YES(?,O(n^1))

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {4,3}
   transitions:
    a1(22) -> 23*
    a1(7) -> 8*
    b1(21) -> 22*
    b1(8) -> 9*
    A1(20) -> 21*
    A1(5) -> 6*
    A1(17) -> 18*
    B1(19) -> 20*
    B1(31) -> 32*
    B1(6) -> 7*
    A0(2) -> 3*
    A0(1) -> 3*
    b0(2) -> 1*
    b0(1) -> 1*
    a0(2) -> 2*
    a0(1) -> 2*
    B0(2) -> 4*
    B0(1) -> 4*
    1 -> 7,21,32,20,6,4,3,31,17
    2 -> 7,21,32,20,6,4,3,19,5
    8 -> 7*
    9 -> 21,18,6,3
    18 -> 6*
    22 -> 21*
    23 -> 7,20,4
    32 -> 20*
  problem:
   
  Qed