YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  a(x1) -> c(b(b(x1)))
  b(c(a(x1))) -> a(a(c(x1)))
  c(x1) -> x1
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> b#(b(x1))
    a#(x1) -> c#(b(b(x1)))
    b#(c(a(x1))) -> c#(x1)
    b#(c(a(x1))) -> a#(c(x1))
    b#(c(a(x1))) -> a#(a(c(x1)))
   TRS:
    a(x1) -> x1
    a(x1) -> c(b(b(x1)))
    b(c(a(x1))) -> a(a(c(x1)))
    c(x1) -> x1
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1))
     a#(x1) -> c#(b(b(x1)))
     b#(c(a(x1))) -> c#(x1)
     b#(c(a(x1))) -> a#(c(x1))
     b#(c(a(x1))) -> a#(a(c(x1)))
    TRS:
     a(x1) -> x1
     a(x1) -> c(b(b(x1)))
     b(c(a(x1))) -> a(a(c(x1)))
     c(x1) -> x1
    graph:
     b#(c(a(x1))) -> a#(c(x1)) -> a#(x1) -> c#(b(b(x1)))
     b#(c(a(x1))) -> a#(c(x1)) -> a#(x1) -> b#(b(x1))
     b#(c(a(x1))) -> a#(c(x1)) -> a#(x1) -> b#(x1)
     b#(c(a(x1))) -> a#(a(c(x1))) -> a#(x1) -> c#(b(b(x1)))
     b#(c(a(x1))) -> a#(a(c(x1))) -> a#(x1) -> b#(b(x1))
     b#(c(a(x1))) -> a#(a(c(x1))) -> a#(x1) -> b#(x1)
     a#(x1) -> b#(b(x1)) -> b#(c(a(x1))) -> a#(a(c(x1)))
     a#(x1) -> b#(b(x1)) -> b#(c(a(x1))) -> a#(c(x1))
     a#(x1) -> b#(b(x1)) -> b#(c(a(x1))) -> c#(x1)
     a#(x1) -> b#(x1) -> b#(c(a(x1))) -> a#(a(c(x1)))
     a#(x1) -> b#(x1) -> b#(c(a(x1))) -> a#(c(x1))
     a#(x1) -> b#(x1) -> b#(c(a(x1))) -> c#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 12/36
     DPs:
      b#(c(a(x1))) -> a#(c(x1))
      a#(x1) -> b#(x1)
      b#(c(a(x1))) -> a#(a(c(x1)))
      a#(x1) -> b#(b(x1))
     TRS:
      a(x1) -> x1
      a(x1) -> c(b(b(x1)))
      b(c(a(x1))) -> a(a(c(x1)))
      c(x1) -> x1
     Arctic Interpretation Processor:
      dimension: 3
      interpretation:
       [b#](x0) = [0 0 0]x0 + [0],
       
       [a#](x0) = [1 0 1]x0 + [1],
       
                 [-& -& 0 ]     [0 ]
       [b](x0) = [-& -& 0 ]x0 + [-&]
                 [0  -& -&]     [-&],
       
                 [0  0  -&]     [0]
       [c](x0) = [0  0  -&]x0 + [0]
                 [0  1  0 ]     [0],
       
                 [0  -& -&]     [0]
       [a](x0) = [1  1  0 ]x0 + [1]
                 [1  0  0 ]     [0]
      orientation:
       b#(c(a(x1))) = [2 2 1]x1 + [2] >= [1 2 1]x1 + [1] = a#(c(x1))
       
       a#(x1) = [1 0 1]x1 + [1] >= [0 0 0]x1 + [0] = b#(x1)
       
       b#(c(a(x1))) = [2 2 1]x1 + [2] >= [2 2 1]x1 + [2] = a#(a(c(x1)))
       
       a#(x1) = [1 0 1]x1 + [1] >= [0  -& 0 ]x1 + [0] = b#(b(x1))
       
               [0  -& -&]     [0]           
       a(x1) = [1  1  0 ]x1 + [1] >= x1 = x1
               [1  0  0 ]     [0]           
       
               [0  -& -&]     [0]    [0  -& -&]     [0]              
       a(x1) = [1  1  0 ]x1 + [1] >= [0  -& -&]x1 + [0] = c(b(b(x1)))
               [1  0  0 ]     [0]    [1  -& 0 ]     [0]              
       
                     [2 2 1]     [2]    [0  0  -&]     [0]              
       b(c(a(x1))) = [2 2 1]x1 + [2] >= [2  2  1 ]x1 + [2] = a(a(c(x1)))
                     [1 1 0]     [1]    [1  1  0 ]     [1]              
       
