YES

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

Proof:
 String Reversal Processor:
  a(a(b(c(x1)))) -> c(a(b(c(b(a(a(b(a(a(x1))))))))))
  Bounds Processor:
   bound: 2
   enrichment: match
   automaton:
    final states: {1}
    transitions:
     f30() -> 2*
     c0(11) -> 1*
     c0(8) -> 9*
     a0(10) -> 11*
     a0(5) -> 6*
     a0(2) -> 3*
     a0(6) -> 7*
     a0(3) -> 4*
     b0(7) -> 8*
     b0(9) -> 10*
     b0(4) -> 5*
     c1(65) -> 66*
     c1(62) -> 63*
     c1(54) -> 55*
     c1(51) -> 52*
     c1(21) -> 22*
     c1(18) -> 19*
     a1(60) -> 61*
     a1(45) -> 46*
     a1(20) -> 21*
     a1(15) -> 16*
     a1(57) -> 58*
     a1(12) -> 13*
     a1(64) -> 65*
     a1(59) -> 60*
     a1(49) -> 50*
     a1(56) -> 57*
     a1(46) -> 47*
     a1(16) -> 17*
     a1(53) -> 54*
     a1(48) -> 49*
     a1(13) -> 14*
     b1(50) -> 51*
     b1(52) -> 53*
     b1(47) -> 48*
     b1(17) -> 18*
     b1(19) -> 20*
     b1(14) -> 15*
     b1(61) -> 62*
     b1(63) -> 64*
     b1(58) -> 59*
     c2(142) -> 143*
     c2(139) -> 140*
     c2(109) -> 110*
     c2(106) -> 107*
     c2(98) -> 99*
     c2(95) -> 96*
     a2(137) -> 138*
     a2(97) -> 98*
     a2(92) -> 93*
     a2(134) -> 135*
     a2(104) -> 105*
     a2(89) -> 90*
     a2(141) -> 142*
     a2(136) -> 137*
     a2(101) -> 102*
     a2(133) -> 134*
     a2(108) -> 109*
     a2(103) -> 104*
     a2(93) -> 94*
     a2(100) -> 101*
     a2(90) -> 91*
     b2(107) -> 108*
     b2(102) -> 103*
     b2(94) -> 95*
     b2(96) -> 97*
     b2(91) -> 92*
     b2(138) -> 139*
     b2(140) -> 141*
     b2(135) -> 136*
     b2(105) -> 106*
     1 -> 3,4
     8 -> 45*
     11 -> 12*
     18 -> 100*
     21 -> 56*
     22 -> 7*
     55 -> 13*
     62 -> 133*
     65 -> 89*
     66 -> 47*
     99 -> 50*
     110 -> 57*
     143 -> 90*
   problem:
    
   Qed