NO

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

Proof:
 Containment Processor: loop length: 1
                        terms:
                         g(x)
                        context: f(x,c(),[])
                        substitution:
                         x -> c()
  Qed