YES

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

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match-rt
  automaton:
   final states: {4}
   transitions:
    b1(11) -> 12*
    b1(13) -> 14*
    a2(58) -> 59*
    a2(60) -> 61*
    a2(97) -> 98*
    a2(120) -> 121*
    a2(95) -> 96*
    a1(12) -> 13*
    a1(27) -> 28*
    a1(10) -> 11*
    a1(131) -> 132*
    a0(4) -> 4*
    b0(4) -> 4*
    c0(4) -> 4*
    b2(138) -> 139*
    b2(61) -> 62*
    b2(96) -> 97*
    b2(116) -> 117*
    b2(59) -> 60*
    c2(146) -> 147*
    c2(137) -> 138*
    c2(106) -> 107*
    c2(115) -> 116*
    c2(167) -> 168*
    c2(152) -> 153*
    c2(160) -> 161*
    c1(54) -> 55*
    c1(47) -> 48*
    c1(86) -> 87*
    132 -> 11*
    168 -> 138*
    48 -> 13*
    12 -> 95,59
    14 -> 11,4
    28 -> 11*
    4 -> 54,10
    11 -> 137,86,28
    117 -> 14*
    153 -> 116*
    116 -> 152,131,120
    121 -> 59*
    138 -> 167*
    161 -> 96*
    139 -> 12*
    13 -> 115,58,47,4,11,27
    62 -> 59,11
    107 -> 59*
    55 -> 13*
    59 -> 106*
    147 -> 61*
    96 -> 160*
    98 -> 59,28
    87 -> 11*
    61 -> 146*
  problem:
   strict:
    a(a(x1)) -> a(b(a(x1)))
   weak:
    b(x1) -> b(c(x1))
  String Reversal Processor:
   strict:
    a(a(x1)) -> a(b(a(x1)))
   weak:
    b(x1) -> c(b(x1))
   Bounds Processor:
    bound: 2
    enrichment: match-rt
    automaton:
     final states: {4}
     transitions:
      b1(32) -> 33*
      b1(13) -> 14*
      b1(10) -> 11*
      a2(21) -> 22*
      a2(19) -> 20*
      a1(11) -> 12*
      a1(9) -> 10*
      a0(4) -> 4*
      c0(4) -> 4*
      b0(4) -> 4*
      b2(20) -> 21*
      b2(47) -> 48*
      b2(29) -> 30*
      b2(38) -> 39*
      c2(40) -> 41*
      c2(30) -> 31*
      c2(48) -> 49*
      c1(33) -> 34*
      12 -> 10,13,4
      14 -> 11*
      4 -> 32,9
      11 -> 19*
      22 -> 10*
      21 -> 40*
      13 -> 29*
      49 -> 48,33
      31 -> 39,30,14
      34 -> 4*
      39 -> 30*
      41 -> 21*
      10 -> 38*
      32 -> 47*
    problem:
     strict:
      
     weak:
      b(x1) -> c(b(x1))
    Qed