8.88/3.81	YES
10.55/4.34	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.55/4.34	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.55/4.34	
10.55/4.34	
10.55/4.34	H-Termination with start terms of the given HASKELL could be proven:
10.55/4.34	
10.55/4.34	(0) HASKELL
10.55/4.34	(1) IFR [EQUIVALENT, 0 ms]
10.55/4.34	(2) HASKELL
10.55/4.34	(3) BR [EQUIVALENT, 0 ms]
10.55/4.34	(4) HASKELL
10.55/4.34	(5) COR [EQUIVALENT, 0 ms]
10.55/4.34	(6) HASKELL
10.55/4.34	(7) Narrow [EQUIVALENT, 25 ms]
10.55/4.34	(8) YES
10.55/4.34	
10.55/4.34	
10.55/4.34	----------------------------------------
10.55/4.34	
10.55/4.34	(0)
10.55/4.34	Obligation:
10.55/4.34	mainModule Main 
10.55/4.34	module Maybe where {
10.55/4.34	import qualified Main;
10.55/4.34	import qualified Monad;
10.55/4.34	import qualified Prelude;
10.55/4.34	}
10.55/4.34	module Main where {
10.55/4.34	import qualified Maybe;
10.55/4.34	import qualified Monad;
10.55/4.34	import qualified Prelude;
10.55/4.34	}
10.55/4.34	module Monad where {
10.55/4.34	import qualified Main;
10.55/4.34	import qualified Maybe;
10.55/4.34	import qualified Prelude;
10.55/4.34	unless :: Monad a => Bool  ->  a ()  ->  a ();
10.55/4.34	unless p s =  if p then return () else s;
10.55/4.34	
10.55/4.34	}
10.55/4.34	
10.55/4.34	----------------------------------------
10.55/4.34	
10.55/4.34	(1) IFR (EQUIVALENT)
10.55/4.34	If Reductions:
10.55/4.34	The following If expression
10.55/4.34	"if p then return () else s"
10.55/4.34	is transformed to
10.55/4.34	"unless0 s True = return ();
10.55/4.34	unless0 s False = s;
10.55/4.34	"
10.55/4.34	
10.55/4.34	----------------------------------------
10.55/4.34	
10.55/4.34	(2)
10.55/4.34	Obligation:
10.55/4.34	mainModule Main 
10.55/4.34	module Maybe where {
10.55/4.34	import qualified Main;
10.55/4.34	import qualified Monad;
10.55/4.34	import qualified Prelude;
10.55/4.34	}
10.55/4.34	module Main where {
10.55/4.34	import qualified Maybe;
10.55/4.34	import qualified Monad;
10.55/4.34	import qualified Prelude;
10.55/4.34	}
10.55/4.34	module Monad where {
10.55/4.34	import qualified Main;
10.55/4.34	import qualified Maybe;
10.55/4.34	import qualified Prelude;
10.55/4.34	unless :: Monad a => Bool  ->  a ()  ->  a ();
10.55/4.34	unless p s = unless0 s p;
10.55/4.34	
10.55/4.34	unless0 s True = return ();
10.55/4.34	unless0 s False = s;
10.55/4.34	
10.55/4.34	}
10.55/4.34	
10.55/4.34	----------------------------------------
10.55/4.34	
10.55/4.34	(3) BR (EQUIVALENT)
10.55/4.34	Replaced joker patterns by fresh variables and removed binding patterns.
