YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {5,4,3,2}
   transitions:
    f1(16) -> 17*
    d1(6) -> 7*
    d1(8) -> 9*
    c1(7) -> 8*
    a0(1) -> 2*
    b0(1) -> 3*
    d0(1) -> 1*
    c0(1) -> 4*
    f0(1) -> 5*
    1 -> 16,6
    9 -> 2*
    17 -> 8,4
  problem:
   
  Qed