MAYBE
We consider the system theBenchmark.

  Alphabet:

    a : [] --> o 
    b : [] --> o 
    f : [o * o] --> o 
    g : [] --> o -> o -> o 

  Rules:

    f((/\x.h x) a, i a) => g (h b) (i (h b)) 

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.

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:

  Alphabet:

    a : [] --> o 
    b : [] --> o 
    f : [o * o] --> o 
    g : [o] --> o -> o 
    ~AP1 : [o -> o * o] --> o 

  Rules:

    f(~AP1(/\x.~AP1(F, x), a), ~AP1(G, a)) => ~AP1(g(~AP1(F, b)), ~AP1(G, ~AP1(F, b))) 
    ~AP1(F, X) => F X 


+++ Citations +++

[Kop11]  C. Kop.  Simplifying Algebraic Functional Systems.  In Proceedings of CAI 2011, volume 6742 of LNCS.  201--215, Springer, 2011.