0.75/0.85	MAYBE
0.75/0.85	We consider the system theBenchmark.
0.75/0.85	
0.75/0.85	  Alphabet:
0.75/0.85	
0.75/0.85	    0 : [] --> a 
0.75/0.85	    rec : [] --> (b -> (a -> c) -> a -> c) -> c -> a -> c 
0.75/0.85	    s : [] --> b -> b 
0.75/0.85	
0.75/0.85	  Rules:
0.75/0.85	
0.75/0.85	    rec f (g 0) => g 
0.75/0.85	    rec f (g (s x)) => f x (rec f (g x)) 
0.75/0.85	
0.75/0.85	Using the transformations described in [Kop11], this system can be brought in a form without leading free variables in the left-hand side, and where the left-hand side of a variable is always a functional term or application headed by a functional term.
0.75/0.85	
0.75/0.85	We now transform the resulting AFS into an AFSM by replacing all free variables by meta-variables (with arity 0).  This leads to the following AFSM:
0.75/0.85	
0.75/0.85	  Alphabet:
0.75/0.85	
0.75/0.85	    0 : [] --> a 
0.75/0.85	    rec : [b -> (a -> c) -> a -> c * c] --> a -> c 
0.75/0.85	    s : [b] --> b 
0.75/0.85	    ~AP1 : [a -> c * a] --> c 
0.75/0.85	    ~AP2 : [b -> c * b] --> c 
0.75/0.85	
0.75/0.85	  Rules:
0.75/0.85	
0.75/0.85	    rec(F, ~AP1(G, 0)) => G 
0.75/0.85	    rec(F, ~AP2(G, s(X))) => F X rec(F, ~AP2(G, X)) 
0.75/0.85	    ~AP1(F, X) => F X 
0.75/0.85	    ~AP2(F, X) => F X 
0.75/0.85	
0.75/0.85	
0.75/0.85	+++ Citations +++
0.75/0.85	
0.75/0.85	[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.
0.75/0.85	EOF