YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {3,2}
   transitions:
    b1(4) -> 5*
    a0(1) -> 2*
    b0(1) -> 3*
    f40() -> 1*
    1 -> 4*
    5 -> 2*
  problem:
   
  Qed