9.09/4.69	YES
10.81/5.15	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.81/5.15	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.81/5.15	
10.81/5.15	
10.81/5.15	H-Termination with start terms of the given HASKELL could be proven:
10.81/5.15	
10.81/5.15	(0) HASKELL
10.81/5.15	(1) BR [EQUIVALENT, 0 ms]
10.81/5.15	(2) HASKELL
10.81/5.15	(3) COR [EQUIVALENT, 0 ms]
10.81/5.15	(4) HASKELL
10.81/5.15	(5) Narrow [EQUIVALENT, 17 ms]
10.81/5.15	(6) YES
10.81/5.15	
10.81/5.15	
10.81/5.15	----------------------------------------
10.81/5.15	
10.81/5.15	(0)
10.81/5.15	Obligation:
10.81/5.15	mainModule Main 
10.81/5.15	module Maybe where {
10.81/5.15	import qualified Main;
10.81/5.15	import qualified Monad;
10.81/5.15	import qualified Prelude;
10.81/5.15	}
10.81/5.15	module Main where {
10.81/5.15	import qualified Maybe;
10.81/5.15	import qualified Monad;
10.81/5.15	import qualified Prelude;
10.81/5.15	}
10.81/5.15	module Monad where {
10.81/5.15	import qualified Main;
10.81/5.15	import qualified Maybe;
10.81/5.15	import qualified Prelude;
10.81/5.15	class Monad a => MonadPlus a where {
10.81/5.15	mzero :: MonadPlus a => a b;
10.81/5.15	}
10.81/5.15	instance MonadPlus Maybe where { 
10.81/5.15	}
10.81/5.15	instance MonadPlus [] where { 
10.81/5.15	mzero = [];
10.81/5.15	}
10.81/5.15	guard :: MonadPlus a => Bool  ->  a ();
10.81/5.15	guard True = return ();
10.81/5.15	guard False = mzero;
10.81/5.15	
10.81/5.15	}
10.81/5.15	
10.81/5.15	----------------------------------------
10.81/5.15	
10.81/5.15	(1) BR (EQUIVALENT)
10.81/5.15	Replaced joker patterns by fresh variables and removed binding patterns.
10.81/5.18	----------------------------------------
10.81/5.18	
10.81/5.18	(2)
10.81/5.18	Obligation:
10.81/5.18	mainModule Main 
10.81/5.18	module Maybe where {
10.81/5.18	import qualified Main;
10.81/5.18	import qualified Monad;
10.81/5.18	import qualified Prelude;
10.81/5.18	}
10.81/5.18	module Main where {
10.81/5.18	import qualified Maybe;
10.81/5.18	import qualified Monad;
10.81/5.18	import qualified Prelude;
10.81/5.18	}
10.81/5.18	module Monad where {
10.81/5.18	import qualified Main;
10.81/5.18	import qualified Maybe;
10.81/5.18	import qualified Prelude;
10.81/5.18	class Monad a => MonadPlus a where {
10.81/5.18	mzero :: MonadPlus a => a b;
10.81/5.18	}
10.81/5.18	instance MonadPlus Maybe where { 
10.81/5.18	}
10.81/5.18	instance MonadPlus [] where { 
10.81/5.18	mzero = [];
10.81/5.18	}
10.81/5.18	guard :: MonadPlus a => Bool  ->  a ();
10.81/5.18	guard True = return ();
10.81/5.18	guard False = mzero;
10.81/5.18	
10.81/5.18	}
10.81/5.18	
10.81/5.18	----------------------------------------
10.81/5.18	
10.81/5.18	(3) COR (EQUIVALENT)
10.81/5.18	Cond Reductions:
10.81/5.18	The following Function with conditions
10.81/5.18	"undefined |Falseundefined;
10.81/5.18	"
10.81/5.18	is transformed to
10.81/5.18	"undefined  = undefined1;
10.81/5.18	"
10.81/5.18	"undefined0 True = undefined;
10.81/5.18	"
10.81/5.18	"undefined1  = undefined0 False;
10.81/5.18	"
10.81/5.18	
10.81/5.18	----------------------------------------
10.81/5.18	
10.81/5.18	(4)
10.81/5.18	Obligation:
10.81/5.18	mainModule Main 
10.81/5.18	module Maybe where {
10.81/5.18	import qualified Main;
10.81/5.18	import qualified Monad;
10.81/5.18	import qualified Prelude;
10.81/5.18	}
10.81/5.18	module Main where {
10.81/5.18	import qualified Maybe;
10.81/5.18	import qualified Monad;
10.81/5.18	import qualified Prelude;
10.81/5.18	}
10.81/5.18	module Monad where {
10.81/5.18	import qualified Main;
10.81/5.18	import qualified Maybe;
10.81/5.18	import qualified Prelude;
10.81/5.18	class Monad a => MonadPlus a where {
10.81/5.18	mzero :: MonadPlus a => a b;
10.81/5.18	}
10.81/5.18	instance MonadPlus Maybe where { 
10.81/5.18	}
10.81/5.18	instance MonadPlus [] where { 
10.81/5.18	mzero = [];
10.81/5.18	}
10.81/5.18	guard :: MonadPlus a => Bool  ->  a ();
10.81/5.18	guard True = return ();
10.81/5.18	guard False = mzero;
10.81/5.18	
10.81/5.18	}
10.81/5.18	
10.81/5.18	----------------------------------------
10.81/5.18	
10.81/5.18	(5) Narrow (EQUIVALENT)
10.81/5.18	Haskell To QDPs
10.81/5.18	
10.81/5.18	digraph dp_graph {
10.81/5.18	node [outthreshold=100, inthreshold=100];1[label="Monad.guard",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.81/5.18	3[label="Monad.guard vy3",fontsize=16,color="burlywood",shape="triangle"];10[label="vy3/False",fontsize=10,color="white",style="solid",shape="box"];3 -> 10[label="",style="solid", color="burlywood", weight=9];
10.81/5.18	10 -> 4[label="",style="solid", color="burlywood", weight=3];
10.81/5.18	11[label="vy3/True",fontsize=10,color="white",style="solid",shape="box"];3 -> 11[label="",style="solid", color="burlywood", weight=9];
10.81/5.18	11 -> 5[label="",style="solid", color="burlywood", weight=3];
10.81/5.18	4[label="Monad.guard False",fontsize=16,color="black",shape="box"];4 -> 6[label="",style="solid", color="black", weight=3];
10.81/5.18	5[label="Monad.guard True",fontsize=16,color="black",shape="box"];5 -> 7[label="",style="solid", color="black", weight=3];
10.81/5.18	6[label="Monad.mzero",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
10.81/5.18	7[label="return ()",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
10.81/5.18	8[label="[]",fontsize=16,color="green",shape="box"];9[label="() : []",fontsize=16,color="green",shape="box"];}
10.81/5.18	
10.81/5.18	----------------------------------------
10.81/5.18	
10.81/5.18	(6)
10.81/5.18	YES
10.81/5.19	EOF