NO

Problem:
 f(a(),a()) -> g(f(a(),a()))
 a() -> b()
 f(b(),x) -> g(f(x,x))
 f(x,b()) -> g(f(x,x))

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