YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {5,4,3,2}
   transitions:
    c1(12) -> 13*
    a1(10) -> 11*
    a1(9) -> 10*
    a2(20) -> 21*
    a2(19) -> 20*
    a0(1) -> 2*
    b0(1) -> 3*
    c0(1) -> 4*
    d0(1) -> 5*
    f80() -> 1*
    1 -> 12,9
    11 -> 4*
    12 -> 19*
    13 -> 5*
    21 -> 13,5
  problem:
   
  Qed