7.73/3.51	YES
9.76/4.05	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.76/4.05	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.76/4.05	
9.76/4.05	
9.76/4.05	H-Termination with start terms of the given HASKELL could be proven:
9.76/4.05	
9.76/4.05	(0) HASKELL
9.76/4.05	(1) BR [EQUIVALENT, 0 ms]
9.76/4.05	(2) HASKELL
9.76/4.05	(3) COR [EQUIVALENT, 0 ms]
9.76/4.05	(4) HASKELL
9.76/4.05	(5) NumRed [SOUND, 0 ms]
9.76/4.05	(6) HASKELL
9.76/4.05	(7) Narrow [EQUIVALENT, 14 ms]
9.76/4.05	(8) YES
9.76/4.05	
9.76/4.05	
9.76/4.05	----------------------------------------
9.76/4.05	
9.76/4.05	(0)
9.76/4.05	Obligation:
9.76/4.05	mainModule Main 
9.76/4.05	module Main where {
9.76/4.05	import qualified Prelude;
9.76/4.05	}
9.76/4.05	
9.76/4.05	----------------------------------------
9.76/4.05	
9.76/4.05	(1) BR (EQUIVALENT)
9.76/4.05	Replaced joker patterns by fresh variables and removed binding patterns.
9.76/4.05	----------------------------------------
9.76/4.05	
9.76/4.05	(2)
9.76/4.05	Obligation:
9.76/4.05	mainModule Main 
9.76/4.05	module Main where {
9.76/4.05	import qualified Prelude;
9.76/4.05	}
9.76/4.05	
9.76/4.05	----------------------------------------
9.76/4.05	
9.76/4.05	(3) COR (EQUIVALENT)
9.76/4.05	Cond Reductions:
9.76/4.05	The following Function with conditions
9.76/4.05	"undefined |Falseundefined;
9.76/4.05	"
9.76/4.05	is transformed to
9.76/4.05	"undefined  = undefined1;
9.76/4.05	"
9.76/4.05	"undefined0 True = undefined;
9.76/4.05	"
9.76/4.05	"undefined1  = undefined0 False;
9.76/4.05	"
9.76/4.05	
9.76/4.05	----------------------------------------
9.76/4.05	
9.76/4.05	(4)
9.76/4.05	Obligation:
9.76/4.05	mainModule Main 
9.76/4.05	module Main where {
9.76/4.05	import qualified Prelude;
9.76/4.05	}
9.76/4.05	
9.76/4.05	----------------------------------------
9.76/4.05	
9.76/4.05	(5) NumRed (SOUND)
9.76/4.05	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
9.76/4.05	----------------------------------------
9.76/4.05	
9.76/4.05	(6)
9.76/4.05	Obligation:
9.76/4.05	mainModule Main 
9.76/4.05	module Main where {
9.76/4.05	import qualified Prelude;
9.76/4.05	}
9.76/4.05	
9.76/4.05	----------------------------------------
9.76/4.05	
9.76/4.05	(7) Narrow (EQUIVALENT)
9.76/4.05	Haskell To QDPs
9.76/4.05	
9.76/4.05	digraph dp_graph {
9.76/4.05	node [outthreshold=100, inthreshold=100];1[label="recip",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.76/4.05	3[label="recip vx3",fontsize=16,color="blue",shape="box"];42[label="recip :: Double -> Double",fontsize=10,color="white",style="solid",shape="box"];3 -> 42[label="",style="solid", color="blue", weight=9];
9.76/4.05	42 -> 4[label="",style="solid", color="blue", weight=3];
9.76/4.05	43[label="recip :: Float -> Float",fontsize=10,color="white",style="solid",shape="box"];3 -> 43[label="",style="solid", color="blue", weight=9];
9.76/4.05	43 -> 5[label="",style="solid", color="blue", weight=3];
9.76/4.05	44[label="recip :: (Ratio a) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];3 -> 44[label="",style="solid", color="blue", weight=9];
9.76/4.05	44 -> 6[label="",style="solid", color="blue", weight=3];
9.76/4.05	4[label="recip vx3",fontsize=16,color="black",shape="box"];4 -> 7[label="",style="solid", color="black", weight=3];
