YES

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

Proof:
 String Reversal Processor:
  b(b(a(a(a(x1))))) -> a(a(a(a(a(b(b(b(b(b(x1))))))))))
  Bounds Processor:
   bound: 2
   enrichment: match
   automaton:
    final states: {1}
    transitions:
     a1(40) -> 41*
     a1(30) -> 31*
     a1(43) -> 44*
     a1(39) -> 40*
     a1(32) -> 33*
     a1(72) -> 73*
     a1(42) -> 43*
     a1(31) -> 32*
     a1(74) -> 75*
     a1(28) -> 29*
     a1(73) -> 74*
     a1(76) -> 77*
     a1(29) -> 30*
     a1(41) -> 42*
     a1(75) -> 76*
     a2(119) -> 120*
     a2(116) -> 117*
     a2(120) -> 121*
     a2(85) -> 86*
     a2(127) -> 128*
     a2(129) -> 130*
     a2(130) -> 131*
     a2(118) -> 119*
     a2(83) -> 84*
     a2(87) -> 88*
     a2(86) -> 87*
     a2(84) -> 85*
     a2(131) -> 132*
     a2(128) -> 129*
     a2(117) -> 118*
     b1(68) -> 69*
     b1(67) -> 68*
     b1(69) -> 70*
     b1(36) -> 37*
     b1(71) -> 72*
     b1(35) -> 36*
     b1(27) -> 28*
     b1(34) -> 35*
     b1(25) -> 26*
     b1(38) -> 39*
     b1(26) -> 27*
     b1(24) -> 25*
     b1(23) -> 24*
     b1(70) -> 71*
     b1(37) -> 38*
     f20() -> 2*
     b0(3) -> 4*
     b0(4) -> 5*
     b0(6) -> 7*
     b0(2) -> 3*
     b0(5) -> 6*
     a0(10) -> 11*
     a0(7) -> 8*
     a0(9) -> 10*
     a0(8) -> 9*
     a0(11) -> 1*
     b2(122) -> 123*
     b2(115) -> 116*
     b2(80) -> 81*
     b2(111) -> 112*
     b2(113) -> 114*
     b2(82) -> 83*
     b2(79) -> 80*
     b2(125) -> 126*
     b2(112) -> 113*
     b2(78) -> 79*
     b2(123) -> 124*
     b2(81) -> 82*
     b2(126) -> 127*
     b2(124) -> 125*
     b2(114) -> 115*
     43 -> 67*
     74 -> 78*
     132 -> 71*
     30 -> 34*
     77 -> 25*
     118 -> 122*
     88 -> 27*
     121 -> 69*
     44 -> 7*
     40 -> 111*
     1 -> 3,4
     9 -> 23*
     33 -> 5,6
   problem:
    
   Qed