YES(?,O(n^1))

Problem:
 f(f(x1)) -> b(b(b(x1)))
 a(f(x1)) -> f(a(a(x1)))
 b(b(x1)) -> c(c(a(c(x1))))
 d(b(x1)) -> d(a(b(x1)))
 c(c(x1)) -> d(d(d(x1)))
 b(d(x1)) -> d(b(x1))
 c(d(d(x1))) -> f(x1)

Proof:
 Bounds Processor:
  bound: 0
  enrichment: match
  automaton:
   final states: {6,5,4,3,2}
   transitions:
    f0(1) -> 2*
    b0(1) -> 4*
    a0(1) -> 3*
    c0(1) -> 6*
    d0(1) -> 5*
    f100() -> 1*
  problem:
   
  Qed