YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> c(b(b(c(a(x1)))))
  b(x1) -> x1
  c(c(x1)) -> a(x1)
  DP Processor:
   DPs:
    b#(a(x1)) -> c#(a(x1))
    b#(a(x1)) -> b#(c(a(x1)))
    b#(a(x1)) -> b#(b(c(a(x1))))
    b#(a(x1)) -> c#(b(b(c(a(x1)))))
    c#(c(x1)) -> a#(x1)
   TRS:
    a(x1) -> x1
    b(a(x1)) -> c(b(b(c(a(x1)))))
    b(x1) -> x1
    c(c(x1)) -> a(x1)
   TDG Processor:
    DPs:
     b#(a(x1)) -> c#(a(x1))
     b#(a(x1)) -> b#(c(a(x1)))
     b#(a(x1)) -> b#(b(c(a(x1))))
     b#(a(x1)) -> c#(b(b(c(a(x1)))))
     c#(c(x1)) -> a#(x1)
    TRS:
     a(x1) -> x1
     b(a(x1)) -> c(b(b(c(a(x1)))))
     b(x1) -> x1
     c(c(x1)) -> a(x1)
    graph:
     b#(a(x1)) -> c#(b(b(c(a(x1))))) -> c#(c(x1)) -> a#(x1)
     b#(a(x1)) -> c#(a(x1)) -> c#(c(x1)) -> a#(x1)
     b#(a(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> c#(b(b(c(a(x1)))))
     b#(a(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(b(c(a(x1))))
     b#(a(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(c(a(x1)))
     b#(a(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> c#(a(x1))
     b#(a(x1)) -> b#(b(c(a(x1)))) -> b#(a(x1)) -> c#(b(b(c(a(x1)))))
     b#(a(x1)) -> b#(b(c(a(x1)))) -> b#(a(x1)) -> b#(b(c(a(x1))))
     b#(a(x1)) -> b#(b(c(a(x1)))) -> b#(a(x1)) -> b#(c(a(x1)))
     b#(a(x1)) -> b#(b(c(a(x1)))) -> b#(a(x1)) -> c#(a(x1))
    CDG Processor:
     DPs:
      b#(a(x1)) -> c#(a(x1))
      b#(a(x1)) -> b#(c(a(x1)))
      b#(a(x1)) -> b#(b(c(a(x1))))
      b#(a(x1)) -> c#(b(b(c(a(x1)))))
      c#(c(x1)) -> a#(x1)
     TRS:
      a(x1) -> x1
      b(a(x1)) -> c(b(b(c(a(x1)))))
      b(x1) -> x1
      c(c(x1)) -> a(x1)
     graph:
      b#(a(x1)) -> c#(b(b(c(a(x1))))) -> c#(c(x1)) -> a#(x1)
      b#(a(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> c#(a(x1))
      b#(a(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(c(a(x1)))
      b#(a(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> b#(b(c(a(x1))))
      b#(a(x1)) -> b#(c(a(x1))) -> b#(a(x1)) -> c#(b(b(c(a(x1)))))
      b#(a(x1)) -> b#(b(c(a(x1)))) -> b#(a(x1)) -> c#(a(x1))
      b#(a(x1)) -> b#(b(c(a(x1)))) -> b#(a(x1)) -> b#(c(a(x1)))
      b#(a(x1)) -> b#(b(c(a(x1)))) -> b#(a(x1)) -> b#(b(c(a(x1))))
      b#(a(x1)) -> b#(b(c(a(x1)))) -> b#(a(x1)) -> c#(b(b(c(a(x1)))))
     SCC Processor:
      #sccs: 1
      #rules: 2
      #arcs: 9/25
      DPs:
       b#(a(x1)) -> b#(c(a(x1)))
       b#(a(x1)) -> b#(b(c(a(x1))))
      TRS:
       a(x1) -> x1
       b(a(x1)) -> c(b(b(c(a(x1)))))
       b(x1) -> x1
       c(c(x1)) -> a(x1)
      Arctic Interpretation Processor:
       dimension: 2
       interpretation:
        [b#](x0) = [-& 0 ]x0 + [0],
        
                  [1  0 ]     [1]
        [c](x0) = [0  -&]x0 + [0],
        
                  [0  1 ]     [0]
        [b](x0) = [-& 0 ]x0 + [0],
        
                  [0  -&]     [-&]
        [a](x0) = [1  0 ]x0 + [1 ]
       orientation:
        b#(a(x1)) = [1 0]x1 + [1] >= [0  -&]x1 + [0] = b#(c(a(x1)))
        
        b#(a(x1)) = [1 0]x1 + [1] >= [0  -&]x1 + [0] = b#(b(c(a(x1))))
        
                [0  -&]     [-&]           
        a(x1) = [1  0 ]x1 + [1 ] >= x1 = x1
        
                   [2 1]     [2]    [2 1]     [2]                    
        b(a(x1)) = [1 0]x1 + [1] >= [1 0]x1 + [1] = c(b(b(c(a(x1)))))
        
                [0  1 ]     [0]           
        b(x1) = [-& 0 ]x1 + [0] >= x1 = x1
        
                   [2 1]     [2]    [0  -&]     [-&]        
        c(c(x1)) = [1 0]x1 + [1] >= [1  0 ]x1 + [1 ] = a(x1)
       problem:
        DPs:
         
        TRS:
         a(x1) -> x1
         b(a(x1)) -> c(b(b(c(a(x1)))))
         b(x1) -> x1
         c(c(x1)) -> a(x1)
       Qed