YES

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

Proof:
 Bounds Processor:
  bound: 1
  enrichment: match-rt
  automaton:
   final states: {3}
   transitions:
    a0(3) -> 3*
    b0(3) -> 3*
    b1(11) -> 12*
    b1(14) -> 15*
    b1(26) -> 27*
    b1(24) -> 25*
    b1(25) -> 26*
    b1(10) -> 11*
    b1(20) -> 21*
    a1(9) -> 10*
    a1(12) -> 13*
    27 -> 25,3
    12 -> 20*
    21 -> 15*
    13 -> 10,14,3
    3 -> 24,9
    15 -> 11*
  problem:
   strict:
    
   weak:
    b(x1) -> b(b(b(x1)))
  Qed