NO

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

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