YES

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

Proof:
 String Reversal Processor:
  strict:
   a(c(b(x1))) -> b(a(b(a(x1))))
   a(a(x1)) -> a(b(c(a(x1))))
  weak:
   b(x1) -> b(c(x1))
  Bounds Processor:
   bound: 2
   enrichment: match-rt
   automaton:
    final states: {4}
    transitions:
     b1(60) -> 61*
     b1(58) -> 59*
     b1(22) -> 23*
     c1(73) -> 74*
     c1(21) -> 22*
     c1(25) -> 26*
     a1(173) -> 174*
     a1(20) -> 21*
     a1(59) -> 60*
     a1(88) -> 89*
     a1(23) -> 24*
     a0(4) -> 4*
     b0(4) -> 4*
     c0(4) -> 4*
     a2(138) -> 139*
     a2(133) -> 134*
     a2(135) -> 136*
     a2(40) -> 41*
     a2(110) -> 111*
     a2(107) -> 108*
     a2(37) -> 38*
     c2(86) -> 87*
     c2(38) -> 39*
     c2(197) -> 198*
     c2(195) -> 196*
     c2(108) -> 109*
     c2(123) -> 124*
     c2(70) -> 71*
     c2(222) -> 223*
     c2(224) -> 225*
     c2(112) -> 113*
     c2(120) -> 121*
     c2(175) -> 176*
     b2(124) -> 125*
     b2(39) -> 40*
     b2(71) -> 72*
     b2(109) -> 110*
     b2(136) -> 137*
     b2(134) -> 135*
     b2(121) -> 122*
     196 -> 121*
     24 -> 21,25,4
     74 -> 60*
     198 -> 124*
     137 -> 139,89
     113 -> 71*
     4 -> 73,20
     174 -> 58*
     124 -> 197,173,133
     22 -> 70*
     109 -> 175*
     121 -> 195*
     72 -> 23*
     21 -> 58*
     58 -> 120*
     125 -> 61*
     26 -> 22*
     139 -> 134*
     60 -> 138,123,88
     71 -> 112*
     59 -> 107*
     134 -> 222*
     225 -> 136*
     39 -> 86*
     41 -> 21*
     122 -> 59*
     136 -> 224*
     87 -> 39*
     89 -> 58*
     61 -> 139,89,21,4
     176 -> 109*
     111 -> 139,89
     23 -> 37*
     223 -> 134*
   problem:
    strict:
     a(c(b(x1))) -> b(a(b(a(x1))))
    weak:
     b(x1) -> b(c(x1))
   Bounds Processor:
    bound: 2
    enrichment: match-rt
    automaton:
     final states: {4}
     transitions:
      b1(11) -> 12*
      b1(13) -> 14*
      c1(41) -> 42*
      c1(21) -> 22*
      c1(25) -> 26*
      a1(12) -> 13*
      a1(10) -> 11*
      a1(53) -> 54*
      a1(15) -> 16*
      a0(4) -> 4*
      c0(4) -> 4*
      b0(4) -> 4*
      a2(27) -> 28*
      a2(29) -> 30*
      a2(55) -> 56*
      c2(64) -> 65*
      c2(61) -> 62*
      c2(70) -> 71*
      c2(50) -> 51*
      c2(48) -> 49*
      c2(72) -> 73*
      b2(28) -> 29*
      b2(62) -> 63*
      b2(30) -> 31*
      b2(51) -> 52*
      56 -> 28*
      42 -> 11*
      30 -> 48*
      63 -> 12*
      14 -> 28,16,11,4
      16 -> 11*
      28 -> 64*
      4 -> 25,10
      11 -> 61,41
      22 -> 13*
      52 -> 14*
      54 -> 11*
      26 -> 13*
      73 -> 51*
      13 -> 50,27,21,15
      71 -> 62*
      49 -> 30*
      31 -> 28,16
      62 -> 70*
      65 -> 28*
      51 -> 72,55,53
    problem:
     strict:
      
     weak:
      b(x1) -> b(c(x1))
    Qed