7.65/3.43	YES
9.36/3.94	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.36/3.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.36/3.94	
9.36/3.94	
9.36/3.94	H-Termination with start terms of the given HASKELL could be proven:
9.36/3.94	
9.36/3.94	(0) HASKELL
9.36/3.94	(1) BR [EQUIVALENT, 0 ms]
9.36/3.94	(2) HASKELL
9.36/3.94	(3) COR [EQUIVALENT, 0 ms]
9.36/3.94	(4) HASKELL
9.36/3.94	(5) NumRed [SOUND, 0 ms]
9.36/3.94	(6) HASKELL
9.36/3.94	(7) Narrow [EQUIVALENT, 24 ms]
9.36/3.94	(8) YES
9.36/3.94	
9.36/3.94	
9.36/3.94	----------------------------------------
9.36/3.94	
9.36/3.94	(0)
9.36/3.94	Obligation:
9.36/3.94	mainModule Main 
9.36/3.94	module Main where {
9.36/3.94	import qualified Prelude;
9.36/3.94	}
9.36/3.94	
9.36/3.94	----------------------------------------
9.36/3.94	
9.36/3.94	(1) BR (EQUIVALENT)
9.36/3.94	Replaced joker patterns by fresh variables and removed binding patterns.
9.36/3.94	----------------------------------------
9.36/3.94	
9.36/3.94	(2)
9.36/3.94	Obligation:
9.36/3.94	mainModule Main 
9.36/3.94	module Main where {
9.36/3.94	import qualified Prelude;
9.36/3.94	}
9.36/3.94	
9.36/3.94	----------------------------------------
9.36/3.94	
9.36/3.94	(3) COR (EQUIVALENT)
9.36/3.94	Cond Reductions:
9.36/3.94	The following Function with conditions
9.36/3.94	"undefined |Falseundefined;
9.36/3.94	"
9.36/3.94	is transformed to
9.36/3.94	"undefined  = undefined1;
9.36/3.94	"
9.36/3.94	"undefined0 True = undefined;
9.36/3.94	"
9.36/3.94	"undefined1  = undefined0 False;
9.36/3.94	"
9.36/3.94	
9.36/3.94	----------------------------------------
9.36/3.94	
9.36/3.94	(4)
9.36/3.94	Obligation:
9.36/3.94	mainModule Main 
9.36/3.94	module Main where {
9.36/3.94	import qualified Prelude;
9.36/3.94	}
9.36/3.94	
9.36/3.94	----------------------------------------
9.36/3.94	
9.36/3.94	(5) NumRed (SOUND)
9.36/3.94	Num Reduction:All numbers are transformed to their corresponding representation with Succ, Pred and Zero.
9.36/3.94	----------------------------------------
9.36/3.94	
9.36/3.94	(6)
9.36/3.94	Obligation:
9.36/3.94	mainModule Main 
9.36/3.94	module Main where {
9.36/3.94	import qualified Prelude;
9.36/3.94	}
9.36/3.94	
9.36/3.94	----------------------------------------
9.36/3.94	
9.36/3.94	(7) Narrow (EQUIVALENT)
9.36/3.94	Haskell To QDPs
9.36/3.94	
9.36/3.94	digraph dp_graph {
9.36/3.94	node [outthreshold=100, inthreshold=100];1[label="fromInt",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.36/3.94	3[label="fromInt vx3",fontsize=16,color="blue",shape="box"];25[label="fromInt :: Int -> Ratio a",fontsize=10,color="white",style="solid",shape="box"];3 -> 25[label="",style="solid", color="blue", weight=9];
9.36/3.94	25 -> 4[label="",style="solid", color="blue", weight=3];
9.36/3.94	26[label="fromInt :: Int -> Float",fontsize=10,color="white",style="solid",shape="box"];3 -> 26[label="",style="solid", color="blue", weight=9];
9.36/3.94	26 -> 5[label="",style="solid", color="blue", weight=3];
9.36/3.94	27[label="fromInt :: Int -> Double",fontsize=10,color="white",style="solid",shape="box"];3 -> 27[label="",style="solid", color="blue", weight=9];
9.36/3.94	27 -> 6[label="",style="solid", color="blue", weight=3];
9.36/3.94	28[label="fromInt :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];3 -> 28[label="",style="solid", color="blue", weight=9];
9.36/3.94	28 -> 7[label="",style="solid", color="blue", weight=3];
9.36/3.94	29[label="fromInt :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];3 -> 29[label="",style="solid", color="blue", weight=9];
