7.73/3.48	YES
9.73/3.98	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.73/3.98	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.73/3.98	
9.73/3.98	
9.73/3.98	H-Termination with start terms of the given HASKELL could be proven:
9.73/3.98	
9.73/3.98	(0) HASKELL
9.73/3.98	(1) BR [EQUIVALENT, 0 ms]
9.73/3.98	(2) HASKELL
9.73/3.98	(3) COR [EQUIVALENT, 0 ms]
9.73/3.98	(4) HASKELL
9.73/3.98	(5) NumRed [SOUND, 0 ms]
9.73/3.98	(6) HASKELL
9.73/3.98	(7) Narrow [EQUIVALENT, 17 ms]
9.73/3.98	(8) YES
9.73/3.98	
9.73/3.98	
9.73/3.98	----------------------------------------
9.73/3.98	
9.73/3.98	(0)
9.73/3.98	Obligation:
9.73/3.98	mainModule Main 
9.73/3.98	module Main where {
9.73/3.98	import qualified Prelude;
9.73/3.98	}
9.73/3.98	
9.73/3.98	----------------------------------------
9.73/3.98	
9.73/3.98	(1) BR (EQUIVALENT)
9.73/3.98	Replaced joker patterns by fresh variables and removed binding patterns.
9.73/3.98	----------------------------------------
9.73/3.98	
9.73/3.98	(2)
9.73/3.98	Obligation:
9.73/3.98	mainModule Main 
9.73/3.98	module Main where {
9.73/3.98	import qualified Prelude;
9.73/3.98	}
9.73/3.98	
9.73/3.98	----------------------------------------
9.73/3.98	
9.73/3.98	(3) COR (EQUIVALENT)
9.73/3.98	Cond Reductions:
9.73/3.98	The following Function with conditions
9.73/3.98	"undefined |Falseundefined;
9.73/3.98	"
9.73/3.98	is transformed to
9.73/3.98	"undefined  = undefined1;
9.73/3.98	"
9.73/3.98	"undefined0 True = undefined;
9.73/3.98	"
9.73/3.98	"undefined1  = undefined0 False;
9.73/3.98	"
9.73/3.98	
9.73/3.98	----------------------------------------
9.73/3.98	
9.73/3.98	(4)
9.73/3.98	Obligation:
9.73/3.98	mainModule Main 
9.73/3.98	module Main where {
9.73/3.98	import qualified Prelude;
9.73/3.98	}
9.73/3.98	
9.73/3.98	----------------------------------------
9.73/3.98	
9.73/3.98	(5) NumRed (SOUND)
9.73/3.98	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
9.73/3.98	----------------------------------------
9.73/3.98	
9.73/3.98	(6)
9.73/3.98	Obligation:
9.73/3.98	mainModule Main 
9.73/3.98	module Main where {
9.73/3.98	import qualified Prelude;
9.73/3.98	}
9.73/3.98	
9.73/3.98	----------------------------------------
9.73/3.98	
9.73/3.98	(7) Narrow (EQUIVALENT)
9.73/3.98	Haskell To QDPs
9.73/3.98	
9.73/3.98	digraph dp_graph {
9.73/3.98	node [outthreshold=100, inthreshold=100];1[label="fromRational",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.73/3.98	3[label="fromRational vx3",fontsize=16,color="blue",shape="box"];32[label="fromRational :: (Ratio Integer) -> Float",fontsize=10,color="white",style="solid",shape="box"];3 -> 32[label="",style="solid", color="blue", weight=9];
9.73/3.98	32 -> 4[label="",style="solid", color="blue", weight=3];
9.73/3.98	33[label="fromRational :: (Ratio Integer) -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];3 -> 33[label="",style="solid", color="blue", weight=9];
9.73/3.98	33 -> 5[label="",style="solid", color="blue", weight=3];
9.73/3.98	34[label="fromRational :: (Ratio Integer) -> Double",fontsize=10,color="white",style="solid",shape="box"];3 -> 34[label="",style="solid", color="blue", weight=9];
9.73/3.98	34 -> 6[label="",style="solid", color="blue", weight=3];
9.73/3.98	4[label="fromRational vx3",fontsize=16,color="black",shape="box"];4 -> 7[label="",style="solid", color="black", weight=3];
9.73/3.98	5[label="fromRational vx3",fontsize=16,color="burlywood",shape="box"];35[label="vx3/vx30 :% vx31",fontsize=10,color="white",style="solid",shape="box"];5 -> 35[label="",style="solid", color="burlywood", weight=9];
9.73/3.98	35 -> 8[label="",style="solid", color="burlywood", weight=3];
9.73/3.98	6[label="fromRational vx3",fontsize=16,color="black",shape="box"];6 -> 9[label="",style="solid", color="black", weight=3];
9.73/3.98	7[label="primRationalToFloat vx3",fontsize=16,color="black",shape="box"];7 -> 10[label="",style="solid", color="black", weight=3];
9.73/3.98	8[label="fromRational (vx30 :% vx31)",fontsize=16,color="black",shape="box"];8 -> 11[label="",style="solid", color="black", weight=3];
9.73/3.98	9[label="primRationalToDouble vx3",fontsize=16,color="black",shape="box"];9 -> 12[label="",style="solid", color="black", weight=3];
9.73/3.98	10[label="rationalToFloat vx3",fontsize=16,color="burlywood",shape="box"];36[label="vx3/vx30 :% vx31",fontsize=10,color="white",style="solid",shape="box"];10 -> 36[label="",style="solid", color="burlywood", weight=9];
9.73/3.98	36 -> 13[label="",style="solid", color="burlywood", weight=3];
9.73/3.98	11[label="fromInteger vx30 :% fromInteger vx31",fontsize=16,color="green",shape="box"];11 -> 14[label="",style="dashed", color="green", weight=3];
