YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> c(a(b(b(x1))))
  b(b(x1)) -> x1
  c(c(x1)) -> a(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)) -> a#(x1)
   TRS:
    a(x1) -> x1
    b(a(x1)) -> c(a(b(b(x1))))
    b(b(x1)) -> x1
    c(c(x1)) -> a(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)) -> a#(x1)
    TRS:
     a(x1) -> x1
     b(a(x1)) -> c(a(b(b(x1))))
     b(b(x1)) -> x1
     c(c(x1)) -> a(x1)
    graph:
     b#(a(x1)) -> c#(a(b(b(x1)))) -> c#(c(x1)) -> a#(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: 2
     #arcs: 9/25
     DPs:
      b#(a(x1)) -> b#(b(x1))
      b#(a(x1)) -> b#(x1)
     TRS:
      a(x1) -> x1
      b(a(x1)) -> c(a(b(b(x1))))
      b(b(x1)) -> x1
      c(c(x1)) -> a(x1)
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [b#](x0) = [-& 0 ]x0 + [0],
       
                 [1  1 ]     [2 ]
       [c](x0) = [-1 -&]x0 + [-&],
       
                 [-& 1 ]     [1]
       [b](x0) = [-1 -4]x0 + [0],
       
                 [0 0]     [1]
       [a](x0) = [0 0]x0 + [1]
      orientation:
       b#(a(x1)) = [0 0]x1 + [1] >= [-1 -4]x1 + [0] = b#(b(x1))
       
       b#(a(x1)) = [0 0]x1 + [1] >= [-& 0 ]x1 + [0] = b#(x1)
       
               [0 0]     [1]           
       a(x1) = [0 0]x1 + [1] >= x1 = x1
       
                  [1  1 ]     [2]    [1  1 ]     [2]                 
       b(a(x1)) = [-1 -1]x1 + [0] >= [-1 -1]x1 + [0] = c(a(b(b(x1))))
       
                  [0  -3]     [1]           
       b(b(x1)) = [-5 0 ]x1 + [0] >= x1 = x1
       
                  [2 2]     [3]    [0 0]     [1]        
       c(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = a(x1)
      problem:
       DPs:
        b#(a(x1)) -> b#(x1)
       TRS:
        a(x1) -> x1
        b(a(x1)) -> c(a(b(b(x1))))
        b(b(x1)) -> x1
        c(c(x1)) -> a(x1)
      EDG Processor:
       DPs:
        b#(a(x1)) -> b#(x1)
       TRS:
        a(x1) -> x1
        b(a(x1)) -> c(a(b(b(x1))))
        b(b(x1)) -> x1
        c(c(x1)) -> a(x1)
       graph:
        b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
       CDG Processor:
        DPs:
         b#(a(x1)) -> b#(x1)
        TRS:
         a(x1) -> x1
         b(a(x1)) -> c(a(b(b(x1))))
         b(b(x1)) -> x1
         c(c(x1)) -> a(x1)
        graph:
         
        Qed