8.71/3.89	YES
10.87/4.43	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.87/4.43	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.87/4.43	
10.87/4.43	
10.87/4.43	H-Termination with start terms of the given HASKELL could be proven:
10.87/4.43	
10.87/4.43	(0) HASKELL
10.87/4.43	(1) IFR [EQUIVALENT, 0 ms]
10.87/4.43	(2) HASKELL
10.87/4.43	(3) BR [EQUIVALENT, 0 ms]
10.87/4.43	(4) HASKELL
10.87/4.43	(5) COR [EQUIVALENT, 0 ms]
10.87/4.43	(6) HASKELL
10.87/4.43	(7) Narrow [EQUIVALENT, 21 ms]
10.87/4.43	(8) YES
10.87/4.43	
10.87/4.43	
10.87/4.43	----------------------------------------
10.87/4.43	
10.87/4.43	(0)
10.87/4.43	Obligation:
10.87/4.43	mainModule Main 
10.87/4.43	module Maybe where {
10.87/4.43	import qualified Main;
10.87/4.43	import qualified Monad;
10.87/4.43	import qualified Prelude;
10.87/4.43	}
10.87/4.43	module Main where {
10.87/4.43	import qualified Maybe;
10.87/4.43	import qualified Monad;
10.87/4.43	import qualified Prelude;
10.87/4.43	}
10.87/4.43	module Monad where {
10.87/4.43	import qualified Main;
10.87/4.43	import qualified Maybe;
10.87/4.43	import qualified Prelude;
10.87/4.43	unless :: Monad a => Bool  ->  a ()  ->  a ();
10.87/4.43	unless p s =  if p then return () else s;
10.87/4.43	
10.87/4.43	}
10.87/4.43	
10.87/4.43	----------------------------------------
10.87/4.43	
10.87/4.43	(1) IFR (EQUIVALENT)
10.87/4.43	If Reductions:
10.87/4.43	The following If expression
10.87/4.43	"if p then return () else s"
10.87/4.43	is transformed to
10.87/4.43	"unless0 s True = return ();
10.87/4.43	unless0 s False = s;
10.87/4.43	"
10.87/4.43	
10.87/4.43	----------------------------------------
10.87/4.43	
10.87/4.43	(2)
10.87/4.43	Obligation:
10.87/4.43	mainModule Main 
10.87/4.43	module Maybe where {
10.87/4.43	import qualified Main;
10.87/4.43	import qualified Monad;
10.87/4.43	import qualified Prelude;
10.87/4.43	}
10.87/4.43	module Main where {
10.87/4.43	import qualified Maybe;
10.87/4.43	import qualified Monad;
10.87/4.43	import qualified Prelude;
10.87/4.43	}
10.87/4.43	module Monad where {
10.87/4.43	import qualified Main;
10.87/4.43	import qualified Maybe;
10.87/4.43	import qualified Prelude;
10.87/4.43	unless :: Monad a => Bool  ->  a ()  ->  a ();
10.87/4.43	unless p s = unless0 s p;
10.87/4.43	
10.87/4.43	unless0 s True = return ();
10.87/4.43	unless0 s False = s;
10.87/4.43	
10.87/4.43	}
10.87/4.43	
10.87/4.43	----------------------------------------
10.87/4.43	
10.87/4.43	(3) BR (EQUIVALENT)
10.87/4.43	Replaced joker patterns by fresh variables and removed binding patterns.
