YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> c(a(b(b(x1))))
  b(x1) -> x1
  c(c(x1)) -> a(b(x1))
  DP Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> b#(b(x1))
    b#(a(x1)) -> a#(b(b(x1)))
    b#(a(x1)) -> c#(a(b(b(x1))))
    c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> a#(b(x1))
   TRS:
    a(x1) -> x1
    b(a(x1)) -> c(a(b(b(x1))))
    b(x1) -> x1
    c(c(x1)) -> a(b(x1))
   TDG Processor:
    DPs:
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(b(x1))
     b#(a(x1)) -> a#(b(b(x1)))
     b#(a(x1)) -> c#(a(b(b(x1))))
     c#(c(x1)) -> b#(x1)
     c#(c(x1)) -> a#(b(x1))
    TRS:
     a(x1) -> x1
     b(a(x1)) -> c(a(b(b(x1))))
     b(x1) -> x1
     c(c(x1)) -> a(b(x1))
    graph:
     c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(b(x1))))
     c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
     c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
     c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> c#(a(b(b(x1)))) -> c#(c(x1)) -> a#(b(x1))
     b#(a(x1)) -> c#(a(b(b(x1)))) -> c#(c(x1)) -> b#(x1)
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> c#(a(b(b(x1))))
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> a#(b(b(x1)))
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(b(x1))
     b#(a(x1)) -> b#(b(x1)) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(b(x1))))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 14/36
     DPs:
      c#(c(x1)) -> b#(x1)
      b#(a(x1)) -> b#(x1)
      b#(a(x1)) -> b#(b(x1))
      b#(a(x1)) -> c#(a(b(b(x1))))
     TRS:
      a(x1) -> x1
      b(a(x1)) -> c(a(b(b(x1))))
      b(x1) -> x1
      c(c(x1)) -> a(b(x1))
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [c#](x0) = [0 0]x0 + [0],
       
       [b#](x0) = [0  -&]x0,
       
                 [0 1]     [0 ]
       [c](x0) = [0 0]x0 + [-&],
       
                 [0 0]  
       [b](x0) = [0 0]x0,
       
                 [1 1]     [0 ]
       [a](x0) = [0 0]x0 + [-&]
      orientation:
       c#(c(x1)) = [0 1]x1 + [0] >= [0  -&]x1 = b#(x1)
       
       b#(a(x1)) = [1 1]x1 + [0] >= [0  -&]x1 = b#(x1)
       
       b#(a(x1)) = [1 1]x1 + [0] >= [0 0]x1 = b#(b(x1))
       
       b#(a(x1)) = [1 1]x1 + [0] >= [1 1]x1 + [0] = c#(a(b(b(x1))))
       
               [1 1]     [0 ]           
       a(x1) = [0 0]x1 + [-&] >= x1 = x1
       
                  [1 1]     [0]    [1 1]     [0]                 
       b(a(x1)) = [1 1]x1 + [0] >= [1 1]x1 + [0] = c(a(b(b(x1))))
       
               [0 0]             
       b(x1) = [0 0]x1 >= x1 = x1
       
                  [1 1]     [0]    [1 1]     [0 ]           
       c(c(x1)) = [0 1]x1 + [0] >= [0 0]x1 + [-&] = a(b(x1))
      problem:
       DPs:
        c#(c(x1)) -> b#(x1)
        b#(a(x1)) -> c#(a(b(b(x1))))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> c(a(b(b(x1))))
        b(x1) -> x1
        c(c(x1)) -> a(b(x1))
      EDG Processor:
       DPs:
        c#(c(x1)) -> b#(x1)
        b#(a(x1)) -> c#(a(b(b(x1))))
       TRS:
        a(x1) -> x1
        b(a(x1)) -> c(a(b(b(x1))))
        b(x1) -> x1
        c(c(x1)) -> a(b(x1))
       graph:
        c#(c(x1)) -> b#(x1) -> b#(a(x1)) -> c#(a(b(b(x1))))
        b#(a(x1)) -> c#(a(b(b(x1)))) -> c#(c(x1)) -> b#(x1)
       Arctic Interpretation Processor:
        dimension: 2
        interpretation:
         [c#](x0) = [-& 0 ]x0 + [0],
         
         [b#](x0) = [2 0]x0 + [0],
         
                   [0 0]     [-&]
         [c](x0) = [3 0]x0 + [0 ],
         
                   [0  -&]     [-&]
         [b](x0) = [3  0 ]x0 + [0 ],
         
                   [3 0]     [0]
         [a](x0) = [0 0]x0 + [0]
        orientation:
         c#(c(x1)) = [3 0]x1 + [0] >= [2 0]x1 + [0] = b#(x1)
         
         b#(a(x1)) = [5 2]x1 + [2] >= [3 0]x1 + [0] = c#(a(b(b(x1))))
         
                 [3 0]     [0]           
         a(x1) = [0 0]x1 + [0] >= x1 = x1
         
                    [3 0]     [0]    [3 0]     [0]                 
         b(a(x1)) = [6 3]x1 + [3] >= [6 3]x1 + [3] = c(a(b(b(x1))))
         
                 [0  -&]     [-&]           
         b(x1) = [3  0 ]x1 + [0 ] >= x1 = x1
         
                    [3 0]     [0]    [3 0]     [0]           
         c(c(x1)) = [3 3]x1 + [0] >= [3 0]x1 + [0] = a(b(x1))
        problem:
         DPs:
          c#(c(x1)) -> b#(x1)
         TRS:
          a(x1) -> x1
          b(a(x1)) -> c(a(b(b(x1))))
          b(x1) -> x1
          c(c(x1)) -> a(b(x1))
        EDG Processor:
         DPs:
          c#(c(x1)) -> b#(x1)
         TRS:
          a(x1) -> x1
          b(a(x1)) -> c(a(b(b(x1))))
          b(x1) -> x1
          c(c(x1)) -> a(b(x1))
         graph:
          
         Qed