YES

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

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