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: 3
   enrichment: match
   automaton:
    final states: {4}
    transitions:
     a3(116) -> 117*
     a3(111) -> 112*
     a3(123) -> 124*
     a3(113) -> 114*
     a3(120) -> 121*
     a1(37) -> 38*
     a1(24) -> 25*
     a1(19) -> 20*
     a1(31) -> 32*
     a1(21) -> 22*
     a1(28) -> 29*
     c3(122) -> 123*
     c3(119) -> 120*
     c1(30) -> 31*
     c1(27) -> 28*
     b3(117) -> 118*
     b3(112) -> 113*
     b3(114) -> 115*
     b3(121) -> 122*
     b3(118) -> 119*
     b3(115) -> 116*
     b1(25) -> 26*
     b1(20) -> 21*
     b1(22) -> 23*
     b1(29) -> 30*
     b1(26) -> 27*
     b1(23) -> 24*
     a2(60) -> 61*
     a2(55) -> 56*
     a2(50) -> 51*
     a2(92) -> 93*
     a2(67) -> 68*
     a2(57) -> 58*
     a2(64) -> 65*
     a2(46) -> 47*
     a2(41) -> 42*
     a2(88) -> 89*
     a2(83) -> 84*
     a2(53) -> 54*
     a2(43) -> 44*
     a2(95) -> 96*
     a2(85) -> 86*
     b0(4) -> 4*
     c2(52) -> 53*
     c2(94) -> 95*
     c2(49) -> 50*
     c2(91) -> 92*
     c2(66) -> 67*
     c2(63) -> 64*
     a0(4) -> 4*
     b2(65) -> 66*
     b2(45) -> 46*
     b2(87) -> 88*
     b2(62) -> 63*
     b2(47) -> 48*
     b2(42) -> 43*
     b2(89) -> 90*
     b2(84) -> 85*
     b2(59) -> 60*
     b2(44) -> 45*
     b2(86) -> 87*
     b2(61) -> 62*
     b2(56) -> 57*
     b2(51) -> 52*
     b2(93) -> 94*
     b2(58) -> 59*
     b2(48) -> 49*
     b2(90) -> 91*
     c0(4) -> 4*
     4 -> 19*
     27 -> 41*
     30 -> 55,37
     32 -> 21,23,4
     38 -> 20*
     54 -> 57,21
     63 -> 111*
     66 -> 83*
     68 -> 26*
     96 -> 43*
     124 -> 85*
   problem:
    
   Qed