YES

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

Proof:
 String Reversal Processor:
  c(c(x1)) -> b(a(x1))
  b(x1) -> a(a(x1))
  b(b(b(x1))) -> b(c(a(x1)))
  a(c(a(x1))) -> c(c(a(x1)))
  Bounds Processor:
   bound: 5
   enrichment: match
   automaton:
    final states: {7,5,4,1}
    transitions:
     a0(3) -> 4*
     a0(2) -> 3*
     c2(162) -> 163*
     c2(95) -> 96*
     c2(155) -> 156*
     c2(96) -> 97*
     c2(110) -> 111*
     c2(154) -> 155*
     a4(174) -> 175*
     a4(175) -> 176*
     a4(120) -> 121*
     a4(141) -> 142*
     a4(119) -> 120*
     a1(20) -> 21*
     a1(17) -> 18*
     a1(8) -> 9*
     a1(30) -> 31*
     a1(18) -> 19*
     c0(6) -> 7*
     c0(3) -> 6*
     a3(104) -> 105*
     a3(47) -> 48*
     a3(122) -> 123*
     a3(170) -> 171*
     a3(167) -> 168*
     a3(98) -> 99*
     a3(105) -> 106*
     a3(48) -> 49*
     a3(123) -> 124*
     b2(111) -> 112*
     b2(42) -> 43*
     b2(87) -> 88*
     b0(3) -> 1*
     b0(6) -> 5*
     f30() -> 2*
     b1(50) -> 51*
     b1(9) -> 10*
     b1(69) -> 70*
     a2(86) -> 87*
     a2(62) -> 63*
     a2(63) -> 64*
     a2(27) -> 28*
     a2(60) -> 61*
     a2(77) -> 78*
     a2(144) -> 145*
     a2(28) -> 29*
     a2(78) -> 79*
     a2(41) -> 42*
     c1(54) -> 55*
     c1(81) -> 82*
     c1(68) -> 69*
     c1(80) -> 81*
     c1(32) -> 33*
     c1(130) -> 131*
     c1(31) -> 32*
     c3(133) -> 134*
     c3(132) -> 133*
     a5(149) -> 150*
     a5(148) -> 149*
     b4(142) -> 143*
     b3(168) -> 169*
     b3(99) -> 100*
     156 -> 19,63
     163 -> 155*
     70 -> 5*
     43 -> 33,18
     19 -> 5*
     131 -> 81*
     142 -> 148*
     132 -> 141*
     168 -> 174*
     154 -> 170*
     48 -> 95,68
     162 -> 167*
     64 -> 162,80,51,17
     42 -> 47*
     69 -> 77*
     7 -> 31,3,8,41
     100 -> 97,78
     169 -> 156*
     112 -> 51,1,6
     106 -> 88,20,4,42
     2 -> 30*
     143 -> 134,123
     82 -> 42,4,9,47
     124 -> 154,130,112,1
     105 -> 132,110
     54 -> 60*
     88 -> 82,4,9,42,27
     6 -> 17*
     171 -> 168*
     121 -> 100,97
     150 -> 143,134
     21 -> 1*
     79 -> 70*
     49 -> 43,33
     31 -> 41*
     99 -> 119*
     130 -> 144*
     55 -> 32*
     95 -> 98*
     9 -> 27,20
     134 -> 123*
     50 -> 62*
     3 -> 8*
     18 -> 50*
     145 -> 87*
     97 -> 78*
     51 -> 32,6,17
     10 -> 7*
     80 -> 86*
     87 -> 104*
     29 -> 54,10
     61 -> 42*
     176 -> 169,63
     111 -> 122*
     33 -> 18*
   problem:
    
   Qed