YES

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

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