8.69/3.83	YES
10.50/4.30	proof of /export/starexec/sandbox/benchmark/theBenchmark.hs
10.50/4.30	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.50/4.30	
10.50/4.30	
10.50/4.30	H-Termination with start terms of the given HASKELL could be proven:
10.50/4.30	
10.50/4.30	(0) HASKELL
10.50/4.30	(1) BR [EQUIVALENT, 0 ms]
10.50/4.30	(2) HASKELL
10.50/4.30	(3) COR [EQUIVALENT, 0 ms]
10.50/4.30	(4) HASKELL
10.50/4.30	(5) Narrow [EQUIVALENT, 10 ms]
10.50/4.30	(6) YES
10.50/4.30	
10.50/4.30	
10.50/4.30	----------------------------------------
10.50/4.30	
10.50/4.30	(0)
10.50/4.30	Obligation:
10.50/4.30	mainModule Main 
10.50/4.30	module Maybe where {
10.50/4.30	import qualified Main;
10.50/4.30	import qualified Monad;
10.50/4.30	import qualified Prelude;
10.50/4.30	}
10.50/4.30	module Main where {
10.50/4.30	import qualified Maybe;
10.50/4.30	import qualified Monad;
10.50/4.30	import qualified Prelude;
10.50/4.30	}
10.50/4.30	module Monad where {
10.50/4.30	import qualified Main;
10.50/4.30	import qualified Maybe;
10.50/4.30	import qualified Prelude;
10.50/4.30	join :: Monad b => b (b a)  ->  b a;
10.50/4.30	join x = x >>= id;
10.50/4.30	
10.50/4.30	}
10.50/4.30	
10.50/4.30	----------------------------------------
10.50/4.30	
10.50/4.30	(1) BR (EQUIVALENT)
10.50/4.30	Replaced joker patterns by fresh variables and removed binding patterns.
10.50/4.30	----------------------------------------
10.50/4.30	
10.50/4.30	(2)
10.50/4.30	Obligation:
10.50/4.30	mainModule Main 
10.50/4.30	module Maybe where {
10.50/4.30	import qualified Main;
10.50/4.30	import qualified Monad;
10.50/4.30	import qualified Prelude;
10.50/4.30	}
10.50/4.30	module Main where {
10.50/4.30	import qualified Maybe;
10.50/4.30	import qualified Monad;
10.50/4.30	import qualified Prelude;
10.50/4.30	}
10.50/4.30	module Monad where {
10.50/4.30	import qualified Main;
10.50/4.30	import qualified Maybe;
10.50/4.30	import qualified Prelude;
10.50/4.30	join :: Monad a => a (a b)  ->  a b;
10.50/4.30	join x = x >>= id;
10.50/4.30	
10.50/4.30	}
10.50/4.30	
10.50/4.30	----------------------------------------
10.50/4.30	
10.50/4.30	(3) COR (EQUIVALENT)
10.50/4.30	Cond Reductions:
10.50/4.30	The following Function with conditions
10.50/4.30	"undefined |Falseundefined;
10.50/4.30	"
10.50/4.30	is transformed to
10.50/4.30	"undefined  = undefined1;
10.50/4.30	"
10.50/4.30	"undefined0 True = undefined;
10.50/4.30	"
10.50/4.30	"undefined1  = undefined0 False;
10.50/4.30	"
10.50/4.30	
10.50/4.30	----------------------------------------
10.50/4.30	
10.50/4.30	(4)
10.50/4.30	Obligation:
10.50/4.30	mainModule Main 
10.50/4.30	module Maybe where {
10.50/4.30	import qualified Main;
10.50/4.30	import qualified Monad;
10.50/4.30	import qualified Prelude;
10.50/4.30	}
10.50/4.30	module Main where {
10.50/4.30	import qualified Maybe;
10.50/4.30	import qualified Monad;
10.50/4.30	import qualified Prelude;
10.50/4.30	}
10.50/4.30	module Monad where {
10.50/4.30	import qualified Main;
10.50/4.30	import qualified Maybe;
10.50/4.30	import qualified Prelude;
10.50/4.30	join :: Monad a => a (a b)  ->  a b;
10.50/4.30	join x = x >>= id;
10.50/4.30	
10.50/4.30	}
10.50/4.30	
10.50/4.30	----------------------------------------
10.50/4.30	
10.50/4.30	(5) Narrow (EQUIVALENT)
10.50/4.30	Haskell To QDPs
10.50/4.30	
10.50/4.30	digraph dp_graph {
10.50/4.30	node [outthreshold=100, inthreshold=100];1[label="Monad.join",fontsize=16,color="grey",shape="box"];1 -> 3[label="",style="dashed", color="grey", weight=3];
10.50/4.30	3[label="Monad.join vy3",fontsize=16,color="black",shape="triangle"];3 -> 4[label="",style="solid", color="black", weight=3];
10.50/4.30	4[label="vy3 >>= id",fontsize=16,color="black",shape="box"];4 -> 5[label="",style="solid", color="black", weight=3];
10.50/4.30	5[label="primbindIO vy3 id",fontsize=16,color="burlywood",shape="box"];15[label="vy3/IO vy30",fontsize=10,color="white",style="solid",shape="box"];5 -> 15[label="",style="solid", color="burlywood", weight=9];
10.50/4.30	15 -> 6[label="",style="solid", color="burlywood", weight=3];
10.50/4.30	16[label="vy3/AProVE_IO vy30",fontsize=10,color="white",style="solid",shape="box"];5 -> 16[label="",style="solid", color="burlywood", weight=9];
10.50/4.30	16 -> 7[label="",style="solid", color="burlywood", weight=3];
10.50/4.30	17[label="vy3/AProVE_Exception vy30",fontsize=10,color="white",style="solid",shape="box"];5 -> 17[label="",style="solid", color="burlywood", weight=9];
10.50/4.31	17 -> 8[label="",style="solid", color="burlywood", weight=3];
10.50/4.31	18[label="vy3/AProVE_Error vy30",fontsize=10,color="white",style="solid",shape="box"];5 -> 18[label="",style="solid", color="burlywood", weight=9];
10.50/4.31	18 -> 9[label="",style="solid", color="burlywood", weight=3];
10.50/4.31	6[label="primbindIO (IO vy30) id",fontsize=16,color="black",shape="box"];6 -> 10[label="",style="solid", color="black", weight=3];
10.50/4.31	7[label="primbindIO (AProVE_IO vy30) id",fontsize=16,color="black",shape="box"];7 -> 11[label="",style="solid", color="black", weight=3];
10.50/4.31	8[label="primbindIO (AProVE_Exception vy30) id",fontsize=16,color="black",shape="box"];8 -> 12[label="",style="solid", color="black", weight=3];
10.50/4.31	9[label="primbindIO (AProVE_Error vy30) id",fontsize=16,color="black",shape="box"];9 -> 13[label="",style="solid", color="black", weight=3];
10.50/4.31	10[label="error []",fontsize=16,color="red",shape="box"];11[label="id vy30",fontsize=16,color="black",shape="box"];11 -> 14[label="",style="solid", color="black", weight=3];
10.50/4.31	12[label="AProVE_Exception vy30",fontsize=16,color="green",shape="box"];13[label="AProVE_Error vy30",fontsize=16,color="green",shape="box"];14[label="vy30",fontsize=16,color="green",shape="box"];}
10.50/4.31	
10.50/4.31	----------------------------------------
10.50/4.31	
10.50/4.31	(6)
10.50/4.31	YES
10.64/4.35	EOF