9.36/3.94	29 -> 8[label="",style="solid", color="blue", weight=3];
9.36/3.94	4[label="fromInt vx3",fontsize=16,color="black",shape="box"];4 -> 9[label="",style="solid", color="black", weight=3];
9.36/3.94	5[label="fromInt vx3",fontsize=16,color="black",shape="box"];5 -> 10[label="",style="solid", color="black", weight=3];
9.36/3.94	6[label="fromInt vx3",fontsize=16,color="black",shape="box"];6 -> 11[label="",style="solid", color="black", weight=3];
9.36/3.94	7[label="fromInt vx3",fontsize=16,color="black",shape="triangle"];7 -> 12[label="",style="solid", color="black", weight=3];
9.36/3.94	8[label="fromInt vx3",fontsize=16,color="black",shape="triangle"];8 -> 13[label="",style="solid", color="black", weight=3];
9.36/3.94	9[label="intToRatio vx3",fontsize=16,color="black",shape="box"];9 -> 14[label="",style="solid", color="black", weight=3];
9.36/3.94	10[label="primIntToFloat vx3",fontsize=16,color="black",shape="box"];10 -> 15[label="",style="solid", color="black", weight=3];
9.36/3.94	11[label="primIntToDouble vx3",fontsize=16,color="black",shape="box"];11 -> 16[label="",style="solid", color="black", weight=3];
9.36/3.94	12[label="Integer vx3",fontsize=16,color="green",shape="box"];13[label="vx3",fontsize=16,color="green",shape="box"];14[label="fromInt vx3 :% fromInt (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];14 -> 17[label="",style="dashed", color="green", weight=3];
9.36/3.94	14 -> 18[label="",style="dashed", color="green", weight=3];
9.36/3.94	15[label="Float vx3 (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];16[label="Double vx3 (Pos (Succ Zero))",fontsize=16,color="green",shape="box"];17[label="fromInt vx3",fontsize=16,color="blue",shape="box"];30[label="fromInt :: Int -> Integer",fontsize=10,color="white",style="solid",shape="box"];17 -> 30[label="",style="solid", color="blue", weight=9];
9.36/3.94	30 -> 19[label="",style="solid", color="blue", weight=3];
9.36/3.94	31[label="fromInt :: Int -> Int",fontsize=10,color="white",style="solid",shape="box"];17 -> 31[label="",style="solid", color="blue", weight=9];
9.36/3.94	31 -> 20[label="",style="solid", color="blue", weight=3];
9.36/3.94	18[label="fromInt (Pos (Succ Zero))",fontsize=16,color="blue",shape="box"];32[label="fromInt :: -> Int Integer",fontsize=10,color="white",style="solid",shape="box"];18 -> 32[label="",style="solid", color="blue", weight=9];
9.36/3.94	32 -> 21[label="",style="solid", color="blue", weight=3];
9.36/3.94	33[label="fromInt :: -> Int Int",fontsize=10,color="white",style="solid",shape="box"];18 -> 33[label="",style="solid", color="blue", weight=9];
9.36/3.94	33 -> 22[label="",style="solid", color="blue", weight=3];
9.36/3.94	19 -> 7[label="",style="dashed", color="red", weight=0];
9.36/3.94	19[label="fromInt vx3",fontsize=16,color="magenta"];20 -> 8[label="",style="dashed", color="red", weight=0];
9.36/3.94	20[label="fromInt vx3",fontsize=16,color="magenta"];21 -> 7[label="",style="dashed", color="red", weight=0];
9.36/3.94	21[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];21 -> 23[label="",style="dashed", color="magenta", weight=3];
9.36/3.94	22 -> 8[label="",style="dashed", color="red", weight=0];
9.36/3.94	22[label="fromInt (Pos (Succ Zero))",fontsize=16,color="magenta"];22 -> 24[label="",style="dashed", color="magenta", weight=3];
9.36/3.94	23[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];24[label="Pos (Succ Zero)",fontsize=16,color="green",shape="box"];}
9.36/3.94	
9.36/3.94	----------------------------------------
9.36/3.94	
9.36/3.94	(8)
9.36/3.94	YES
9.60/3.97	EOF