YES

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

Proof:
 String Reversal Processor:
  a(c(b(a(a(c(x1)))))) -> c(b(a(a(c(c(b(a(a(x1)))))))))
  Bounds Processor:
   bound: 3
   enrichment: match
   automaton:
    final states: {4}
    transitions:
     c3(89) -> 90*
     c3(84) -> 85*
     c3(85) -> 86*
     c1(19) -> 20*
     c1(23) -> 24*
     c1(18) -> 19*
     b3(88) -> 89*
     b3(83) -> 84*
     b1(22) -> 23*
     b1(17) -> 18*
     a3(87) -> 88*
     a3(82) -> 83*
     a3(86) -> 87*
     a3(81) -> 82*
     a1(25) -> 26*
     a1(20) -> 21*
     a1(15) -> 16*
     a1(31) -> 32*
     a1(21) -> 22*
     a1(16) -> 17*
     c2(75) -> 76*
     c2(70) -> 71*
     c2(37) -> 38*
     c2(59) -> 60*
     c2(71) -> 72*
     c2(41) -> 42*
     c2(36) -> 37*
     c2(63) -> 64*
     c2(58) -> 59*
     a0(4) -> 4*
     b2(40) -> 41*
     b2(35) -> 36*
     b2(62) -> 63*
     b2(57) -> 58*
     b2(74) -> 75*
     b2(69) -> 70*
     c0(4) -> 4*
     a2(65) -> 66*
     a2(60) -> 61*
     a2(55) -> 56*
     a2(72) -> 73*
     a2(67) -> 68*
     a2(39) -> 40*
     a2(34) -> 35*
     a2(61) -> 62*
     a2(56) -> 57*
     a2(73) -> 74*
     a2(68) -> 69*
     a2(38) -> 39*
     a2(33) -> 34*
     b0(4) -> 4*
     4 -> 15*
     18 -> 55*
     19 -> 33,25
     23 -> 65,31
     24 -> 34,26,16,4
     26 -> 16*
     32 -> 16*
     37 -> 67*
     42 -> 35,17,16
     59 -> 81*
     64 -> 68,34,26
     66 -> 56*
     76 -> 17*
     90 -> 69,17,35
   problem:
    
   Qed