10.55/4.34	----------------------------------------
10.55/4.34	
10.55/4.34	(4)
10.55/4.34	Obligation:
10.55/4.34	mainModule Main 
10.55/4.34	module Maybe where {
10.55/4.34	import qualified Main;
10.55/4.34	import qualified Monad;
10.55/4.34	import qualified Prelude;
10.55/4.34	}
10.55/4.34	module Main where {
10.55/4.34	import qualified Maybe;
10.55/4.34	import qualified Monad;
10.55/4.34	import qualified Prelude;
10.55/4.34	}
10.55/4.34	module Monad where {
10.55/4.34	import qualified Main;
10.55/4.34	import qualified Maybe;
10.55/4.34	import qualified Prelude;
10.55/4.34	unless :: Monad a => Bool  ->  a ()  ->  a ();
10.55/4.34	unless p s = unless0 s p;
10.55/4.34	
10.55/4.34	unless0 s True = return ();
10.55/4.34	unless0 s False = s;
10.55/4.34	
10.55/4.34	}
10.55/4.34	
10.55/4.34	----------------------------------------
10.55/4.34	
10.55/4.34	(5) COR (EQUIVALENT)
10.55/4.34	Cond Reductions:
10.55/4.34	The following Function with conditions
10.55/4.34	"undefined |Falseundefined;
10.55/4.34	"
10.55/4.34	is transformed to
10.55/4.34	"undefined  = undefined1;
10.55/4.34	"
10.55/4.34	"undefined0 True = undefined;
10.55/4.34	"
10.55/4.34	"undefined1  = undefined0 False;
10.55/4.34	"
10.55/4.34	
10.55/4.34	----------------------------------------
10.55/4.34	
10.55/4.34	(6)
10.55/4.34	Obligation:
10.55/4.34	mainModule Main 
10.55/4.34	module Maybe where {
10.55/4.34	import qualified Main;
10.55/4.34	import qualified Monad;
10.55/4.34	import qualified Prelude;
10.55/4.34	}
10.55/4.34	module Main where {
10.55/4.34	import qualified Maybe;
10.55/4.34	import qualified Monad;
10.55/4.34	import qualified Prelude;
10.55/4.34	}
10.55/4.34	module Monad where {
10.55/4.34	import qualified Main;
10.55/4.34	import qualified Maybe;
10.55/4.34	import qualified Prelude;
10.55/4.34	unless :: Monad a => Bool  ->  a ()  ->  a ();
10.55/4.34	unless p s = unless0 s p;
10.55/4.34	
10.55/4.34	unless0 s True = return ();
10.55/4.34	unless0 s False = s;
10.55/4.34	
10.55/4.34	}
10.55/4.34	
10.55/4.34	----------------------------------------
10.55/4.34	
10.55/4.34	(7) Narrow (EQUIVALENT)
10.55/4.34	Haskell To QDPs
10.55/4.34	
10.55/4.34	digraph dp_graph {
10.55/4.34	node [outthreshold=100, inthreshold=100];1[label="Monad.unless",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.55/4.34	3[label="Monad.unless vy3",fontsize=16,color="grey",shape="box"];3 -> 4[label="",style="dashed", color="grey", weight=3];
10.55/4.34	4[label="Monad.unless vy3 vy4",fontsize=16,color="black",shape="triangle"];4 -> 5[label="",style="solid", color="black", weight=3];
10.55/4.34	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];
10.55/4.34	11 -> 6[label="",style="solid", color="burlywood", weight=3];
10.55/4.34	12[label="vy3/True",fontsize=10,color="white",style="solid",shape="box"];5 -> 12[label="",style="solid", color="burlywood", weight=9];
10.55/4.34	12 -> 7[label="",style="solid", color="burlywood", weight=3];
10.55/4.34	6[label="Monad.unless0 vy4 False",fontsize=16,color="black",shape="box"];6 -> 8[label="",style="solid", color="black", weight=3];
10.55/4.34	7[label="Monad.unless0 vy4 True",fontsize=16,color="black",shape="box"];7 -> 9[label="",style="solid", color="black", weight=3];
10.55/4.34	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];
10.55/4.34	10[label="Just ()",fontsize=16,color="green",shape="box"];}
10.55/4.34	
10.55/4.34	----------------------------------------
10.55/4.34	
10.55/4.34	(8)
10.55/4.34	YES
10.89/4.37	EOF