YES

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

Proof:
 String Reversal Processor:
  a(a(b(a(b(x1))))) -> a(b(a(b(a(b(b(a(a(x1)))))))))
  Bounds Processor:
   bound: 1
   enrichment: match
   automaton:
    final states: {1}
    transitions:
     a1(19) -> 20*
     a1(11) -> 12*
     a1(12) -> 13*
     a1(17) -> 18*
     a1(15) -> 16*
     b1(13) -> 14*
     b1(16) -> 17*
     b1(18) -> 19*
     b1(14) -> 15*
     f20() -> 2*
     b0(4) -> 5*
     b0(9) -> 10*
     b0(7) -> 8*
     b0(5) -> 6*
     a0(10) -> 1*
     a0(6) -> 7*
     a0(2) -> 3*
     a0(8) -> 9*
     a0(3) -> 4*
     7 -> 11*
     1 -> 3,4
     20 -> 4*
   problem:
    
   Qed