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:
 Arctic Interpretation Processor:
  dimension: 2
  interpretation:
             [0  3 ]  
   [a](x0) = [-& 0 ]x0,
   
             [2 3]  
   [b](x0) = [0 0]x0,
   
             [0 3]  
   [c](x0) = [0 0]x0
  orientation:
              [3 3]      [3 3]             
   c(c(x1)) = [0 3]x1 >= [0 0]x1 = a(b(x1))
   
           [2 3]      [0  3 ]             
   b(x1) = [0 0]x1 >= [-& 0 ]x1 = a(a(x1))
   
                 [6 7]      [5 6]                
   b(b(b(x1))) = [4 5]x1 >= [2 3]x1 = a(c(b(x1)))
   
                 [3 6]      [3 6]                
   a(c(a(x1))) = [0 3]x1 >= [0 3]x1 = a(c(c(x1)))
  problem:
   c(c(x1)) -> a(b(x1))
   b(x1) -> a(a(x1))
   a(c(a(x1))) -> a(c(c(x1)))
  String Reversal Processor:
   c(c(x1)) -> b(a(x1))
   b(x1) -> a(a(x1))
   a(c(a(x1))) -> c(c(a(x1)))
   Bounds Processor:
    bound: 4
    enrichment: match
    automaton:
     final states: {5,4,1}
     transitions:
      f30() -> 2*
      b0(3) -> 1*
      a0(2) -> 3*
      a0(3) -> 4*
      c0(6) -> 5*
      c0(3) -> 6*
      a1(10) -> 11*
      a1(41) -> 42*
      a1(26) -> 27*
      a1(13) -> 14*
      b1(27) -> 28*
      b1(11) -> 12*
      a2(30) -> 31*
      a2(20) -> 21*
      a2(57) -> 58*
      a2(29) -> 30*
      a2(21) -> 22*
      a2(48) -> 49*
      c1(52) -> 53*
      c1(39) -> 40*
      c1(51) -> 52*
      c1(38) -> 39*
      b2(49) -> 50*
      b2(58) -> 59*
      a3(72) -> 73*
      a3(67) -> 68*
      a3(66) -> 67*
      a3(78) -> 79*
      a3(73) -> 74*
      c2(75) -> 76*
      c2(76) -> 77*
      b3(79) -> 80*
      a4(85) -> 86*
      a4(84) -> 85*
      2 -> 41*
      3 -> 10*
      5 -> 42,38,48,3,10
      6 -> 26*
      11 -> 20,13
      12 -> 5*
      14 -> 1*
      22 -> 38,12,5
      27 -> 29*
      28 -> 39,6
      31 -> 75,51,28,6,26
      38 -> 48*
      40 -> 27*
      42 -> 38*
      49 -> 66*
      50 -> 40,27,29
      51 -> 57*
      53 -> 49,66,11,13,4,20
      58 -> 72*
      59 -> 53,4,11
      68 -> 50,40
      74 -> 59*
      75 -> 78*
      77 -> 30*
      79 -> 84*
      80 -> 77,30
      86 -> 80,77
    problem:
     
    Qed