7.53/3.43	YES
9.22/3.88	proof of /export/starexec/sandbox2/benchmark/theBenchmark.hs
9.22/3.88	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
9.22/3.88	
9.22/3.88	
9.22/3.88	H-Termination with start terms of the given HASKELL could be proven:
9.22/3.88	
9.22/3.88	(0) HASKELL
9.22/3.88	(1) BR [EQUIVALENT, 0 ms]
9.22/3.88	(2) HASKELL
9.22/3.88	(3) COR [EQUIVALENT, 0 ms]
9.22/3.88	(4) HASKELL
9.22/3.88	(5) Narrow [EQUIVALENT, 0 ms]
9.22/3.88	(6) YES
9.22/3.88	
9.22/3.88	
9.22/3.88	----------------------------------------
9.22/3.88	
9.22/3.88	(0)
9.22/3.88	Obligation:
9.22/3.88	mainModule Main 
9.22/3.88	module Main where {
9.22/3.88	import qualified Prelude;
9.22/3.88	import qualified Queue;
9.22/3.88	}
9.22/3.88	module Queue where {
9.22/3.88	import qualified Main;
9.22/3.88	import qualified Prelude;
9.22/3.88	data Queue a = Q [a] [a] [a] ;
9.22/3.88	
9.22/3.88	emptyQueue :: Queue a;
9.22/3.88	emptyQueue = Q [] [] [];
9.22/3.88	
9.22/3.88	}
9.22/3.88	
9.22/3.88	----------------------------------------
9.22/3.88	
9.22/3.88	(1) BR (EQUIVALENT)
9.22/3.88	Replaced joker patterns by fresh variables and removed binding patterns.
9.22/3.88	----------------------------------------
9.22/3.88	
9.22/3.88	(2)
9.22/3.88	Obligation:
9.22/3.88	mainModule Main 
9.22/3.88	module Main where {
9.22/3.88	import qualified Prelude;
9.22/3.88	import qualified Queue;
9.22/3.88	}
9.22/3.88	module Queue where {
9.22/3.88	import qualified Main;
9.22/3.88	import qualified Prelude;
9.22/3.88	data Queue a = Q [a] [a] [a] ;
9.22/3.88	
9.22/3.88	emptyQueue :: Queue a;
9.22/3.88	emptyQueue = Q [] [] [];
9.22/3.88	
9.22/3.88	}
9.22/3.88	
9.22/3.88	----------------------------------------
9.22/3.88	
9.22/3.88	(3) COR (EQUIVALENT)
9.22/3.88	Cond Reductions:
9.22/3.88	The following Function with conditions
9.22/3.88	"undefined |Falseundefined;
9.22/3.88	"
9.22/3.88	is transformed to
9.22/3.88	"undefined  = undefined1;
9.22/3.88	"
9.22/3.88	"undefined0 True = undefined;
9.22/3.88	"
9.22/3.88	"undefined1  = undefined0 False;
9.22/3.88	"
9.22/3.88	
9.22/3.88	----------------------------------------
9.22/3.88	
9.22/3.88	(4)
9.22/3.88	Obligation:
9.22/3.88	mainModule Main 
9.22/3.88	module Main where {
9.22/3.88	import qualified Prelude;
9.22/3.88	import qualified Queue;
9.22/3.88	}
9.22/3.88	module Queue where {
9.22/3.88	import qualified Main;
9.22/3.88	import qualified Prelude;
9.22/3.88	data Queue a = Q [a] [a] [a] ;
9.22/3.88	
9.22/3.88	emptyQueue :: Queue a;
9.22/3.88	emptyQueue = Q [] [] [];
9.22/3.88	
9.22/3.88	}
9.22/3.88	
9.22/3.88	----------------------------------------
9.22/3.88	
9.22/3.88	(5) Narrow (EQUIVALENT)
9.22/3.88	Haskell To QDPs
9.22/3.88	
9.22/3.88	digraph dp_graph {
9.22/3.88	node [outthreshold=100, inthreshold=100];1[label="Queue.emptyQueue",fontsize=16,color="black",shape="box"];1 -> 3[label="",style="solid", color="black", weight=3];
9.22/3.88	3[label="Queue.Q [] [] []",fontsize=16,color="green",shape="box"];}
9.22/3.88	
9.22/3.88	----------------------------------------
9.22/3.88	
9.22/3.88	(6)
9.22/3.88	YES
9.34/3.92	EOF