YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(a(x1)) -> a(b(c(b(x1))))
  b(x1) -> a(x1)
  c(c(c(x1))) -> x1
  DP Processor:
   DPs:
    b#(a(x1)) -> b#(x1)
    b#(a(x1)) -> c#(b(x1))
    b#(a(x1)) -> b#(c(b(x1)))
    b#(a(x1)) -> a#(b(c(b(x1))))
    b#(x1) -> a#(x1)
   TRS:
    a(x1) -> x1
    b(a(x1)) -> a(b(c(b(x1))))
    b(x1) -> a(x1)
    c(c(c(x1))) -> x1
   TDG Processor:
    DPs:
     b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> b#(c(b(x1)))
     b#(a(x1)) -> a#(b(c(b(x1))))
     b#(x1) -> a#(x1)
    TRS:
     a(x1) -> x1
     b(a(x1)) -> a(b(c(b(x1))))
     b(x1) -> a(x1)
     c(c(c(x1))) -> x1
    graph:
     b#(a(x1)) -> b#(c(b(x1))) -> b#(x1) -> a#(x1)
     b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> a#(b(c(b(x1))))
     b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> b#(c(b(x1)))
     b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> b#(c(b(x1))) -> b#(a(x1)) -> b#(x1)
     b#(a(x1)) -> b#(x1) -> b#(x1) -> a#(x1)
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> a#(b(c(b(x1))))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(c(b(x1)))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> c#(b(x1))
     b#(a(x1)) -> b#(x1) -> b#(a(x1)) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 10/25
     DPs:
      b#(a(x1)) -> b#(c(b(x1)))
      b#(a(x1)) -> b#(x1)
     TRS:
      a(x1) -> x1
      b(a(x1)) -> a(b(c(b(x1))))
      b(x1) -> a(x1)
      c(c(c(x1))) -> x1
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [b#](x0) = [-4 0 ]x0 + [0],
       
                 [1  -1]     [-4]
       [c](x0) = [0  -4]x0 + [-&],
       
                 [0 0]     [-&]
       [b](x0) = [1 2]x0 + [2 ],
       
                 [0  -1]     [-&]
       [a](x0) = [1  1 ]x0 + [1 ]
      orientation:
       b#(a(x1)) = [1 1]x1 + [1] >= [0 0]x1 + [0] = b#(c(b(x1)))
       
       b#(a(x1)) = [1 1]x1 + [1] >= [-4 0 ]x1 + [0] = b#(x1)
       
               [0  -1]     [-&]           
       a(x1) = [1  1 ]x1 + [1 ] >= x1 = x1
       
                  [1 1]     [1]    [1 1]     [1]                 
       b(a(x1)) = [3 3]x1 + [3] >= [3 3]x1 + [3] = a(b(c(b(x1))))
       
               [0 0]     [-&]    [0  -1]     [-&]        
       b(x1) = [1 2]x1 + [2 ] >= [1  1 ]x1 + [1 ] = a(x1)
       
                     [3 1]     [-2]           
       c(c(c(x1))) = [2 0]x1 + [-3] >= x1 = x1
      problem:
       DPs:
        
       TRS:
        a(x1) -> x1
        b(a(x1)) -> a(b(c(b(x1))))
        b(x1) -> a(x1)
        c(c(c(x1))) -> x1
      Qed