YES

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

Proof:
 String Reversal Processor:
  b(b(a(a(x1)))) -> a(a(a(a(a(b(b(b(x1))))))))
  Bounds Processor:
   bound: 3
   enrichment: match
   automaton:
    final states: {1}
    transitions:
     a1(50) -> 51*
     a1(40) -> 41*
     a1(15) -> 16*
     a1(52) -> 53*
     a1(42) -> 43*
     a1(17) -> 18*
     a1(49) -> 50*
     a1(44) -> 45*
     a1(14) -> 15*
     a1(51) -> 52*
     a1(41) -> 42*
     a1(16) -> 17*
     a1(53) -> 54*
     a1(43) -> 44*
     a1(13) -> 14*
     b1(10) -> 11*
     b1(47) -> 48*
     b1(37) -> 38*
     b1(12) -> 13*
     b1(39) -> 40*
     b1(46) -> 47*
     b1(11) -> 12*
     b1(48) -> 49*
     b1(38) -> 39*
     a2(152) -> 153*
     a2(112) -> 113*
     a2(87) -> 88*
     a2(77) -> 78*
     a2(149) -> 150*
     a2(114) -> 115*
     a2(89) -> 90*
     a2(79) -> 80*
     a2(151) -> 152*
     a2(116) -> 117*
     a2(86) -> 87*
     a2(76) -> 77*
     a2(148) -> 149*
     a2(113) -> 114*
     a2(88) -> 89*
     a2(78) -> 79*
     a2(150) -> 151*
     a2(115) -> 116*
     a2(85) -> 86*
     a2(80) -> 81*
     b2(75) -> 76*
     b2(147) -> 148*
     b2(82) -> 83*
     b2(109) -> 110*
     b2(84) -> 85*
     b2(74) -> 75*
     b2(146) -> 147*
     b2(111) -> 112*
     b2(83) -> 84*
     b2(73) -> 74*
     b2(145) -> 146*
     b2(110) -> 111*
     f20() -> 2*
     a3(157) -> 158*
     a3(122) -> 123*
     a3(159) -> 160*
     a3(124) -> 125*
     a3(161) -> 162*
     a3(121) -> 122*
     a3(158) -> 159*
     a3(123) -> 124*
     a3(160) -> 161*
     a3(125) -> 126*
     a0(5) -> 6*
     a0(7) -> 8*
     a0(9) -> 1*
     a0(6) -> 7*
     a0(8) -> 9*
     b3(154) -> 155*
     b3(119) -> 120*
     b3(156) -> 157*
     b3(118) -> 119*
     b3(155) -> 156*
     b3(120) -> 121*
     b0(2) -> 3*
     b0(4) -> 5*
     b0(3) -> 4*
     1 -> 3,4
     6 -> 37*
     8 -> 10*
     13 -> 82*
     15 -> 73*
     17 -> 46*
     18 -> 5*
     41 -> 145*
     43 -> 109*
     45 -> 12*
     54 -> 39*
     81 -> 48*
     90 -> 75*
     113 -> 154*
     115 -> 118*
     117 -> 83*
     126 -> 85*
     153 -> 111*
     162 -> 120*
   problem:
    
   Qed