7.84/3.54	YES
9.51/4.01	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
9.51/4.01	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.51/4.01	
9.51/4.01	
9.51/4.01	H-Termination with start terms of the given HASKELL could be proven:
9.51/4.01	
9.51/4.01	(0) HASKELL
9.51/4.01	(1) BR [EQUIVALENT, 0 ms]
9.51/4.01	(2) HASKELL
9.51/4.01	(3) COR [EQUIVALENT, 0 ms]
9.51/4.01	(4) HASKELL
9.51/4.01	(5) Narrow [EQUIVALENT, 0 ms]
9.51/4.01	(6) YES
9.51/4.01	
9.51/4.01	
9.51/4.01	----------------------------------------
9.51/4.01	
9.51/4.01	(0)
9.51/4.01	Obligation:
9.51/4.01	mainModule Main 
9.51/4.01	module Maybe where {
9.51/4.01	import qualified Main;
9.51/4.01	import qualified Prelude;
9.51/4.01	isNothing :: Maybe a  ->  Bool;
9.51/4.01	isNothing Nothing = True;
9.51/4.01	isNothing _ = False;
9.51/4.01	
9.51/4.01	}
9.51/4.01	module Main where {
9.51/4.01	import qualified Maybe;
9.51/4.01	import qualified Prelude;
9.51/4.01	}
9.51/4.01	
9.51/4.01	----------------------------------------
9.51/4.01	
9.51/4.01	(1) BR (EQUIVALENT)
9.51/4.01	Replaced joker patterns by fresh variables and removed binding patterns.
9.51/4.01	----------------------------------------
9.51/4.01	
9.51/4.01	(2)
9.51/4.01	Obligation:
9.51/4.01	mainModule Main 
9.51/4.01	module Maybe where {
9.51/4.01	import qualified Main;
9.51/4.01	import qualified Prelude;
9.51/4.01	isNothing :: Maybe a  ->  Bool;
9.51/4.01	isNothing Nothing = True;
9.51/4.01	isNothing vy = False;
9.51/4.01	
9.51/4.01	}
9.51/4.01	module Main where {
9.51/4.01	import qualified Maybe;
9.51/4.01	import qualified Prelude;
9.51/4.01	}
9.51/4.01	
9.51/4.01	----------------------------------------
9.51/4.01	
9.51/4.01	(3) COR (EQUIVALENT)
9.51/4.01	Cond Reductions:
9.51/4.01	The following Function with conditions
9.51/4.01	"undefined |Falseundefined;
9.51/4.01	"
9.51/4.01	is transformed to
9.51/4.01	"undefined  = undefined1;
9.51/4.01	"
9.51/4.01	"undefined0 True = undefined;
9.51/4.01	"
9.51/4.01	"undefined1  = undefined0 False;
9.51/4.01	"
9.51/4.01	
9.51/4.01	----------------------------------------
9.51/4.01	
9.51/4.01	(4)
9.51/4.01	Obligation:
9.51/4.01	mainModule Main 
9.51/4.01	module Maybe where {
9.51/4.01	import qualified Main;
9.51/4.01	import qualified Prelude;
9.51/4.01	isNothing :: Maybe a  ->  Bool;
9.51/4.01	isNothing Nothing = True;
9.51/4.01	isNothing vy = False;
9.51/4.01	
9.51/4.01	}
9.51/4.01	module Main where {
9.51/4.01	import qualified Maybe;
9.51/4.01	import qualified Prelude;
9.51/4.01	}
9.51/4.01	
9.51/4.01	----------------------------------------
9.51/4.01	
9.51/4.01	(5) Narrow (EQUIVALENT)
9.51/4.01	Haskell To QDPs
9.51/4.01	
9.51/4.01	digraph dp_graph {
9.51/4.01	node [outthreshold=100, inthreshold=100];1[label="Maybe.isNothing",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
9.51/4.01	3[label="Maybe.isNothing vz3",fontsize=16,color="burlywood",shape="triangle"];8[label="vz3/Nothing",fontsize=10,color="white",style="solid",shape="box"];3 -> 8[label="",style="solid", color="burlywood", weight=9];
9.51/4.01	8 -> 4[label="",style="solid", color="burlywood", weight=3];
9.51/4.01	9[label="vz3/Just vz30",fontsize=10,color="white",style="solid",shape="box"];3 -> 9[label="",style="solid", color="burlywood", weight=9];
9.51/4.01	9 -> 5[label="",style="solid", color="burlywood", weight=3];
9.51/4.01	4[label="Maybe.isNothing Nothing",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3];
9.51/4.01	5[label="Maybe.isNothing (Just vz30)",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
9.51/4.01	6[label="True",fontsize=16,color="green",shape="box"];7[label="False",fontsize=16,color="green",shape="box"];}
9.51/4.01	
9.51/4.01	----------------------------------------
9.51/4.01	
9.51/4.01	(6)
9.51/4.01	YES
9.71/4.08	EOF