YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> a(c(b(c(x1))))
  c(c(x1)) -> a(b(c(x1)))
  DP Processor:
   DPs:
    b#(a(x1)) -> c#(x1)
    b#(a(x1)) -> b#(c(x1))
    b#(a(x1)) -> c#(b(c(x1)))
    b#(a(x1)) -> a#(c(b(c(x1))))
    c#(c(x1)) -> b#(c(x1))
    c#(c(x1)) -> a#(b(c(x1)))
   TRS:
    a(x1) -> x1
    b(a(x1)) -> a(c(b(c(x1))))
    c(c(x1)) -> a(b(c(x1)))
   TDG Processor:
    DPs:
     b#(a(x1)) -> c#(x1)
     b#(a(x1)) -> b#(c(x1))
     b#(a(x1)) -> c#(b(c(x1)))
     b#(a(x1)) -> a#(c(b(c(x1))))
     c#(c(x1)) -> b#(c(x1))
     c#(c(x1)) -> a#(b(c(x1)))
    TRS:
     a(x1) -> x1
     b(a(x1)) -> a(c(b(c(x1))))
     c(c(x1)) -> a(b(c(x1)))
    graph:
     c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> a#(c(b(c(x1))))
     c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(b(c(x1)))
     c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> b#(c(x1))
     c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(x1)
     b#(a(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> a#(b(c(x1)))
     b#(a(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> b#(c(x1))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(b(c(x1)))
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> b#(c(x1))
     b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> a#(c(b(c(x1))))
     b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(b(c(x1)))
     b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> b#(c(x1))
     b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 12/36
     DPs:
      c#(c(x1)) -> b#(c(x1))
      b#(a(x1)) -> c#(x1)
      b#(a(x1)) -> b#(c(x1))
      b#(a(x1)) -> c#(b(c(x1)))
     TRS:
      a(x1) -> x1
      b(a(x1)) -> a(c(b(c(x1))))
      c(c(x1)) -> a(b(c(x1)))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       b(a(x1)) -> a(c(b(c(x1))))
       c(c(x1)) -> a(b(c(x1)))
      interpretation:
       [b#](x0) = [0 0]x0 + [3],
       
                 [2  0 ]     [0]
       [b](x0) = [0  -&]x0 + [0],
       
       [c#](x0) = [0 2]x0 + [0],
       
                 [0 2]     [2]
       [a](x0) = [0 0]x0 + [2],
       
                 [-& 0 ]     [0]
       [c](x0) = [-& 2 ]x0 + [2]
      orientation:
       c#(c(x1)) = [-& 4 ]x1 + [4] >= [-& 2 ]x1 + [3] = b#(c(x1))
       
       b#(a(x1)) = [0 2]x1 + [3] >= [0 2]x1 + [0] = c#(x1)
       
       b#(a(x1)) = [0 2]x1 + [3] >= [-& 2 ]x1 + [3] = b#(c(x1))
       
       b#(a(x1)) = [0 2]x1 + [3] >= [-& 2 ]x1 + [2] = c#(b(c(x1)))
       
               [0 2]     [2]           
       a(x1) = [0 0]x1 + [2] >= x1 = x1
       
                  [2 4]     [4]    [-& 4 ]     [4]                 
       b(a(x1)) = [0 2]x1 + [2] >= [-& 2 ]x1 + [2] = a(c(b(c(x1))))
       
                  [-& 2 ]     [2]    [-& 2 ]     [2]              
       c(c(x1)) = [-& 4 ]x1 + [4] >= [-& 2 ]x1 + [2] = a(b(c(x1)))
      problem:
       DPs:
        b#(a(x1)) -> c#(x1)
        b#(a(x1)) -> b#(c(x1))
        b#(a(x1)) -> c#(b(c(x1)))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> a(c(b(c(x1))))
        c(c(x1)) -> a(b(c(x1)))
      Restore Modifier:
       DPs:
        b#(a(x1)) -> c#(x1)
        b#(a(x1)) -> b#(c(x1))
        b#(a(x1)) -> c#(b(c(x1)))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> a(c(b(c(x1))))
        c(c(x1)) -> a(b(c(x1)))
       EDG Processor:
        DPs:
         b#(a(x1)) -> c#(x1)
         b#(a(x1)) -> b#(c(x1))
         b#(a(x1)) -> c#(b(c(x1)))
        TRS:
         a(x1) -> x1
         b(a(x1)) -> a(c(b(c(x1))))
         c(c(x1)) -> a(b(c(x1)))
        graph:
         b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(x1)
         b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> b#(c(x1))
         b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(b(c(x1)))
        SCC Processor:
         #sccs: 1
         #rules: 1
         #arcs: 3/9
         DPs:
          b#(a(x1)) -> b#(c(x1))
         TRS:
          a(x1) -> x1
          b(a(x1)) -> a(c(b(c(x1))))
          c(c(x1)) -> a(b(c(x1)))
         Arctic Interpretation Processor:
          dimension: 2
          usable rules:
           a(x1) -> x1
           b(a(x1)) -> a(c(b(c(x1))))
           c(c(x1)) -> a(b(c(x1)))
          interpretation:
           [b#](x0) = [-& 0 ]x0 + [0],
           
                     [-& 0 ]     [0]
           [b](x0) = [-& 1 ]x0 + [0],
           
                     [0  -&]     [1]
           [a](x0) = [1  0 ]x0 + [1],
           
                     [1  0 ]     [1 ]
           [c](x0) = [0  -&]x0 + [-&]
          orientation:
           b#(a(x1)) = [1 0]x1 + [1] >= [0  -&]x1 + [0] = b#(c(x1))
           
                   [0  -&]     [1]           
           a(x1) = [1  0 ]x1 + [1] >= x1 = x1
           
                      [1 0]     [1]    [1  -&]     [1]                 
           b(a(x1)) = [2 1]x1 + [2] >= [2  -&]x1 + [2] = a(c(b(c(x1))))
           
                      [2 1]     [2]    [0  -&]     [1]              
           c(c(x1)) = [1 0]x1 + [1] >= [1  -&]x1 + [1] = a(b(c(x1)))
          problem:
           DPs:
            
           TRS:
            a(x1) -> x1
            b(a(x1)) -> a(c(b(c(x1))))
            c(c(x1)) -> a(b(c(x1)))
          Qed