YES

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

Proof:
 String Reversal Processor:
  b(b(b(a(a(a(x1)))))) -> a(a(a(a(b(b(b(b(x1))))))))
  Bounds Processor:
   bound: 1
   enrichment: match
   automaton:
    final states: {1}
    transitions:
     a1(34) -> 35*
     a1(23) -> 24*
     a1(25) -> 26*
     a1(32) -> 33*
     a1(35) -> 36*
     a1(33) -> 34*
     a1(26) -> 27*
     a1(24) -> 25*
     b1(21) -> 22*
     b1(30) -> 31*
     b1(20) -> 21*
     b1(31) -> 32*
     b1(29) -> 30*
     b1(22) -> 23*
     b1(28) -> 29*
     b1(19) -> 20*
     f20() -> 2*
     b0(3) -> 4*
     b0(4) -> 5*
     b0(2) -> 3*
     b0(5) -> 6*
     a0(6) -> 7*
     a0(7) -> 8*
     a0(9) -> 1*
     a0(8) -> 9*
     27 -> 6*
     7 -> 19*
     36 -> 22*
     1 -> 3,4,5
     25 -> 28*
   problem:
    
   Qed