YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> x1
  c(c(a(x1))) -> a(c(a(c(b(c(x1))))))
  DP Processor:
   DPs:
    c#(c(a(x1))) -> c#(x1)
    c#(c(a(x1))) -> b#(c(x1))
    c#(c(a(x1))) -> c#(b(c(x1)))
    c#(c(a(x1))) -> a#(c(b(c(x1))))
    c#(c(a(x1))) -> c#(a(c(b(c(x1)))))
    c#(c(a(x1))) -> a#(c(a(c(b(c(x1))))))
   TRS:
    a(x1) -> x1
    b(a(x1)) -> x1
    c(c(a(x1))) -> a(c(a(c(b(c(x1))))))
   TDG Processor:
    DPs:
     c#(c(a(x1))) -> c#(x1)
     c#(c(a(x1))) -> b#(c(x1))
     c#(c(a(x1))) -> c#(b(c(x1)))
     c#(c(a(x1))) -> a#(c(b(c(x1))))
     c#(c(a(x1))) -> c#(a(c(b(c(x1)))))
     c#(c(a(x1))) -> a#(c(a(c(b(c(x1))))))
    TRS:
     a(x1) -> x1
     b(a(x1)) -> x1
     c(c(a(x1))) -> a(c(a(c(b(c(x1))))))
    graph:
     c#(c(a(x1))) -> c#(b(c(x1))) ->
     c#(c(a(x1))) -> a#(c(a(c(b(c(x1))))))
     c#(c(a(x1))) -> c#(b(c(x1))) -> c#(c(a(x1))) -> c#(a(c(b(c(x1)))))
     c#(c(a(x1))) -> c#(b(c(x1))) -> c#(c(a(x1))) -> a#(c(b(c(x1))))
     c#(c(a(x1))) -> c#(b(c(x1))) -> c#(c(a(x1))) -> c#(b(c(x1)))
     c#(c(a(x1))) -> c#(b(c(x1))) -> c#(c(a(x1))) -> b#(c(x1))
     c#(c(a(x1))) -> c#(b(c(x1))) -> c#(c(a(x1))) -> c#(x1)
     c#(c(a(x1))) -> c#(a(c(b(c(x1))))) ->
     c#(c(a(x1))) -> a#(c(a(c(b(c(x1))))))
     c#(c(a(x1))) -> c#(a(c(b(c(x1))))) ->
     c#(c(a(x1))) -> c#(a(c(b(c(x1)))))
     c#(c(a(x1))) -> c#(a(c(b(c(x1))))) ->
     c#(c(a(x1))) -> a#(c(b(c(x1))))
     c#(c(a(x1))) -> c#(a(c(b(c(x1))))) ->
     c#(c(a(x1))) -> c#(b(c(x1)))
     c#(c(a(x1))) -> c#(a(c(b(c(x1))))) ->
     c#(c(a(x1))) -> b#(c(x1))
     c#(c(a(x1))) -> c#(a(c(b(c(x1))))) -> c#(c(a(x1))) -> c#(x1)
     c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> a#(c(a(c(b(c(x1))))))
     c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(a(c(b(c(x1)))))
     c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> a#(c(b(c(x1))))
     c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(b(c(x1)))
     c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> b#(c(x1))
     c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 18/36
     DPs:
      c#(c(a(x1))) -> c#(b(c(x1)))
      c#(c(a(x1))) -> c#(x1)
      c#(c(a(x1))) -> c#(a(c(b(c(x1)))))
     TRS:
      a(x1) -> x1
      b(a(x1)) -> x1
      c(c(a(x1))) -> a(c(a(c(b(c(x1))))))
     Arctic Interpretation Processor:
      dimension: 3
      interpretation:
       [c#](x0) = [0 0 0]x0 + [0],
       
                 [0  0  0 ]     [0 ]
       [c](x0) = [1  0  0 ]x0 + [0 ]
                 [0  -& 0 ]     [-&],
       
                 [-& -& 0 ]     [0]
       [b](x0) = [-& -& 0 ]x0 + [0]
                 [-& -& 0 ]     [0],
       
