8.98/9.10	MAYBE
8.98/9.10	We consider the system theBenchmark.
8.98/9.10	
8.98/9.10	  Alphabet:
8.98/9.10	
8.98/9.10	    a : [] --> o 
8.98/9.10	    b : [] --> o 
8.98/9.10	    f : [o * o] --> o 
8.98/9.10	    g : [] --> o -> o -> o 
8.98/9.10	
8.98/9.10	  Rules:
8.98/9.10	
8.98/9.10	    f((/\x.h x) a, i a) => g (h b) (i (h b)) 
8.98/9.10	
8.98/9.10	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.
8.98/9.10	
8.98/9.10	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:
8.98/9.10	
8.98/9.10	  Alphabet:
8.98/9.10	
8.98/9.10	    a : [] --> o 
8.98/9.10	    b : [] --> o 
8.98/9.10	    f : [o * o] --> o 
8.98/9.10	    g : [o] --> o -> o 
8.98/9.10	    ~AP1 : [o -> o * o] --> o 
8.98/9.10	
8.98/9.10	  Rules:
8.98/9.10	
8.98/9.10	    f(~AP1(/\x.~AP1(F, x), a), ~AP1(G, a)) => ~AP1(g(~AP1(F, b)), ~AP1(G, ~AP1(F, b))) 
8.98/9.10	    ~AP1(F, X) => F X 
8.98/9.10	
8.98/9.10	
8.98/9.10	+++ Citations +++
8.98/9.10	
8.98/9.10	[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.
8.98/9.11	EOF