9.27/3.94	YES
10.95/4.40	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.95/4.40	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.95/4.40	
10.95/4.40	
10.95/4.40	H-Termination with start terms of the given HASKELL could be proven:
10.95/4.40	
10.95/4.40	(0) HASKELL
10.95/4.40	(1) BR [EQUIVALENT, 0 ms]
10.95/4.40	(2) HASKELL
10.95/4.40	(3) COR [EQUIVALENT, 0 ms]
10.95/4.40	(4) HASKELL
10.95/4.40	(5) Narrow [EQUIVALENT, 25 ms]
10.95/4.40	(6) YES
10.95/4.40	
10.95/4.40	
10.95/4.40	----------------------------------------
10.95/4.40	
10.95/4.40	(0)
10.95/4.40	Obligation:
10.95/4.40	mainModule Main 
10.95/4.40	module Maybe where {
10.95/4.40	import qualified Main;
10.95/4.40	import qualified Monad;
10.95/4.40	import qualified Prelude;
10.95/4.40	}
10.95/4.40	module Main where {
10.95/4.40	import qualified Maybe;
10.95/4.40	import qualified Monad;
10.95/4.40	import qualified Prelude;
10.95/4.40	}
10.95/4.40	module Monad where {
10.95/4.40	import qualified Main;
10.95/4.40	import qualified Maybe;
10.95/4.40	import qualified Prelude;
10.95/4.40	class Monad a => MonadPlus a where {
10.95/4.40	mzero :: MonadPlus a => a b;
10.95/4.40	}
10.95/4.40	instance MonadPlus Maybe where { 
10.95/4.40	mzero = Nothing;
10.95/4.40	}
10.95/4.40	instance MonadPlus [] where { 
10.95/4.40	mzero = [];
10.95/4.40	}
10.95/4.40	guard :: MonadPlus a => Bool  ->  a ();
10.95/4.40	guard True = return ();
10.95/4.40	guard False = mzero;
10.95/4.40	
10.95/4.40	}
10.95/4.40	
10.95/4.40	----------------------------------------
10.95/4.40	
10.95/4.40	(1) BR (EQUIVALENT)
10.95/4.40	Replaced joker patterns by fresh variables and removed binding patterns.
10.95/4.40	----------------------------------------
10.95/4.40	
10.95/4.40	(2)
10.95/4.40	Obligation:
10.95/4.40	mainModule Main 
10.95/4.40	module Maybe where {
10.95/4.40	import qualified Main;
10.95/4.40	import qualified Monad;
10.95/4.40	import qualified Prelude;
10.95/4.40	}
10.95/4.40	module Main where {
10.95/4.40	import qualified Maybe;
10.95/4.40	import qualified Monad;
10.95/4.40	import qualified Prelude;
10.95/4.40	}
10.95/4.40	module Monad where {
10.95/4.40	import qualified Main;
10.95/4.40	import qualified Maybe;
10.95/4.40	import qualified Prelude;
10.95/4.40	class Monad a => MonadPlus a where {
10.95/4.40	mzero :: MonadPlus a => a b;
10.95/4.40	}
10.95/4.40	instance MonadPlus Maybe where { 
10.95/4.40	mzero = Nothing;
10.95/4.40	}
10.95/4.40	instance MonadPlus [] where { 
10.95/4.40	mzero = [];
10.95/4.40	}
10.95/4.40	guard :: MonadPlus a => Bool  ->  a ();
10.95/4.40	guard True = return ();
10.95/4.40	guard False = mzero;
10.95/4.40	
10.95/4.40	}
10.95/4.40	
10.95/4.40	----------------------------------------
10.95/4.40	
10.95/4.40	(3) COR (EQUIVALENT)
10.95/4.40	Cond Reductions:
10.95/4.40	The following Function with conditions
10.95/4.40	"undefined |Falseundefined;
10.95/4.40	"
10.95/4.40	is transformed to
10.95/4.40	"undefined  = undefined1;
10.95/4.40	"
10.95/4.40	"undefined0 True = undefined;
10.95/4.40	"
10.95/4.40	"undefined1  = undefined0 False;
10.95/4.40	"
10.95/4.40	
10.95/4.40	----------------------------------------
10.95/4.40	
10.95/4.40	(4)
10.95/4.40	Obligation:
10.95/4.40	mainModule Main 
10.95/4.40	module Maybe where {
10.95/4.40	import qualified Main;
10.95/4.40	import qualified Monad;
10.95/4.40	import qualified Prelude;
10.95/4.40	}
10.95/4.40	module Main where {
10.95/4.40	import qualified Maybe;