               [0  0  -&]     [0]           
       c(x1) = [0  0  -&]x1 + [0] >= x1 = x1
               [0  1  0 ]     [0]           
      problem:
       DPs:
        b#(c(a(x1))) -> a#(c(x1))
        a#(x1) -> b#(x1)
        b#(c(a(x1))) -> a#(a(c(x1)))
       TRS:
        a(x1) -> x1
        a(x1) -> c(b(b(x1)))
        b(c(a(x1))) -> a(a(c(x1)))
        c(x1) -> x1
      EDG Processor:
       DPs:
        b#(c(a(x1))) -> a#(c(x1))
        a#(x1) -> b#(x1)
        b#(c(a(x1))) -> a#(a(c(x1)))
       TRS:
        a(x1) -> x1
        a(x1) -> c(b(b(x1)))
        b(c(a(x1))) -> a(a(c(x1)))
        c(x1) -> x1
       graph:
        b#(c(a(x1))) -> a#(c(x1)) -> a#(x1) -> b#(x1)
        b#(c(a(x1))) -> a#(a(c(x1))) -> a#(x1) -> b#(x1)
        a#(x1) -> b#(x1) -> b#(c(a(x1))) -> a#(c(x1))
        a#(x1) -> b#(x1) -> b#(c(a(x1))) -> a#(a(c(x1)))
       Arctic Interpretation Processor:
        dimension: 2
        interpretation:
         [b#](x0) = [-& 0 ]x0 + [0],
         
         [a#](x0) = [-& 0 ]x0 + [0],
         
                   [-1 -4]     [0 ]
         [b](x0) = [0  -1]x0 + [-&],
         
                   [0  1 ]     [0]
         [c](x0) = [-2 0 ]x0 + [0],
         
                   [0 0]     [1]
         [a](x0) = [0 1]x0 + [2]
        orientation:
         b#(c(a(x1))) = [0 1]x1 + [2] >= [-2 0 ]x1 + [0] = a#(c(x1))
         
         a#(x1) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = b#(x1)
         
         b#(c(a(x1))) = [0 1]x1 + [2] >= [0 1]x1 + [2] = a#(a(c(x1)))
         
                 [0 0]     [1]           
         a(x1) = [0 1]x1 + [2] >= x1 = x1
         
                 [0 0]     [1]    [0  -1]     [1]              
         a(x1) = [0 1]x1 + [2] >= [-1 -2]x1 + [0] = c(b(b(x1)))
         
                       [0 1]     [2]    [0 1]     [2]              
         b(c(a(x1))) = [1 2]x1 + [3] >= [1 2]x1 + [3] = a(a(c(x1)))
         
                 [0  1 ]     [0]           
         c(x1) = [-2 0 ]x1 + [0] >= x1 = x1
        problem:
         DPs:
          a#(x1) -> b#(x1)
          b#(c(a(x1))) -> a#(a(c(x1)))
         TRS:
          a(x1) -> x1
          a(x1) -> c(b(b(x1)))
          b(c(a(x1))) -> a(a(c(x1)))
          c(x1) -> x1
        EDG Processor:
         DPs:
          a#(x1) -> b#(x1)
          b#(c(a(x1))) -> a#(a(c(x1)))
         TRS:
          a(x1) -> x1
          a(x1) -> c(b(b(x1)))
          b(c(a(x1))) -> a(a(c(x1)))
          c(x1) -> x1
         graph:
          b#(c(a(x1))) -> a#(a(c(x1))) -> a#(x1) -> b#(x1)
          a#(x1) -> b#(x1) -> b#(c(a(x1))) -> a#(a(c(x1)))
         Arctic Interpretation Processor:
          dimension: 2
          interpretation:
           [b#](x0) = [0 1]x0 + [0],
           
           [a#](x0) = [0 1]x0 + [0],
           
                     [-& 1 ]     [2]
           [b](x0) = [-& -1]x0 + [0],
           
                     [0 0]     [-&]
           [c](x0) = [0 0]x0 + [0 ],
           
                     [1  1 ]     [3]
           [a](x0) = [-& 0 ]x0 + [2]
          orientation:
           a#(x1) = [0 1]x1 + [0] >= [0 1]x1 + [0] = b#(x1)
           
           b#(c(a(x1))) = [2 2]x1 + [4] >= [1 1]x1 + [3] = a#(a(c(x1)))
           
                   [1  1 ]     [3]           
           a(x1) = [-& 0 ]x1 + [2] >= x1 = x1
           
                   [1  1 ]     [3]    [-& 0 ]     [2]              
           a(x1) = [-& 0 ]x1 + [2] >= [-& 0 ]x1 + [2] = c(b(b(x1)))
           
                         [2 2]     [4]    [2 2]     [4]              
           b(c(a(x1))) = [0 0]x1 + [2] >= [0 0]x1 + [2] = a(a(c(x1)))
           
                   [0 0]     [-&]           
           c(x1) = [0 0]x1 + [0 ] >= x1 = x1
          problem:
           DPs:
            a#(x1) -> b#(x1)
           TRS:
            a(x1) -> x1
            a(x1) -> c(b(b(x1)))
            b(c(a(x1))) -> a(a(c(x1)))
            c(x1) -> x1
          EDG Processor:
           DPs:
            a#(x1) -> b#(x1)
           TRS:
            a(x1) -> x1
            a(x1) -> c(b(b(x1)))
            b(c(a(x1))) -> a(a(c(x1)))
            c(x1) -> x1
           graph:
            
           Qed