NO

Problem:
 strict:
  a(b(c(x1))) -> c(x1)
 weak:
  c(x1) -> c(b(a(x1)))

Proof:
 Unfolding Processor:
  loop length: 2
  terms:
   c(b(c(x9)))
   c(b(a(b(c(x9)))))
  context: []
  substitution:
   x9 -> x9
  Qed