10.95/4.40	import qualified Monad;
10.95/4.40	import qualified Prelude;
10.95/4.40	}
10.95/4.40	module Monad where {
10.95/4.40	import qualified Main;
10.95/4.40	import qualified Maybe;
10.95/4.40	import qualified Prelude;
10.95/4.40	class Monad a => MonadPlus a where {
10.95/4.40	mzero :: MonadPlus a => a b;
10.95/4.40	}
10.95/4.40	instance MonadPlus Maybe where { 
10.95/4.40	mzero = Nothing;
10.95/4.40	}
10.95/4.40	instance MonadPlus [] where { 
10.95/4.40	mzero = [];
10.95/4.40	}
10.95/4.40	guard :: MonadPlus a => Bool  ->  a ();
10.95/4.40	guard True = return ();
10.95/4.40	guard False = mzero;
10.95/4.40	
10.95/4.40	}
10.95/4.40	
10.95/4.40	----------------------------------------
10.95/4.40	
10.95/4.40	(5) Narrow (EQUIVALENT)
10.95/4.40	Haskell To QDPs
10.95/4.40	
10.95/4.40	digraph dp_graph {
10.95/4.40	node [outthreshold=100, inthreshold=100];1[label="Monad.guard",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.95/4.40	3[label="Monad.guard vy3",fontsize=16,color="burlywood",shape="triangle"];16[label="vy3/False",fontsize=10,color="white",style="solid",shape="box"];3 -> 16[label="",style="solid", color="burlywood", weight=9];
10.95/4.40	16 -> 4[label="",style="solid", color="burlywood", weight=3];
10.95/4.40	17[label="vy3/True",fontsize=10,color="white",style="solid",shape="box"];3 -> 17[label="",style="solid", color="burlywood", weight=9];
10.95/4.40	17 -> 5[label="",style="solid", color="burlywood", weight=3];
10.95/4.40	4[label="Monad.guard False",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3];
10.95/4.40	5[label="Monad.guard True",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
10.95/4.40	6[label="Monad.mzero",fontsize=16,color="blue",shape="box"];18[label="Monad.mzero :: [] ()",fontsize=10,color="white",style="solid",shape="box"];6 -> 18[label="",style="solid", color="blue", weight=9];
10.95/4.40	18 -> 8[label="",style="solid", color="blue", weight=3];
10.95/4.40	19[label="Monad.mzero :: Maybe ()",fontsize=10,color="white",style="solid",shape="box"];6 -> 19[label="",style="solid", color="blue", weight=9];
10.95/4.40	19 -> 9[label="",style="solid", color="blue", weight=3];
10.95/4.40	7[label="return ()",fontsize=16,color="blue",shape="box"];20[label="return :: () -> [] ()",fontsize=10,color="white",style="solid",shape="box"];7 -> 20[label="",style="solid", color="blue", weight=9];
10.95/4.41	20 -> 10[label="",style="solid", color="blue", weight=3];
10.95/4.41	21[label="return :: () -> Maybe ()",fontsize=10,color="white",style="solid",shape="box"];7 -> 21[label="",style="solid", color="blue", weight=9];
10.95/4.41	21 -> 11[label="",style="solid", color="blue", weight=3];
10.95/4.41	8[label="Monad.mzero",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
10.95/4.41	9[label="Monad.mzero",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10.95/4.41	10[label="return ()",fontsize=16,color="black",shape="box"];10 -> 14[label="",style="solid", color="black", weight=3];
10.95/4.41	11[label="return ()",fontsize=16,color="black",shape="box"];11 -> 15[label="",style="solid", color="black", weight=3];
10.95/4.41	12[label="[]",fontsize=16,color="green",shape="box"];13[label="Nothing",fontsize=16,color="green",shape="box"];14[label="() : []",fontsize=16,color="green",shape="box"];15[label="Just ()",fontsize=16,color="green",shape="box"];}
10.95/4.41	
10.95/4.41	----------------------------------------
10.95/4.41	
10.95/4.41	(6)
10.95/4.41	YES
10.99/4.45	EOF