YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    a1(19) -> 20*
    a1(13) -> 14*
    b1(5) -> 6*
    b1(11) -> 12*
    a2(27) -> 28*
    a2(21) -> 22*
    f0(2) -> 3*
    f0(1) -> 3*
    a0(2) -> 1*
    a0(1) -> 1*
    b0(2) -> 4*
    b0(1) -> 4*
    g0(2) -> 2*
    g0(1) -> 2*
    1 -> 13,11
    2 -> 19,5
    5 -> 27*
    6 -> 3*
    11 -> 21*
    12 -> 3*
    14 -> 4*
    20 -> 4*
    22 -> 12*
    28 -> 6,3
  problem:
   
  Qed