9.76/4.05	5[label="recip vx3",fontsize=16,color="black",shape="box"];5 -> 8[label="",style="solid", color="black", weight=3];
9.76/4.05	6[label="recip vx3",fontsize=16,color="burlywood",shape="box"];45[label="vx3/vx30 :% vx31",fontsize=10,color="white",style="solid",shape="box"];6 -> 45[label="",style="solid", color="burlywood", weight=9];
9.76/4.05	45 -> 9[label="",style="solid", color="burlywood", weight=3];
9.76/4.05	7[label="fromInt (Pos (Succ Zero)) / vx3",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
9.76/4.05	8[label="fromInt (Pos (Succ Zero)) / vx3",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9.76/4.05	9[label="recip (vx30 :% vx31)",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3];
9.76/4.05	10[label="primDivDouble (fromInt (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3];
9.76/4.05	11[label="primDivFloat (fromInt (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3];
9.76/4.05	12[label="vx31 :% vx30",fontsize=16,color="green",shape="box"];13[label="primDivDouble (primIntToDouble (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];13 -> 15[label="",style="solid", color="black", weight=3];
9.76/4.05	14[label="primDivFloat (primIntToFloat (Pos (Succ Zero))) vx3",fontsize=16,color="black",shape="box"];14 -> 16[label="",style="solid", color="black", weight=3];
9.76/4.05	15[label="primDivDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero))) vx3",fontsize=16,color="burlywood",shape="box"];46[label="vx3/Double vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];15 -> 46[label="",style="solid", color="burlywood", weight=9];
9.76/4.05	46 -> 17[label="",style="solid", color="burlywood", weight=3];
9.76/4.05	16[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) vx3",fontsize=16,color="burlywood",shape="box"];47[label="vx3/Float vx30 vx31",fontsize=10,color="white",style="solid",shape="box"];16 -> 47[label="",style="solid", color="burlywood", weight=9];
9.76/4.05	47 -> 18[label="",style="solid", color="burlywood", weight=3];
9.76/4.05	17[label="primDivDouble (Double (Pos (Succ Zero)) (Pos (Succ Zero))) (Double vx30 vx31)",fontsize=16,color="black",shape="box"];17 -> 19[label="",style="solid", color="black", weight=3];
9.76/4.05	18[label="primDivFloat (Float (Pos (Succ Zero)) (Pos (Succ Zero))) (Float vx30 vx31)",fontsize=16,color="black",shape="box"];18 -> 20[label="",style="solid", color="black", weight=3];
9.76/4.05	19[label="Double (Pos (Succ Zero) * vx31) (Pos (Succ Zero) * vx30)",fontsize=16,color="green",shape="box"];19 -> 21[label="",style="dashed", color="green", weight=3];
9.76/4.05	19 -> 22[label="",style="dashed", color="green", weight=3];
9.76/4.05	20[label="Float (Pos (Succ Zero) * vx31) (Pos (Succ Zero) * vx30)",fontsize=16,color="green",shape="box"];20 -> 23[label="",style="dashed", color="green", weight=3];
9.76/4.05	20 -> 24[label="",style="dashed", color="green", weight=3];
9.76/4.05	21[label="Pos (Succ Zero) * vx31",fontsize=16,color="black",shape="triangle"];21 -> 25[label="",style="solid", color="black", weight=3];
9.76/4.05	22 -> 21[label="",style="dashed", color="red", weight=0];
9.76/4.05	22[label="Pos (Succ Zero) * vx30",fontsize=16,color="magenta"];22 -> 26[label="",style="dashed", color="magenta", weight=3];
9.76/4.05	23 -> 21[label="",style="dashed", color="red", weight=0];
