0.00/0.00	NO
0.00/0.00	We consider the system theBenchmark.
0.00/0.00	
0.00/0.00	  Alphabet:
0.00/0.00	
0.00/0.00	    false : [] --> a 
0.00/0.00	    if : [a * b * b] --> b 
0.00/0.00	    true : [] --> a 
0.00/0.00	    until : [b -> a * b -> b * b] --> b 
0.00/0.00	
0.00/0.00	  Rules:
0.00/0.00	
0.00/0.00	    if(true, x, y) => x 
0.00/0.00	    if(false, x, y) => y 
0.00/0.00	    until(f, g, x) => if(f x, x, until(f, g, g x)) 
0.00/0.00	
0.00/0.00	This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0).
0.00/0.00	
0.00/0.00	It is easy to see that this system is non-terminating:
0.00/0.00	
0.00/0.00	  until(f, g, x) 
0.00/0.00	    => if(f x, x, until(f, g, g x)) 
0.00/0.00	    |> until(f, g, g x) 
0.00/0.00	
0.00/0.00	That is, a term s reduces to a term t which has a subterm that is an instance of the original term.
0.00/0.00	
0.00/0.00	EOF