YES

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

Proof:
 String Reversal Processor:
  f(f(X)) -> f(b(a(f(X))))
  g(a(f(X))) -> b(X)
  b(X) -> a(X)
  Bounds Processor:
   bound: 1
   enrichment: match
   automaton:
    final states: {7,6,1}
    transitions:
     a0(2) -> 7*
     a0(3) -> 4*
     a1(14) -> 15*
     a1(8) -> 9*
     f40() -> 2*
     f0(5) -> 1*
     f0(2) -> 3*
     b0(2) -> 6*
     b0(4) -> 5*
     1 -> 3*
     2 -> 14*
     4 -> 8*
     9 -> 5*
     15 -> 6*
   problem:
    
   Qed