YES(?,O(n^1))

Problem:
 f(f(x)) -> g(f(x))
 g(g(x)) -> f(x)

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    f0(1) -> 2*
    g0(1) -> 3*
    f40() -> 1*
  problem:
   
  Qed