7.51/3.51	YES
9.03/3.96	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.03/3.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.03/3.96	
9.03/3.96	
9.03/3.96	H-Termination with start terms of the given HASKELL could be proven:
9.03/3.96	
9.03/3.96	(0) HASKELL
9.03/3.96	(1) BR [EQUIVALENT, 0 ms]
9.03/3.96	(2) HASKELL
9.03/3.96	(3) COR [EQUIVALENT, 0 ms]
9.03/3.96	(4) HASKELL
9.03/3.96	(5) Narrow [EQUIVALENT, 0 ms]
9.03/3.96	(6) YES
9.03/3.96	
9.03/3.96	
9.03/3.96	----------------------------------------
9.03/3.96	
9.03/3.96	(0)
9.03/3.96	Obligation:
9.03/3.96	mainModule Main 
9.03/3.96	module Main where {
9.03/3.96	import qualified Prelude;
9.03/3.96	data Main.Maybe a = Nothing  | Just a ;
9.03/3.96	
9.03/3.96	fmapMaybe :: (a  ->  b)  ->  Main.Maybe a  ->  Main.Maybe b;
9.03/3.96	fmapMaybe f Main.Nothing = Main.Nothing;
9.03/3.96	fmapMaybe f (Main.Just x) = Main.Just (f x);
9.03/3.96	
9.03/3.96	}
9.03/3.96	
9.03/3.96	----------------------------------------
9.03/3.96	
9.03/3.96	(1) BR (EQUIVALENT)
9.03/3.96	Replaced joker patterns by fresh variables and removed binding patterns.
9.03/3.96	----------------------------------------
9.03/3.96	
9.03/3.96	(2)
9.03/3.96	Obligation:
9.03/3.96	mainModule Main 
9.03/3.96	module Main where {
9.03/3.96	import qualified Prelude;
9.03/3.96	data Main.Maybe a = Nothing  | Just a ;
9.03/3.96	
9.03/3.96	fmapMaybe :: (a  ->  b)  ->  Main.Maybe a  ->  Main.Maybe b;
9.03/3.96	fmapMaybe f Main.Nothing = Main.Nothing;
9.03/3.96	fmapMaybe f (Main.Just x) = Main.Just (f x);
9.03/3.96	
9.03/3.96	}
9.03/3.96	
9.03/3.96	----------------------------------------
9.03/3.96	
9.03/3.96	(3) COR (EQUIVALENT)
9.03/3.96	Cond Reductions:
9.03/3.96	The following Function with conditions
9.03/3.96	"undefined |Falseundefined;
9.03/3.96	"
9.03/3.96	is transformed to
9.03/3.96	"undefined  = undefined1;
9.03/3.96	"
9.03/3.96	"undefined0 True = undefined;
9.03/3.96	"
9.03/3.96	"undefined1  = undefined0 False;
9.03/3.96	"
9.03/3.96	
9.03/3.96	----------------------------------------
9.03/3.96	
9.03/3.96	(4)
9.03/3.96	Obligation:
9.03/3.96	mainModule Main 
9.03/3.96	module Main where {
9.03/3.96	import qualified Prelude;
9.03/3.96	data Main.Maybe a = Nothing  | Just a ;
9.03/3.96	
9.03/3.96	fmapMaybe :: (a  ->  b)  ->  Main.Maybe a  ->  Main.Maybe b;
9.03/3.96	fmapMaybe f Main.Nothing = Main.Nothing;
9.03/3.96	fmapMaybe f (Main.Just x) = Main.Just (f x);
9.03/3.96	
9.03/3.96	}
9.03/3.96	
9.03/3.96	----------------------------------------
9.03/3.96	
9.03/3.96	(5) Narrow (EQUIVALENT)
9.03/3.96	Haskell To QDPs
9.03/3.96	
9.03/3.96	digraph dp_graph {
9.03/3.96	node [outthreshold=100, inthreshold=100];1[label="fmapMaybe",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.03/3.96	3[label="fmapMaybe vx3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.03/3.96	4[label="fmapMaybe vx3 vx4",fontsize=16,color="burlywood",shape="triangle"];11[label="vx4/Nothing",fontsize=10,color="white",style="solid",shape="box"];4 -> 11[label="",style="solid", color="burlywood", weight=9];
9.03/3.96	11 -> 5[label="",style="solid", color="burlywood", weight=3];
9.03/3.96	12[label="vx4/Just vx40",fontsize=10,color="white",style="solid",shape="box"];4 -> 12[label="",style="solid", color="burlywood", weight=9];
9.03/3.96	12 -> 6[label="",style="solid", color="burlywood", weight=3];
9.03/3.96	5[label="fmapMaybe vx3 Nothing",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
9.03/3.96	6[label="fmapMaybe vx3 (Just vx40)",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
9.03/3.96	7[label="Nothing",fontsize=16,color="green",shape="box"];8[label="Just (vx3 vx40)",fontsize=16,color="green",shape="box"];8 -> 9[label="",style="dashed", color="green", weight=3];
9.03/3.96	9[label="vx3 vx40",fontsize=16,color="green",shape="box"];9 -> 10[label="",style="dashed", color="green", weight=3];
9.03/3.96	10[label="vx40",fontsize=16,color="green",shape="box"];}
9.03/3.96	
9.03/3.96	----------------------------------------
9.03/3.96	
9.03/3.96	(6)
9.03/3.96	YES
9.03/4.00	EOF