9.76/4.05	23[label="Pos (Succ Zero) * vx31",fontsize=16,color="magenta"];23 -> 27[label="",style="dashed", color="magenta", weight=3];
9.76/4.05	24 -> 21[label="",style="dashed", color="red", weight=0];
9.76/4.05	24[label="Pos (Succ Zero) * vx30",fontsize=16,color="magenta"];24 -> 28[label="",style="dashed", color="magenta", weight=3];
9.76/4.05	25[label="primMulInt (Pos (Succ Zero)) vx31",fontsize=16,color="burlywood",shape="box"];48[label="vx31/Pos vx310",fontsize=10,color="white",style="solid",shape="box"];25 -> 48[label="",style="solid", color="burlywood", weight=9];
9.76/4.05	48 -> 29[label="",style="solid", color="burlywood", weight=3];
9.76/4.05	49[label="vx31/Neg vx310",fontsize=10,color="white",style="solid",shape="box"];25 -> 49[label="",style="solid", color="burlywood", weight=9];
9.76/4.05	49 -> 30[label="",style="solid", color="burlywood", weight=3];
9.76/4.05	26[label="vx30",fontsize=16,color="green",shape="box"];27[label="vx31",fontsize=16,color="green",shape="box"];28[label="vx30",fontsize=16,color="green",shape="box"];29[label="primMulInt (Pos (Succ Zero)) (Pos vx310)",fontsize=16,color="black",shape="box"];29 -> 31[label="",style="solid", color="black", weight=3];
9.76/4.05	30[label="primMulInt (Pos (Succ Zero)) (Neg vx310)",fontsize=16,color="black",shape="box"];30 -> 32[label="",style="solid", color="black", weight=3];
9.76/4.05	31[label="Pos (primMulNat (Succ Zero) vx310)",fontsize=16,color="green",shape="box"];31 -> 33[label="",style="dashed", color="green", weight=3];
9.76/4.05	32[label="Neg (primMulNat (Succ Zero) vx310)",fontsize=16,color="green",shape="box"];32 -> 34[label="",style="dashed", color="green", weight=3];
9.76/4.05	33[label="primMulNat (Succ Zero) vx310",fontsize=16,color="burlywood",shape="triangle"];50[label="vx310/Succ vx3100",fontsize=10,color="white",style="solid",shape="box"];33 -> 50[label="",style="solid", color="burlywood", weight=9];
9.76/4.05	50 -> 35[label="",style="solid", color="burlywood", weight=3];
9.76/4.05	51[label="vx310/Zero",fontsize=10,color="white",style="solid",shape="box"];33 -> 51[label="",style="solid", color="burlywood", weight=9];
9.76/4.05	51 -> 36[label="",style="solid", color="burlywood", weight=3];
9.76/4.05	34 -> 33[label="",style="dashed", color="red", weight=0];
9.76/4.05	34[label="primMulNat (Succ Zero) vx310",fontsize=16,color="magenta"];34 -> 37[label="",style="dashed", color="magenta", weight=3];
9.76/4.05	35[label="primMulNat (Succ Zero) (Succ vx3100)",fontsize=16,color="black",shape="box"];35 -> 38[label="",style="solid", color="black", weight=3];
9.76/4.05	36[label="primMulNat (Succ Zero) Zero",fontsize=16,color="black",shape="box"];36 -> 39[label="",style="solid", color="black", weight=3];
9.76/4.05	37[label="vx310",fontsize=16,color="green",shape="box"];38[label="primPlusNat (primMulNat Zero (Succ vx3100)) (Succ vx3100)",fontsize=16,color="black",shape="box"];38 -> 40[label="",style="solid", color="black", weight=3];
9.76/4.05	39[label="Zero",fontsize=16,color="green",shape="box"];40[label="primPlusNat Zero (Succ vx3100)",fontsize=16,color="black",shape="box"];40 -> 41[label="",style="solid", color="black", weight=3];
9.76/4.05	41[label="Succ vx3100",fontsize=16,color="green",shape="box"];}
9.76/4.05	
9.76/4.05	----------------------------------------
9.76/4.05	
9.76/4.05	(8)
9.76/4.05	YES
9.87/4.10	EOF