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:
       [c#](x0) = [0  -&]x0 + [0],
       
       [b#](x0) = [0  -&]x0 + [0],
       
                 [-& 0 ]     [0]
       [c](x0) = [-& 3 ]x0 + [3],
       
                 [3  0 ]     [0]
       [b](x0) = [0  -&]x0 + [0],
       
                 [0  3 ]     [3]
       [a](x0) = [-& 0 ]x0 + [0]
      orientation:
       c#(c(x1)) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = b#(c(x1))
       
       b#(a(x1)) = [0 3]x1 + [3] >= [0  -&]x1 + [0] = c#(x1)
       
       b#(a(x1)) = [0 3]x1 + [3] >= [-& 0 ]x1 + [0] = b#(c(x1))
       
       b#(a(x1)) = [0 3]x1 + [3] >= [-& 3 ]x1 + [3] = c#(b(c(x1)))
       
               [0  3 ]     [3]           
       a(x1) = [-& 0 ]x1 + [0] >= x1 = x1
       
                  [3 6]     [6]    [-& 6 ]     [6]                 
       b(a(x1)) = [0 3]x1 + [3] >= [-& 3 ]x1 + [3] = a(c(b(c(x1))))
       
                  [-& 3 ]     [3]    [-& 3 ]     [3]              
       c(c(x1)) = [-& 6 ]x1 + [6] >= [-& 0 ]x1 + [0] = a(b(c(x1)))
      problem:
       DPs:
        c#(c(x1)) -> b#(c(x1))
        b#(a(x1)) -> 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:
        c#(c(x1)) -> b#(c(x1))
        b#(a(x1)) -> 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:
         c#(c(x1)) -> b#(c(x1))
         b#(a(x1)) -> 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:
         c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(x1)
         c#(c(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(b(c(x1)))
         b#(a(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> b#(c(x1))
         b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> 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:
          [c#](x0) = [0  -&]x0 + [0],
          
          [b#](x0) = [-& 0 ]x0 + [0],
          
                    [2  0 ]     [3]
          [c](x0) = [0  -&]x0 + [1],
          
                    [-& 0 ]     [0]
          [b](x0) = [0  2 ]x0 + [0],
          
                    [0 2]     [0]
          [a](x0) = [2 0]x0 + [3]
         orientation:
          c#(c(x1)) = [2 0]x1 + [3] >= [0  -&]x1 + [1] = b#(c(x1))
          
          b#(a(x1)) = [2 0]x1 + [3] >= [0  -&]x1 + [0] = c#(x1)
          
          b#(a(x1)) = [2 0]x1 + [3] >= [0  -&]x1 + [1] = c#(b(c(x1)))
          
                  [0 2]     [0]           
          a(x1) = [2 0]x1 + [3] >= x1 = x1
          
                     [2 0]     [3]    [2 0]     [3]                 
          b(a(x1)) = [4 2]x1 + [5] >= [4 2]x1 + [5] = a(c(b(c(x1))))
          
                     [4 2]     [5]    [4 2]     [5]              
          c(c(x1)) = [2 0]x1 + [3] >= [2 0]x1 + [3] = 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