9.73/3.98	11 -> 15[label="",style="dashed", color="green", weight=3];
9.73/3.98	12[label="rationalToDouble vx3",fontsize=16,color="burlywood",shape="box"];37[label="vx3/vx30 :% vx31",fontsize=10,color="white",style="solid",shape="box"];12 -> 37[label="",style="solid", color="burlywood", weight=9];
9.73/3.98	37 -> 16[label="",style="solid", color="burlywood", weight=3];
9.73/3.98	13[label="rationalToFloat (vx30 :% vx31)",fontsize=16,color="burlywood",shape="box"];38[label="vx30/Integer vx300",fontsize=10,color="white",style="solid",shape="box"];13 -> 38[label="",style="solid", color="burlywood", weight=9];
9.73/3.98	38 -> 17[label="",style="solid", color="burlywood", weight=3];
9.73/3.98	14[label="fromInteger vx30",fontsize=16,color="blue",shape="box"];39[label="fromInteger :: Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];14 -> 39[label="",style="solid", color="blue", weight=9];
9.73/3.98	39 -> 18[label="",style="solid", color="blue", weight=3];
9.73/3.98	40[label="fromInteger :: Integer -> Int",fontsize=10,color="white",style="solid",shape="box"];14 -> 40[label="",style="solid", color="blue", weight=9];
9.73/3.98	40 -> 19[label="",style="solid", color="blue", weight=3];
9.73/3.98	15[label="fromInteger vx31",fontsize=16,color="blue",shape="box"];41[label="fromInteger :: Integer -> Integer",fontsize=10,color="white",style="solid",shape="box"];15 -> 41[label="",style="solid", color="blue", weight=9];
9.73/3.98	41 -> 20[label="",style="solid", color="blue", weight=3];
9.73/3.98	42[label="fromInteger :: Integer -> Int",fontsize=10,color="white",style="solid",shape="box"];15 -> 42[label="",style="solid", color="blue", weight=9];
9.73/3.98	42 -> 21[label="",style="solid", color="blue", weight=3];
9.73/3.98	16[label="rationalToDouble (vx30 :% vx31)",fontsize=16,color="burlywood",shape="box"];43[label="vx30/Integer vx300",fontsize=10,color="white",style="solid",shape="box"];16 -> 43[label="",style="solid", color="burlywood", weight=9];
9.73/3.98	43 -> 22[label="",style="solid", color="burlywood", weight=3];
9.73/3.98	17[label="rationalToFloat (Integer vx300 :% vx31)",fontsize=16,color="burlywood",shape="box"];44[label="vx31/Integer vx310",fontsize=10,color="white",style="solid",shape="box"];17 -> 44[label="",style="solid", color="burlywood", weight=9];
9.73/3.98	44 -> 23[label="",style="solid", color="burlywood", weight=3];
9.73/3.98	18[label="fromInteger vx30",fontsize=16,color="black",shape="triangle"];18 -> 24[label="",style="solid", color="black", weight=3];
9.73/3.98	19[label="fromInteger vx30",fontsize=16,color="burlywood",shape="triangle"];45[label="vx30/Integer vx300",fontsize=10,color="white",style="solid",shape="box"];19 -> 45[label="",style="solid", color="burlywood", weight=9];
9.73/3.98	45 -> 25[label="",style="solid", color="burlywood", weight=3];
9.73/3.98	20 -> 18[label="",style="dashed", color="red", weight=0];
9.73/3.98	20[label="fromInteger vx31",fontsize=16,color="magenta"];20 -> 26[label="",style="dashed", color="magenta", weight=3];
9.73/3.98	21 -> 19[label="",style="dashed", color="red", weight=0];
9.73/3.98	21[label="fromInteger vx31",fontsize=16,color="magenta"];21 -> 27[label="",style="dashed", color="magenta", weight=3];
9.73/3.98	22[label="rationalToDouble (Integer vx300 :% vx31)",fontsize=16,color="burlywood",shape="box"];46[label="vx31/Integer vx310",fontsize=10,color="white",style="solid",shape="box"];22 -> 46[label="",style="solid", color="burlywood", weight=9];
9.73/3.98	46 -> 28[label="",style="solid", color="burlywood", weight=3];
9.73/3.98	23[label="rationalToFloat (Integer vx300 :% Integer vx310)",fontsize=16,color="black",shape="box"];23 -> 29[label="",style="solid", color="black", weight=3];
9.73/3.98	24[label="vx30",fontsize=16,color="green",shape="box"];25[label="fromInteger (Integer vx300)",fontsize=16,color="black",shape="box"];25 -> 30[label="",style="solid", color="black", weight=3];
9.73/3.98	26[label="vx31",fontsize=16,color="green",shape="box"];27[label="vx31",fontsize=16,color="green",shape="box"];28[label="rationalToDouble (Integer vx300 :% Integer vx310)",fontsize=16,color="black",shape="box"];28 -> 31[label="",style="solid", color="black", weight=3];
9.73/3.98	29[label="Float vx300 vx310",fontsize=16,color="green",shape="box"];30[label="vx300",fontsize=16,color="green",shape="box"];31[label="Double vx300 vx310",fontsize=16,color="green",shape="box"];}
9.73/3.98	
9.73/3.98	----------------------------------------
9.73/3.98	
9.73/3.98	(8)
9.73/3.98	YES
9.78/4.02	EOF