9.76/4.07	43[label="EQ",fontsize=16,color="green",shape="box"];44[label="toEnum0 False (Neg (Succ Zero))",fontsize=16,color="black",shape="box"];44 -> 45[label="",style="solid", color="black", weight=3];
9.76/4.07	45[label="error []",fontsize=16,color="red",shape="box"];}
9.76/4.07	
9.76/4.07	----------------------------------------
9.76/4.07	
9.76/4.07	(8)
9.76/4.07	YES
9.76/4.12	EOF