10.87/4.43	----------------------------------------
10.87/4.43	
10.87/4.43	(4)
10.87/4.43	Obligation:
10.87/4.43	mainModule Main 
10.87/4.43	module Maybe where {
10.87/4.43	import qualified Main;
10.87/4.43	import qualified Monad;
10.87/4.43	import qualified Prelude;
10.87/4.43	}
10.87/4.43	module Main where {
10.87/4.43	import qualified Maybe;
10.87/4.43	import qualified Monad;
10.87/4.43	import qualified Prelude;
10.87/4.43	}
10.87/4.43	module Monad where {
10.87/4.43	import qualified Main;
10.87/4.43	import qualified Maybe;
10.87/4.43	import qualified Prelude;
10.87/4.43	unless :: Monad a => Bool  ->  a ()  ->  a ();
10.87/4.43	unless p s = unless0 s p;
10.87/4.43	
10.87/4.43	unless0 s True = return ();
10.87/4.43	unless0 s False = s;
10.87/4.43	
10.87/4.43	}
10.87/4.43	
10.87/4.43	----------------------------------------
10.87/4.43	
10.87/4.43	(5) COR (EQUIVALENT)
10.87/4.43	Cond Reductions:
10.87/4.43	The following Function with conditions
10.87/4.43	"undefined |Falseundefined;
10.87/4.43	"
10.87/4.43	is transformed to
10.87/4.43	"undefined  = undefined1;
10.87/4.43	"
10.87/4.43	"undefined0 True = undefined;
10.87/4.43	"
10.87/4.43	"undefined1  = undefined0 False;
10.87/4.43	"
10.87/4.43	
10.87/4.43	----------------------------------------
10.87/4.43	
10.87/4.43	(6)
10.87/4.43	Obligation:
10.87/4.43	mainModule Main 
10.87/4.43	module Maybe where {
10.87/4.43	import qualified Main;
10.87/4.43	import qualified Monad;
10.87/4.43	import qualified Prelude;
10.87/4.43	}
10.87/4.43	module Main where {
10.87/4.43	import qualified Maybe;
10.87/4.43	import qualified Monad;
10.87/4.43	import qualified Prelude;
10.87/4.43	}
10.87/4.43	module Monad where {
10.87/4.43	import qualified Main;
10.87/4.43	import qualified Maybe;
10.87/4.43	import qualified Prelude;
10.87/4.43	unless :: Monad a => Bool  ->  a ()  ->  a ();
10.87/4.43	unless p s = unless0 s p;
10.87/4.43	
10.87/4.43	unless0 s True = return ();
10.87/4.43	unless0 s False = s;
10.87/4.43	
10.87/4.43	}
10.87/4.43	
10.87/4.43	----------------------------------------
10.87/4.43	
10.87/4.43	(7) Narrow (EQUIVALENT)
10.87/4.43	Haskell To QDPs
10.87/4.43	
10.87/4.43	digraph dp_graph {
10.87/4.43	node [outthreshold=100, inthreshold=100];1[label="Monad.unless",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.87/4.43	3[label="Monad.unless vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.87/4.43	4[label="Monad.unless vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
10.87/4.43	5[label="Monad.unless0 vy4 vy3",fontsize=16,color="burlywood",shape="box"];17[label="vy3/False",fontsize=10,color="white",style="solid",shape="box"];5 -> 17[label="",style="solid", color="burlywood", weight=9];
10.87/4.43	17 -> 6[label="",style="solid", color="burlywood", weight=3];
10.87/4.43	18[label="vy3/True",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
10.87/4.43	18 -> 7[label="",style="solid", color="burlywood", weight=3];
10.87/4.43	6[label="Monad.unless0 vy4 False",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
10.87/4.43	7[label="Monad.unless0 vy4 True",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
10.87/4.43	8[label="vy4",fontsize=16,color="green",shape="box"];9[label="return ()",fontsize=16,color="blue",shape="box"];19[label="return :: () -> IO ()",fontsize=10,color="white",style="solid",shape="box"];9 -> 19[label="",style="solid", color="blue", weight=9];
10.87/4.43	19 -> 10[label="",style="solid", color="blue", weight=3];
10.87/4.43	20[label="return :: () -> [] ()",fontsize=10,color="white",style="solid",shape="box"];9 -> 20[label="",style="solid", color="blue", weight=9];
10.87/4.43	20 -> 11[label="",style="solid", color="blue", weight=3];
10.87/4.43	21[label="return :: () -> Maybe ()",fontsize=10,color="white",style="solid",shape="box"];9 -> 21[label="",style="solid", color="blue", weight=9];
10.87/4.43	21 -> 12[label="",style="solid", color="blue", weight=3];
10.87/4.43	10[label="return ()",fontsize=16,color="black",shape="box"];10 -> 13[label="",style="solid", color="black", weight=3];
10.87/4.43	11[label="return ()",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3];
10.87/4.43	12[label="return ()",fontsize=16,color="black",shape="box"];12 -> 15[label="",style="solid", color="black", weight=3];
10.87/4.43	13[label="primretIO ()",fontsize=16,color="black",shape="box"];13 -> 16[label="",style="solid", color="black", weight=3];
10.87/4.43	14[label="() : []",fontsize=16,color="green",shape="box"];15[label="Just ()",fontsize=16,color="green",shape="box"];16[label="AProVE_IO ()",fontsize=16,color="green",shape="box"];}
10.87/4.43	
10.87/4.43	----------------------------------------
10.87/4.43	
10.87/4.43	(8)
10.87/4.43	YES
10.91/4.52	EOF