YES

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

Proof:
 String Reversal Processor:
  b(a(b(a(c(x1))))) -> a(c(b(a(c(b(b(a(b(b(a(b(a(x1)))))))))))))
  Bounds Processor:
   bound: 2
   enrichment: match
   automaton:
    final states: {1}
    transitions:
     f30() -> 2*
     a0(7) -> 8*
     a0(2) -> 3*
     a0(14) -> 1*
     a0(4) -> 5*
     a0(11) -> 12*
     c0(10) -> 11*
     c0(13) -> 14*
     b0(5) -> 6*
     b0(12) -> 13*
     b0(9) -> 10*
     b0(6) -> 7*
     b0(8) -> 9*
     b0(3) -> 4*
     a1(20) -> 21*
     a1(15) -> 16*
     a1(62) -> 63*
     a1(57) -> 58*
     a1(27) -> 28*
     a1(17) -> 18*
     a1(69) -> 70*
     a1(59) -> 60*
     a1(24) -> 25*
     a1(76) -> 77*
     a1(71) -> 72*
     a1(66) -> 67*
     a1(83) -> 84*
     a1(73) -> 74*
     a1(80) -> 81*
     c1(65) -> 66*
     c1(82) -> 83*
     c1(79) -> 80*
     c1(26) -> 27*
     c1(68) -> 69*
     c1(23) -> 24*
     b1(75) -> 76*
     b1(60) -> 61*
     b1(25) -> 26*
     b1(77) -> 78*
     b1(72) -> 73*
     b1(67) -> 68*
     b1(22) -> 23*
     b1(74) -> 75*
     b1(64) -> 65*
     b1(19) -> 20*
     b1(81) -> 82*
     b1(61) -> 62*
     b1(21) -> 22*
     b1(16) -> 17*
     b1(78) -> 79*
     b1(63) -> 64*
     b1(58) -> 59*
     b1(18) -> 19*
     a2(122) -> 123*
     a2(118) -> 119*
     a2(113) -> 114*
     a2(125) -> 126*
     a2(115) -> 116*
     c2(124) -> 125*
     c2(121) -> 122*
     b2(117) -> 118*
     b2(119) -> 120*
     b2(114) -> 115*
     b2(116) -> 117*
     b2(123) -> 124*
     b2(120) -> 121*
     1 -> 4,6
     10 -> 57*
     13 -> 15*
     23 -> 113*
     26 -> 71*
     28 -> 9*
     70 -> 17*
     84 -> 59*
     126 -> 73*
   problem:
    
   Qed