YES

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

Proof:
 String Reversal Processor:
  b(b(a(a(x1)))) -> a(a(a(b(b(b(x1))))))
  Bounds Processor:
   bound: 3
   enrichment: match
   automaton:
    final states: {1}
    transitions:
     a1(32) -> 33*
     a1(12) -> 13*
     a1(34) -> 35*
     a1(11) -> 12*
     a1(33) -> 34*
     a1(13) -> 14*
     b1(30) -> 31*
     b1(10) -> 11*
     b1(29) -> 30*
     b1(9) -> 10*
     b1(31) -> 32*
     b1(8) -> 9*
     a2(60) -> 61*
     a2(40) -> 41*
     a2(62) -> 63*
     a2(39) -> 40*
     a2(61) -> 62*
     a2(41) -> 42*
     b2(57) -> 58*
     b2(37) -> 38*
     b2(59) -> 60*
     b2(36) -> 37*
     b2(58) -> 59*
     b2(38) -> 39*
     f20() -> 2*
     a3(67) -> 68*
     a3(69) -> 70*
     a3(68) -> 69*
     a0(5) -> 6*
     a0(7) -> 1*
     a0(6) -> 7*
     b3(65) -> 66*
     b3(64) -> 65*
     b3(66) -> 67*
     b0(2) -> 3*
     b0(4) -> 5*
     b0(3) -> 4*
     1 -> 3,4
     6 -> 8*
     11 -> 36*
     13 -> 29*
     14 -> 5*
     33 -> 57*
     35 -> 10*
     42 -> 31*
     61 -> 64*
     63 -> 37*
     70 -> 39*
   problem:
    
   Qed