YES

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

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