NO

Problem:
 b() -> a()
 b() -> c()
 c() -> h(b())
 c() -> d()
 a() -> h(a())
 d() -> h(d())

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