YES

Problem:
 a(b(x)) -> a(c(b(x)))

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4}
   transitions:
    a1(11) -> 12*
    c1(10) -> 11*
    b1(9) -> 10*
    a0(4) -> 4*
    b0(4) -> 4*
    c0(4) -> 4*
    4 -> 9*
    12 -> 4*
  problem:
   
  Qed