YES

Problem:
 f(f(X)) -> f(a(b(f(X))))
 f(a(g(X))) -> b(X)
 b(X) -> a(X)

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {7,6,1}
   transitions:
    f0(2) -> 3*
    f0(5) -> 1*
    b0(3) -> 4*
    b0(2) -> 6*
    a1(10) -> 11*
    a1(12) -> 13*
    f40() -> 2*
    a0(4) -> 5*
    a0(2) -> 7*
    11 -> 6*
    2 -> 10*
    6 -> 3,12
    13 -> 4*
    1 -> 3,12
    3 -> 12*
  problem:
   
  Qed