NO

Problem:
 g(f(a())) -> f(g(f(a())))
 g(f(a())) -> f(f(a()))
 f(f(a())) -> f(a())

Proof:
 Containment Processor: loop length: 1
                        terms:
                         g(f(a()))
                        context: f([])
                        substitution:
                         
  Qed