YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3}
   transitions:
    a1(20) -> 21*
    a1(9) -> 10*
    a1(4) -> 5*
    a1(8) -> 9*
    b1(5) -> 6*
    b1(7) -> 8*
    c1(6) -> 7*
    a0(2) -> 3*
    a0(1) -> 3*
    b0(2) -> 1*
    b0(1) -> 1*
    c0(2) -> 2*
    c0(1) -> 2*
    1 -> 20*
    2 -> 4*
    10 -> 5,3
    21 -> 5*
  problem:
   
  Qed