YES

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

Proof:
 String Reversal Processor:
  a(c(b(x1))) -> c(b(a(b(a(x1)))))
  b(x1) -> c(c(x1))
  d(c(x1)) -> a(c(b(a(x1))))
  a(a(x1)) -> a(b(c(a(x1))))
  Bounds Processor:
   bound: 4
   enrichment: match
   automaton:
    final states: {5}
    transitions:
     b0(5) -> 5*
     a3(148) -> 149*
     a3(145) -> 146*
     a3(109) -> 110*
     a3(203) -> 204*
     a3(105) -> 106*
     a3(103) -> 104*
     a3(199) -> 200*
     c3(118) -> 119*
     c3(178) -> 179*
     c3(125) -> 126*
     c3(124) -> 125*
     c3(135) -> 136*
     c3(139) -> 140*
     c3(107) -> 108*
     c3(200) -> 201*
     c3(128) -> 129*
     c3(117) -> 118*
     c3(146) -> 147*
     c3(138) -> 139*
     c3(127) -> 128*
     c3(179) -> 180*
     c3(136) -> 137*
     a1(143) -> 144*
     a1(12) -> 13*
     a1(45) -> 46*
     a1(81) -> 82*
     a1(14) -> 15*
     a1(25) -> 26*
     a1(98) -> 99*
     d0(5) -> 5*
     c2(153) -> 154*
     c2(51) -> 52*
     c2(39) -> 40*
     c2(84) -> 85*
     c2(69) -> 70*
     c2(225) -> 226*
     c2(73) -> 74*
     c2(72) -> 73*
     c2(65) -> 66*
     c2(70) -> 71*
     c2(64) -> 65*
     b2(38) -> 39*
     b2(85) -> 86*
     b2(48) -> 49*
     b2(154) -> 155*
     b2(36) -> 37*
     b2(50) -> 51*
     c0(5) -> 5*
     a0(5) -> 5*
     b1(13) -> 14*
     b1(15) -> 16*
     b1(28) -> 29*
     a2(35) -> 36*
     a2(158) -> 159*
     a2(96) -> 97*
     a2(86) -> 87*
     a2(49) -> 50*
     a2(221) -> 222*
     a2(219) -> 220*
     a2(156) -> 157*
     a2(47) -> 48*
     a2(83) -> 84*
     a2(37) -> 38*
     a2(152) -> 153*
     a2(160) -> 161*
     c1(27) -> 28*
     c1(18) -> 19*
     c1(24) -> 25*
     c1(16) -> 17*
     c4(190) -> 191*
     c4(239) -> 240*
     c4(172) -> 173*
     c4(173) -> 174*
     c4(188) -> 189*
     c4(187) -> 188*
     c4(240) -> 241*
     c4(191) -> 192*
     b3(147) -> 148*
     b3(201) -> 202*
     b3(106) -> 107*
     b3(104) -> 105*
     192 -> 148*
     155 -> 47*
     144 -> 13*
     19 -> 16*
     74 -> 16*
     159 -> 153*
     154 -> 178*
     17 -> 159,153,82,13,27,5
     48 -> 135*
     189 -> 105*
     46 -> 13*
     137 -> 49*
     126 -> 37*
     104 -> 222,84,110,97,36,124,187
     140 -> 39*
     85 -> 117*
     12 -> 152*
     14 -> 160,24
     16 -> 81*
     106 -> 172*
     66 -> 14,24
     45 -> 156*
     28 -> 69*
     180 -> 155,47
     143 -> 219*
     82 -> 13*
     204 -> 200*
     174 -> 107*
     52 -> 84,26,5
     220 -> 84*
     201 -> 239*
     161 -> 84*
     36 -> 124*
     86 -> 145*
     38 -> 138,109
     26 -> 153,13,27,5
     222 -> 84*
     13 -> 64,47,27
     71 -> 29*
     40 -> 153,48,13,27
     49 -> 199*
     99 -> 13*
     241 -> 202,103
     110 -> 104*
     37 -> 203*
     147 -> 190*
     5 -> 18,12
     108 -> 153,48
     50 -> 225,127,103,98,96
     226 -> 85*
     119 -> 86*
     149 -> 48*
     129 -> 51*
     15 -> 72,45,35
     97 -> 36*
     51 -> 143*
     98 -> 221*
     87 -> 99,157,36,46,48,13,27
     81 -> 158*
     202 -> 103*
     29 -> 25*
     25 -> 83*
     157 -> 153*
   problem:
    
   Qed