NO

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

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