We consider the system app.

  Alphabet:

    fapp : [a -> b * a] --> b 

  Rules:

    fapp(f, x) => f x 

This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0).

Symbol fapp is an encoding for application that is only used in innocuous ways.  We can simplify the program (without losing non-termination) by removing it.  This gives:

  Alphabet:


  Rules: