9.27/3.81	YES
11.03/4.35	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
11.03/4.35	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
11.03/4.35	
11.03/4.35	
11.03/4.35	H-Termination with start terms of the given HASKELL could be proven:
11.03/4.35	
11.03/4.35	(0) HASKELL
11.03/4.35	(1) IFR [EQUIVALENT, 0 ms]
11.03/4.35	(2) HASKELL
11.03/4.35	(3) BR [EQUIVALENT, 0 ms]
11.03/4.35	(4) HASKELL
11.03/4.35	(5) COR [EQUIVALENT, 0 ms]
11.03/4.35	(6) HASKELL
11.03/4.35	(7) Narrow [EQUIVALENT, 14 ms]
11.03/4.35	(8) YES
11.03/4.35	
11.03/4.35	
11.03/4.35	----------------------------------------
11.03/4.35	
11.03/4.35	(0)
11.03/4.35	Obligation:
11.03/4.35	mainModule Main 
11.03/4.35	module Maybe where {
11.03/4.35	import qualified Main;
11.03/4.35	import qualified Monad;
11.03/4.35	import qualified Prelude;
11.03/4.35	}
11.03/4.35	module Main where {
11.03/4.35	import qualified Maybe;
11.03/4.35	import qualified Monad;
11.03/4.35	import qualified Prelude;
11.03/4.35	}
11.03/4.35	module Monad where {
11.03/4.35	import qualified Main;
11.03/4.35	import qualified Maybe;
11.03/4.35	import qualified Prelude;
11.03/4.35	unless :: Monad a => Bool  ->  a ()  ->  a ();
11.03/4.35	unless p s =  if p then return () else s;
11.03/4.35	
11.03/4.35	}
11.03/4.35	
11.03/4.35	----------------------------------------
11.03/4.35	
11.03/4.35	(1) IFR (EQUIVALENT)
11.03/4.35	If Reductions:
11.03/4.35	The following If expression
11.03/4.35	"if p then return () else s"
11.03/4.35	is transformed to
11.03/4.35	"unless0 s True = return ();
11.03/4.35	unless0 s False = s;
11.03/4.35	"
11.03/4.35	
11.03/4.35	----------------------------------------
11.03/4.35	
11.03/4.35	(2)
11.03/4.35	Obligation:
11.03/4.35	mainModule Main 
11.03/4.35	module Maybe where {
11.03/4.35	import qualified Main;
11.03/4.35	import qualified Monad;
11.03/4.35	import qualified Prelude;
11.03/4.35	}
11.03/4.35	module Main where {
11.03/4.35	import qualified Maybe;
11.03/4.35	import qualified Monad;
11.03/4.35	import qualified Prelude;
11.03/4.35	}
11.03/4.35	module Monad where {
11.03/4.35	import qualified Main;
11.03/4.35	import qualified Maybe;
11.03/4.35	import qualified Prelude;
11.03/4.35	unless :: Monad a => Bool  ->  a ()  ->  a ();
11.03/4.35	unless p s = unless0 s p;
11.03/4.35	
11.03/4.35	unless0 s True = return ();
11.03/4.35	unless0 s False = s;
11.03/4.35	
11.03/4.35	}
11.03/4.35	
11.03/4.35	----------------------------------------
11.03/4.35	
11.03/4.35	(3) BR (EQUIVALENT)
11.03/4.35	Replaced joker patterns by fresh variables and removed binding patterns.
