YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {7,6,5,4,3,2}
   transitions:
    b1(12) -> 13*
    a1(10) -> 11*
    a2(18) -> 19*
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 4*
    d0(1) -> 5*
    f0(1) -> 6*
    g0(1) -> 7*
    f120() -> 1*
    1 -> 12,10
    11 -> 3*
    12 -> 18*
    13 -> 5*
    19 -> 13,5
  problem:
   
  Qed