YES

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

Proof:
 String Reversal Processor:
  a(a(x)) -> c(b(x))
  b(b(x)) -> c(a(x))
  c(c(x)) -> b(a(x))
  DP Processor:
   DPs:
    a#(a(x)) -> b#(x)
    a#(a(x)) -> c#(b(x))
    b#(b(x)) -> a#(x)
    b#(b(x)) -> c#(a(x))
    c#(c(x)) -> a#(x)
    c#(c(x)) -> b#(a(x))
   TRS:
    a(a(x)) -> c(b(x))
    b(b(x)) -> c(a(x))
    c(c(x)) -> b(a(x))
   TDG Processor:
    DPs:
     a#(a(x)) -> b#(x)
     a#(a(x)) -> c#(b(x))
     b#(b(x)) -> a#(x)
     b#(b(x)) -> c#(a(x))
     c#(c(x)) -> a#(x)
     c#(c(x)) -> b#(a(x))
    TRS:
     a(a(x)) -> c(b(x))
     b(b(x)) -> c(a(x))
     c(c(x)) -> b(a(x))
    graph:
     c#(c(x)) -> b#(a(x)) -> b#(b(x)) -> c#(a(x))
     c#(c(x)) -> b#(a(x)) -> b#(b(x)) -> a#(x)
     c#(c(x)) -> a#(x) -> a#(a(x)) -> c#(b(x))
     c#(c(x)) -> a#(x) -> a#(a(x)) -> b#(x)
     b#(b(x)) -> c#(a(x)) -> c#(c(x)) -> b#(a(x))
     b#(b(x)) -> c#(a(x)) -> c#(c(x)) -> a#(x)
     b#(b(x)) -> a#(x) -> a#(a(x)) -> c#(b(x))
     b#(b(x)) -> a#(x) -> a#(a(x)) -> b#(x)
     a#(a(x)) -> c#(b(x)) -> c#(c(x)) -> b#(a(x))
     a#(a(x)) -> c#(b(x)) -> c#(c(x)) -> a#(x)
     a#(a(x)) -> b#(x) -> b#(b(x)) -> c#(a(x))
     a#(a(x)) -> b#(x) -> b#(b(x)) -> a#(x)
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [c#](x0) = x0,
      
      [b#](x0) = x0,
      
      [a#](x0) = 4x0,
      
      [b](x0) = 4x0,
      
      [c](x0) = 4x0,
      
      [a](x0) = 4x0
     orientation:
      a#(a(x)) = 8x >= x = b#(x)
      
      a#(a(x)) = 8x >= 4x = c#(b(x))
      
      b#(b(x)) = 4x >= 4x = a#(x)
      
      b#(b(x)) = 4x >= 4x = c#(a(x))
      
      c#(c(x)) = 4x >= 4x = a#(x)
      
      c#(c(x)) = 4x >= 4x = b#(a(x))
      
      a(a(x)) = 8x >= 8x = c(b(x))
      
      b(b(x)) = 8x >= 8x = c(a(x))
      
      c(c(x)) = 8x >= 8x = b(a(x))
     problem:
      DPs:
       b#(b(x)) -> a#(x)
       b#(b(x)) -> c#(a(x))
       c#(c(x)) -> a#(x)
       c#(c(x)) -> b#(a(x))
      TRS:
       a(a(x)) -> c(b(x))
       b(b(x)) -> c(a(x))
       c(c(x)) -> b(a(x))
     EDG Processor:
      DPs:
       b#(b(x)) -> a#(x)
       b#(b(x)) -> c#(a(x))
       c#(c(x)) -> a#(x)
       c#(c(x)) -> b#(a(x))
      TRS:
       a(a(x)) -> c(b(x))
       b(b(x)) -> c(a(x))
       c(c(x)) -> b(a(x))
      graph:
       c#(c(x)) -> b#(a(x)) -> b#(b(x)) -> a#(x)
       c#(c(x)) -> b#(a(x)) -> b#(b(x)) -> c#(a(x))
       b#(b(x)) -> c#(a(x)) -> c#(c(x)) -> a#(x)
       b#(b(x)) -> c#(a(x)) -> c#(c(x)) -> b#(a(x))
      SCC Processor:
       #sccs: 1
       #rules: 2
       #arcs: 4/16
       DPs:
        c#(c(x)) -> b#(a(x))
        b#(b(x)) -> c#(a(x))
       TRS:
        a(a(x)) -> c(b(x))
        b(b(x)) -> c(a(x))
        c(c(x)) -> b(a(x))
       Arctic Interpretation Processor:
        dimension: 2
        interpretation:
         [c#](x0) = [2 0]x0 + [3],
         
         [b#](x0) = [2 0]x0 + [0],
         
                   [1  0 ]     [2]
         [b](x0) = [0  -&]x0 + [1],
         
                   [0 1]     [0]
         [c](x0) = [0 0]x0 + [2],
         
                   [-& 0 ]     [0]
         [a](x0) = [1  0 ]x0 + [2]
        orientation:
         c#(c(x)) = [2 3]x + [3] >= [1 2]x + [2] = b#(a(x))
         
         b#(b(x)) = [3 2]x + [4] >= [1 2]x + [3] = c#(a(x))
         
                   [1 0]    [2]    [1 0]    [2]          
         a(a(x)) = [1 1]x + [2] >= [1 0]x + [2] = c(b(x))
         
                   [2 1]    [3]    [2 1]    [3]          
         b(b(x)) = [1 0]x + [2] >= [1 0]x + [2] = c(a(x))
         
                   [1 1]    [3]    [1  1 ]    [2]          
         c(c(x)) = [0 1]x + [2] >= [-& 0 ]x + [1] = b(a(x))
        problem:
         DPs:
          b#(b(x)) -> c#(a(x))
         TRS:
          a(a(x)) -> c(b(x))
          b(b(x)) -> c(a(x))
          c(c(x)) -> b(a(x))
        EDG Processor:
         DPs:
          b#(b(x)) -> c#(a(x))
         TRS:
          a(a(x)) -> c(b(x))
          b(b(x)) -> c(a(x))
          c(c(x)) -> b(a(x))
         graph:
          
         Qed