11.03/4.35	----------------------------------------
11.03/4.35	
11.03/4.35	(4)
11.03/4.35	Obligation:
11.03/4.35	mainModule Main 
11.03/4.35	module Maybe where {
11.03/4.35	import qualified Main;
11.03/4.35	import qualified Monad;
11.03/4.35	import qualified Prelude;
11.03/4.35	}
11.03/4.35	module Main where {
11.03/4.35	import qualified Maybe;
11.03/4.35	import qualified Monad;
11.03/4.35	import qualified Prelude;
11.03/4.35	}
11.03/4.35	module Monad where {
11.03/4.35	import qualified Main;
11.03/4.35	import qualified Maybe;
11.03/4.35	import qualified Prelude;
11.03/4.35	unless :: Monad a => Bool  ->  a ()  ->  a ();
11.03/4.35	unless p s = unless0 s p;
11.03/4.35	
11.03/4.35	unless0 s True = return ();
11.03/4.35	unless0 s False = s;
11.03/4.35	
11.03/4.35	}
11.03/4.35	
11.03/4.35	----------------------------------------
11.03/4.35	
11.03/4.35	(5) COR (EQUIVALENT)
11.03/4.35	Cond Reductions:
11.03/4.35	The following Function with conditions
11.03/4.35	"undefined |Falseundefined;
11.03/4.35	"
11.03/4.35	is transformed to
11.03/4.35	"undefined  = undefined1;
11.03/4.35	"
11.03/4.35	"undefined0 True = undefined;
11.03/4.35	"
11.03/4.35	"undefined1  = undefined0 False;
11.03/4.35	"
11.03/4.35	
11.03/4.35	----------------------------------------
11.03/4.35	
11.03/4.35	(6)
11.03/4.35	Obligation:
11.03/4.35	mainModule Main 
11.03/4.35	module Maybe where {
11.03/4.35	import qualified Main;
11.03/4.35	import qualified Monad;
11.03/4.35	import qualified Prelude;
11.03/4.35	}
11.03/4.35	module Main where {
11.03/4.35	import qualified Maybe;
11.03/4.35	import qualified Monad;
11.03/4.35	import qualified Prelude;
11.03/4.35	}
11.03/4.35	module Monad where {
11.03/4.35	import qualified Main;
11.03/4.35	import qualified Maybe;
11.03/4.35	import qualified Prelude;
11.03/4.35	unless :: Monad a => Bool  ->  a ()  ->  a ();
11.03/4.35	unless p s = unless0 s p;
11.03/4.35	
11.03/4.35	unless0 s True = return ();
11.03/4.35	unless0 s False = s;
11.03/4.35	
11.03/4.35	}
11.03/4.35	
11.03/4.35	----------------------------------------
11.03/4.35	
11.03/4.35	(7) Narrow (EQUIVALENT)
11.03/4.35	Haskell To QDPs
11.03/4.35	
11.03/4.35	digraph dp_graph {
11.03/4.35	node [outthreshold=100, inthreshold=100];1[label="Monad.unless",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
11.03/4.35	3[label="Monad.unless vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
11.03/4.35	4[label="Monad.unless vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
11.03/4.35	5[label="Monad.unless0 vy4 vy3",fontsize=16,color="burlywood",shape="box"];11[label="vy3/False",fontsize=10,color="white",style="solid",shape="box"];5 -> 11[label="",style="solid", color="burlywood", weight=9];
11.03/4.35	11 -> 6[label="",style="solid", color="burlywood", weight=3];
11.03/4.35	12[label="vy3/True",fontsize=10,color="white",style="solid",shape="box"];5 -> 12[label="",style="solid", color="burlywood", weight=9];
11.03/4.35	12 -> 7[label="",style="solid", color="burlywood", weight=3];
11.03/4.35	6[label="Monad.unless0 vy4 False",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
11.03/4.35	7[label="Monad.unless0 vy4 True",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
11.03/4.35	8[label="vy4",fontsize=16,color="green",shape="box"];9[label="return ()",fontsize=16,color="black",shape="box"];9 -> 10[label="",style="solid", color="black", weight=3];
11.03/4.35	10[label="() : []",fontsize=16,color="green",shape="box"];}
11.03/4.35	
11.03/4.35	----------------------------------------
11.03/4.35	
11.03/4.35	(8)
11.03/4.35	YES
11.33/4.39	EOF