YES

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

Proof:
 String Reversal Processor:
  a(a(x1)) -> c(c(b(a(x1))))
  a(c(x1)) -> x1
  b(c(x1)) -> a(a(x1))
  DP Processor:
   DPs:
    a#(a(x1)) -> b#(a(x1))
    b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> a#(a(x1))
   TRS:
    a(a(x1)) -> c(c(b(a(x1))))
    a(c(x1)) -> x1
    b(c(x1)) -> a(a(x1))
   TDG Processor:
    DPs:
     a#(a(x1)) -> b#(a(x1))
     b#(c(x1)) -> a#(x1)
     b#(c(x1)) -> a#(a(x1))
    TRS:
     a(a(x1)) -> c(c(b(a(x1))))
     a(c(x1)) -> x1
     b(c(x1)) -> a(a(x1))
    graph:
     b#(c(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(x1))
     b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1))
     a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(a(x1))
     a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1)
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(a(x1)) -> c(c(b(a(x1))))
      a(c(x1)) -> x1
      b(c(x1)) -> a(a(x1))
     interpretation:
      [b#](x0) = [2 1]x0 + [0],
      
      [a#](x0) = [0 1]x0 + [0],
      
                [1 0]     [0]
      [b](x0) = [2 1]x0 + [0],
      
                [-& 0 ]     [0]
      [c](x0) = [0  -&]x0 + [3],
      
                [-& 0 ]     [0]
      [a](x0) = [0  1 ]x0 + [3]
     orientation:
      a#(a(x1)) = [1 2]x1 + [4] >= [1 2]x1 + [4] = b#(a(x1))
      
      b#(c(x1)) = [1 2]x1 + [4] >= [0 1]x1 + [0] = a#(x1)
      
      b#(c(x1)) = [1 2]x1 + [4] >= [1 2]x1 + [4] = a#(a(x1))
      
                 [0 1]     [3]    [0 1]     [3]                 
      a(a(x1)) = [1 2]x1 + [4] >= [1 2]x1 + [4] = c(c(b(a(x1))))
      
                 [0  -&]     [3]           
      a(c(x1)) = [1  0 ]x1 + [4] >= x1 = x1
      
                 [0 1]     [3]    [0 1]     [3]           
      b(c(x1)) = [1 2]x1 + [4] >= [1 2]x1 + [4] = a(a(x1))
     problem:
      DPs:
       a#(a(x1)) -> b#(a(x1))
       b#(c(x1)) -> a#(a(x1))
      TRS:
       a(a(x1)) -> c(c(b(a(x1))))
       a(c(x1)) -> x1
       b(c(x1)) -> a(a(x1))
     Restore Modifier:
      DPs:
       a#(a(x1)) -> b#(a(x1))
       b#(c(x1)) -> a#(a(x1))
      TRS:
       a(a(x1)) -> c(c(b(a(x1))))
       a(c(x1)) -> x1
       b(c(x1)) -> a(a(x1))
      EDG Processor:
       DPs:
        a#(a(x1)) -> b#(a(x1))
        b#(c(x1)) -> a#(a(x1))
       TRS:
        a(a(x1)) -> c(c(b(a(x1))))
        a(c(x1)) -> x1
        b(c(x1)) -> a(a(x1))
       graph:
        b#(c(x1)) -> a#(a(x1)) -> a#(a(x1)) -> b#(a(x1))
        a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(a(x1))
       Arctic Interpretation Processor:
        dimension: 3
        usable rules:
         a(a(x1)) -> c(c(b(a(x1))))
         a(c(x1)) -> x1
         b(c(x1)) -> a(a(x1))
        interpretation:
         [b#](x0) = [0  -& 0 ]x0 + [0],
         
         [a#](x0) = [-& -& 0 ]x0 + [0],
         
                   [0  -& 0 ]     [0]
         [b](x0) = [0  0  1 ]x0 + [0]
                   [0  -& 0 ]     [0],
         
                   [0  0  -&]     [0]
         [c](x0) = [0  -& 0 ]x0 + [0]
                   [0  1  -&]     [1],
         
                   [-& 0  -&]     [0]
         [a](x0) = [0  1  -&]x0 + [1]
                   [-& 0  -&]     [0]
        orientation:
         a#(a(x1)) = [-& 0  -&]x1 + [0] >= [-& 0  -&]x1 + [0] = b#(a(x1))
         
         b#(c(x1)) = [0  1  -&]x1 + [1] >= [-& 0  -&]x1 + [0] = a#(a(x1))
         
                    [0  1  -&]     [1]    [0  1  -&]     [1]                 
         a(a(x1)) = [1  2  -&]x1 + [2] >= [1  2  -&]x1 + [2] = c(c(b(a(x1))))
                    [0  1  -&]     [1]    [0  1  -&]     [1]                 
         
                    [0  -& 0 ]     [0]           
         a(c(x1)) = [1  0  1 ]x1 + [1] >= x1 = x1
                    [0  -& 0 ]     [0]           
         
                    [0  1  -&]     [1]    [0  1  -&]     [1]           
         b(c(x1)) = [1  2  0 ]x1 + [2] >= [1  2  -&]x1 + [2] = a(a(x1))
                    [0  1  -&]     [1]    [0  1  -&]     [1]           
        problem:
         DPs:
          a#(a(x1)) -> b#(a(x1))
         TRS:
          a(a(x1)) -> c(c(b(a(x1))))
          a(c(x1)) -> x1
          b(c(x1)) -> a(a(x1))
        Restore Modifier:
         DPs:
          a#(a(x1)) -> b#(a(x1))
         TRS:
          a(a(x1)) -> c(c(b(a(x1))))
          a(c(x1)) -> x1
          b(c(x1)) -> a(a(x1))
         EDG Processor:
          DPs:
           a#(a(x1)) -> b#(a(x1))
          TRS:
           a(a(x1)) -> c(c(b(a(x1))))
           a(c(x1)) -> x1
           b(c(x1)) -> a(a(x1))
          graph:
           
          Qed