7.95/3.56	YES
9.79/4.10	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.79/4.10	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.79/4.10	
9.79/4.10	
9.79/4.10	H-Termination with start terms of the given HASKELL could be proven:
9.79/4.10	
9.79/4.10	(0) HASKELL
9.79/4.10	(1) CR [EQUIVALENT, 0 ms]
9.79/4.10	(2) HASKELL
9.79/4.10	(3) BR [EQUIVALENT, 0 ms]
9.79/4.10	(4) HASKELL
9.79/4.10	(5) COR [EQUIVALENT, 0 ms]
9.79/4.10	(6) HASKELL
9.79/4.10	(7) Narrow [EQUIVALENT, 0 ms]
9.79/4.10	(8) YES
9.79/4.10	
9.79/4.10	
9.79/4.10	----------------------------------------
9.79/4.10	
9.79/4.10	(0)
9.79/4.10	Obligation:
9.79/4.10	mainModule Main 
9.79/4.10	module Maybe where {
9.79/4.10	import qualified Main;
9.79/4.10	import qualified Prelude;
9.79/4.10	fromMaybe :: a  ->  Maybe a  ->  a;
9.79/4.10	fromMaybe d x = case x of { 
9.79/4.10	Nothing-> d; 
9.79/4.10	Just v-> v; 
9.79/4.10	 } ;
9.79/4.10	
9.79/4.10	}
9.79/4.10	module Main where {
9.79/4.10	import qualified Maybe;
9.79/4.10	import qualified Prelude;
9.79/4.10	}
9.79/4.10	
9.79/4.10	----------------------------------------
9.79/4.10	
9.79/4.10	(1) CR (EQUIVALENT)
9.79/4.10	Case Reductions:
9.79/4.10	The following Case expression
9.79/4.10	"case x of {
9.79/4.10	Nothing  -> d;
9.79/4.10	Just v  -> v}
9.79/4.10	"
9.79/4.10	is transformed to
9.79/4.10	"fromMaybe0 d Nothing = d;
9.79/4.10	fromMaybe0 d (Just v) = v;
9.79/4.10	"
9.79/4.10	
9.79/4.10	----------------------------------------
9.79/4.10	
9.79/4.10	(2)
9.79/4.10	Obligation:
9.79/4.10	mainModule Main 
9.79/4.10	module Maybe where {
9.79/4.10	import qualified Main;
9.79/4.10	import qualified Prelude;
9.79/4.10	fromMaybe :: a  ->  Maybe a  ->  a;
9.79/4.10	fromMaybe d x = fromMaybe0 d x;
9.79/4.10	
9.79/4.10	fromMaybe0 d Nothing = d;
9.79/4.10	fromMaybe0 d (Just v) = v;
9.79/4.10	
9.79/4.10	}
9.79/4.10	module Main where {
9.79/4.10	import qualified Maybe;
9.79/4.10	import qualified Prelude;
9.79/4.10	}
9.79/4.10	
9.79/4.10	----------------------------------------
9.79/4.10	
9.79/4.10	(3) BR (EQUIVALENT)
9.79/4.10	Replaced joker patterns by fresh variables and removed binding patterns.
9.79/4.10	----------------------------------------
9.79/4.10	
9.79/4.10	(4)
9.79/4.10	Obligation:
9.79/4.10	mainModule Main 
9.79/4.10	module Maybe where {
9.79/4.10	import qualified Main;
9.79/4.10	import qualified Prelude;
9.79/4.10	fromMaybe :: a  ->  Maybe a  ->  a;
9.79/4.10	fromMaybe d x = fromMaybe0 d x;
9.79/4.10	
9.79/4.10	fromMaybe0 d Nothing = d;
9.79/4.10	fromMaybe0 d (Just v) = v;
9.79/4.10	
9.79/4.10	}
9.79/4.10	module Main where {
9.79/4.10	import qualified Maybe;
9.79/4.10	import qualified Prelude;
9.79/4.10	}
9.79/4.10	
9.79/4.10	----------------------------------------
9.79/4.10	
9.79/4.10	(5) COR (EQUIVALENT)
9.79/4.10	Cond Reductions:
9.79/4.10	The following Function with conditions
9.79/4.10	"undefined |Falseundefined;
9.79/4.10	"
9.79/4.10	is transformed to
9.79/4.10	"undefined  = undefined1;
9.79/4.10	"
9.79/4.10	"undefined0 True = undefined;
9.79/4.10	"
9.79/4.10	"undefined1  = undefined0 False;
9.79/4.10	"
9.79/4.10	
9.79/4.10	----------------------------------------
9.79/4.10	
9.79/4.10	(6)
9.79/4.10	Obligation:
9.79/4.10	mainModule Main 
9.79/4.10	module Maybe where {
9.79/4.10	import qualified Main;
9.79/4.10	import qualified Prelude;
9.79/4.10	fromMaybe :: a  ->  Maybe a  ->  a;
9.79/4.10	fromMaybe d x = fromMaybe0 d x;
9.79/4.10	
9.79/4.10	fromMaybe0 d Nothing = d;
9.79/4.10	fromMaybe0 d (Just v) = v;
9.79/4.10	
9.79/4.10	}
9.79/4.10	module Main where {
9.79/4.10	import qualified Maybe;
9.79/4.10	import qualified Prelude;
9.79/4.10	}
9.79/4.10	
9.79/4.10	----------------------------------------
9.79/4.10	
9.79/4.10	(7) Narrow (EQUIVALENT)
9.79/4.10	Haskell To QDPs
9.79/4.10	
9.79/4.10	digraph dp_graph {
9.79/4.10	node [outthreshold=100, inthreshold=100];1[label="Maybe.fromMaybe",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.79/4.10	3[label="Maybe.fromMaybe vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
9.79/4.10	4[label="Maybe.fromMaybe vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
9.79/4.10	5[label="Maybe.fromMaybe0 vy3 vy4",fontsize=16,color="burlywood",shape="box"];10[label="vy4/Nothing",fontsize=10,color="white",style="solid",shape="box"];5 -> 10[label="",style="solid", color="burlywood", weight=9];
9.79/4.10	10 -> 6[label="",style="solid", color="burlywood", weight=3];
9.79/4.10	11[label="vy4/Just vy40",fontsize=10,color="white",style="solid",shape="box"];5 -> 11[label="",style="solid", color="burlywood", weight=9];
9.79/4.10	11 -> 7[label="",style="solid", color="burlywood", weight=3];
9.79/4.10	6[label="Maybe.fromMaybe0 vy3 Nothing",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
9.79/4.10	7[label="Maybe.fromMaybe0 vy3 (Just vy40)",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
9.79/4.10	8[label="vy3",fontsize=16,color="green",shape="box"];9[label="vy40",fontsize=16,color="green",shape="box"];}
9.79/4.10	
9.79/4.10	----------------------------------------
9.79/4.10	
9.79/4.10	(8)
9.79/4.10	YES
10.01/4.52	EOF