YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> a(c(b(c(b(c(x1))))))
  c(c(x1)) -> a(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)) -> b#(c(b(c(x1))))
    b#(a(x1)) -> c#(b(c(b(c(x1)))))
    b#(a(x1)) -> a#(c(b(c(b(c(x1))))))
    c#(c(x1)) -> a#(x1)
   TRS:
    a(x1) -> x1
    b(a(x1)) -> a(c(b(c(b(c(x1))))))
    c(c(x1)) -> a(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)) -> b#(c(b(c(x1))))
     b#(a(x1)) -> c#(b(c(b(c(x1)))))
     b#(a(x1)) -> a#(c(b(c(b(c(x1))))))
     c#(c(x1)) -> a#(x1)
    TRS:
     a(x1) -> x1
     b(a(x1)) -> a(c(b(c(b(c(x1))))))
     c(c(x1)) -> a(x1)
    graph:
     b#(a(x1)) -> c#(b(c(b(c(x1))))) -> c#(c(x1)) -> a#(x1)
     b#(a(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> a#(x1)
     b#(a(x1)) -> c#(x1) -> c#(c(x1)) -> a#(x1)
     b#(a(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> a#(c(b(c(b(c(x1))))))
     b#(a(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> c#(b(c(b(c(x1)))))
     b#(a(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> b#(c(b(c(x1))))
     b#(a(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> c#(b(c(x1)))
     b#(a(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> b#(c(x1))
     b#(a(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> c#(x1)
     b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> a#(c(b(c(b(c(x1))))))
     b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(b(c(b(c(x1)))))
     b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> b#(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)
    CDG Processor:
     DPs:
      b#(a(x1)) -> c#(x1)
      b#(a(x1)) -> b#(c(x1))
      b#(a(x1)) -> c#(b(c(x1)))
      b#(a(x1)) -> b#(c(b(c(x1))))
      b#(a(x1)) -> c#(b(c(b(c(x1)))))
      b#(a(x1)) -> a#(c(b(c(b(c(x1))))))
      c#(c(x1)) -> a#(x1)
     TRS:
      a(x1) -> x1
      b(a(x1)) -> a(c(b(c(b(c(x1))))))
      c(c(x1)) -> a(x1)
     graph:
      b#(a(x1)) -> c#(b(c(b(c(x1))))) -> c#(c(x1)) -> a#(x1)
      b#(a(x1)) -> c#(b(c(x1))) -> c#(c(x1)) -> a#(x1)
      b#(a(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> c#(x1)
      b#(a(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> b#(c(x1))
      b#(a(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> c#(b(c(x1)))
      b#(a(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> b#(c(b(c(x1))))
      b#(a(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> c#(b(c(b(c(x1)))))
      b#(a(x1)) -> b#(c(b(c(x1)))) -> b#(a(x1)) -> a#(c(b(c(b(c(x1))))))
      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)))
      b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> b#(c(b(c(x1))))
      b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> c#(b(c(b(c(x1)))))
      b#(a(x1)) -> b#(c(x1)) -> b#(a(x1)) -> a#(c(b(c(b(c(x1))))))
     SCC Processor:
      #sccs: 1
      #rules: 2
      #arcs: 14/49
      DPs:
       b#(a(x1)) -> b#(c(b(c(x1))))
       b#(a(x1)) -> b#(c(x1))
      TRS:
       a(x1) -> x1
       b(a(x1)) -> a(c(b(c(b(c(x1))))))
       c(c(x1)) -> a(x1)
      Arctic Interpretation Processor:
       dimension: 2
       interpretation:
        [b#](x0) = [2 1]x0 + [0],
        
                  [-& 0 ]     [0]
        [c](x0) = [0  1 ]x0 + [3],
        
                  [1  0 ]     [0]
        [b](x0) = [0  -&]x0 + [2],
        
                  [0 1]     [3]
        [a](x0) = [1 0]x0 + [0]
       orientation:
        b#(a(x1)) = [2 3]x1 + [5] >= [1 2]x1 + [4] = b#(c(b(c(x1))))
        
        b#(a(x1)) = [2 3]x1 + [5] >= [1 2]x1 + [4] = b#(c(x1))
        
                [0 1]     [3]           
        a(x1) = [1 0]x1 + [0] >= x1 = x1
        
                   [1 2]     [4]    [1 2]     [4]                       
        b(a(x1)) = [0 1]x1 + [3] >= [0 1]x1 + [3] = a(c(b(c(b(c(x1))))))
        
                   [0 1]     [3]    [0 1]     [3]        
        c(c(x1)) = [1 2]x1 + [4] >= [1 0]x1 + [0] = a(x1)
       problem:
        DPs:
         
        TRS:
         a(x1) -> x1
         b(a(x1)) -> a(c(b(c(b(c(x1))))))
         c(c(x1)) -> a(x1)
       Qed