YES

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

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