YES

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

Proof:
 Arctic Interpretation Processor:
  dimension: 2
  interpretation:
             [0  0 ]  
   [a](x0) = [-& -&]x0,
   
             [0 0]  
   [b](x0) = [0 0]x0,
   
             [0 1]  
   [c](x0) = [0 0]x0
  orientation:
              [1 1]      [0  0 ]                         
   c(c(x1)) = [0 1]x1 >= [-& -&]x1 = a(a(a(b(b(b(x1))))))
   
                    [0 0]      [0 0]                               
   b(b(b(a(x1)))) = [0 0]x1 >= [0 0]x1 = b(b(b(b(b(b(b(b(x1))))))))
   
                    [1 1]      [1 1]                            
   b(b(c(c(x1)))) = [1 1]x1 >= [1 1]x1 = c(c(c(a(a(a(a(x1)))))))
  problem:
   b(b(b(a(x1)))) -> b(b(b(b(b(b(b(b(x1))))))))
   b(b(c(c(x1)))) -> c(c(c(a(a(a(a(x1)))))))
  String Reversal Processor:
   a(b(b(b(x1)))) -> b(b(b(b(b(b(b(b(x1))))))))
   c(c(b(b(x1)))) -> a(a(a(a(c(c(c(x1)))))))
   Bounds Processor:
    bound: 2
    enrichment: match
    automaton:
     final states: {4}
     transitions:
      a1(27) -> 28*
      a1(29) -> 30*
      a1(26) -> 27*
      a1(28) -> 29*
      c1(25) -> 26*
      c1(24) -> 25*
      c1(23) -> 24*
      b1(20) -> 21*
      b1(15) -> 16*
      b1(17) -> 18*
      b1(19) -> 20*
      b1(14) -> 15*
      b1(21) -> 22*
      b1(16) -> 17*
      b1(18) -> 19*
      a2(50) -> 51*
      a2(52) -> 53*
      a2(51) -> 52*
      a2(53) -> 54*
      a0(4) -> 4*
      c2(55) -> 56*
      c2(57) -> 58*
      c2(47) -> 48*
      c2(59) -> 60*
      c2(49) -> 50*
      c2(81) -> 82*
      c2(61) -> 62*
      c2(63) -> 64*
      c2(48) -> 49*
      b0(4) -> 4*
      c0(4) -> 4*
      4 -> 23,14
      14 -> 59*
      15 -> 4,14
      16 -> 81*
      17 -> 63*
      18 -> 57*
      19 -> 55,14,23
      20 -> 47,23
      21 -> 61,23
      22 -> 4*
      30 -> 25,24,4
      54 -> 60,48,49,24,4,25
      56 -> 48*
      58 -> 48*
      60 -> 48*
      62 -> 48*
      64 -> 48*
      82 -> 48*
    problem:
     
    Qed