                 [0  -& -&]     [-&]
       [a](x0) = [1  0  1 ]x0 + [1 ]
                 [0  0  0 ]     [1 ]
      orientation:
       c#(c(a(x1))) = [1 0 1]x1 + [1] >= [0  -& 0 ]x1 + [0] = c#(b(c(x1)))
       
       c#(c(a(x1))) = [1 0 1]x1 + [1] >= [0 0 0]x1 + [0] = c#(x1)
       
       c#(c(a(x1))) = [1 0 1]x1 + [1] >= [1  -& 1 ]x1 + [1] = c#(a(c(b(c(x1)))))
       
               [0  -& -&]     [-&]           
       a(x1) = [1  0  1 ]x1 + [1 ] >= x1 = x1
               [0  0  0 ]     [1 ]           
       
                  [0 0 0]     [1]           
       b(a(x1)) = [0 0 0]x1 + [1] >= x1 = x1
                  [0 0 0]     [1]           
       
                     [1 0 1]     [1]    [1  -& 1 ]     [1]                       
       c(c(a(x1))) = [2 1 2]x1 + [2] >= [2  -& 2 ]x1 + [2] = a(c(a(c(b(c(x1))))))
                     [1 0 1]     [1]    [1  -& 1 ]     [1]                       
      problem:
       DPs:
        c#(c(a(x1))) -> c#(x1)
        c#(c(a(x1))) -> c#(a(c(b(c(x1)))))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> x1
        c(c(a(x1))) -> a(c(a(c(b(c(x1))))))
      EDG Processor:
       DPs:
        c#(c(a(x1))) -> c#(x1)
        c#(c(a(x1))) -> c#(a(c(b(c(x1)))))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> x1
        c(c(a(x1))) -> a(c(a(c(b(c(x1))))))
       graph:
        c#(c(a(x1))) -> c#(a(c(b(c(x1))))) ->
        c#(c(a(x1))) -> c#(x1)
        c#(c(a(x1))) -> c#(a(c(b(c(x1))))) ->
        c#(c(a(x1))) -> c#(a(c(b(c(x1)))))
        c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(x1)
        c#(c(a(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(a(c(b(c(x1)))))
       Arctic Interpretation Processor:
        dimension: 3
        interpretation:
         [c#](x0) = [-& 1  0 ]x0 + [0],
         
                   [0  -1 -&]     [-2]
         [c](x0) = [-& -& 1 ]x0 + [0 ]
                   [0  0  0 ]     [0 ],
         
                   [0  -& -1]     [-2]
         [b](x0) = [-2 -& 0 ]x0 + [0 ]
                   [0  -& -&]     [-1],
         
                   [0  -& 0 ]     [0]
         [a](x0) = [-& 0  -&]x0 + [0]
                   [1  0  0 ]     [0]
        orientation:
         c#(c(a(x1))) = [3 2 2]x1 + [2] >= [-& 1  0 ]x1 + [0] = c#(x1)
         
         c#(c(a(x1))) = [3 2 2]x1 + [2] >= [2 1 0]x1 + [1] = c#(a(c(b(c(x1)))))
         
                 [0  -& 0 ]     [0]           
         a(x1) = [-& 0  -&]x1 + [0] >= x1 = x1
                 [1  0  0 ]     [0]           
         
                    [0  -1 0 ]     [0]           
         b(a(x1)) = [1  0  0 ]x1 + [0] >= x1 = x1
                    [0  -& 0 ]     [0]           
         
                       [1 0 0]     [0]    [1 0 0]     [0]                       
         c(c(a(x1))) = [2 1 1]x1 + [1] >= [2 1 1]x1 + [1] = a(c(a(c(b(c(x1))))))
                       [2 1 1]     [1]    [2 1 1]     [1]                       
        problem:
         DPs:
          
         TRS:
          a(x1) -> x1
          b(a(x1)) -> x1
          c(c(a(x1))) -> a(c(a(c(b(c(x1))))))
        Qed