NO

Problem:
 F(x) -> A()
 F(x) -> G(F(x))
 G(F(x)) -> F(H(x))
 G(F(x)) -> B()

Proof:
 Containment Processor: loop length: 1
                        terms:
                         F(x)
                        context: G([])
                        substitution:
                         x -> x
  Qed