YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(b(a(x1))) -> c(b(b(b(x1))))
  b(c(x1)) -> a(a(x1))
  DP Processor:
   DPs:
    b#(b(a(x1))) -> b#(x1)
    b#(b(a(x1))) -> b#(b(x1))
    b#(b(a(x1))) -> b#(b(b(x1)))
    b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> a#(a(x1))
   TRS:
    a(x1) -> x1
    b(b(a(x1))) -> c(b(b(b(x1))))
    b(c(x1)) -> a(a(x1))
   TDG Processor:
    DPs:
     b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(b(b(x1)))
     b#(c(x1)) -> a#(x1)
     b#(c(x1)) -> a#(a(x1))
    TRS:
     a(x1) -> x1
     b(b(a(x1))) -> c(b(b(b(x1))))
     b(c(x1)) -> a(a(x1))
    graph:
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(c(x1)) -> a#(a(x1))
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(c(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> b#(b(b(x1)))
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(b(x1)) -> b#(c(x1)) -> a#(a(x1))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(c(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(b(x1)))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(x1) -> b#(c(x1)) -> a#(a(x1))
     b#(b(a(x1))) -> b#(x1) -> b#(c(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(b(x1)))
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 15/25
     DPs:
      b#(b(a(x1))) -> b#(b(b(x1)))
      b#(b(a(x1))) -> b#(x1)
      b#(b(a(x1))) -> b#(b(x1))
     TRS:
      a(x1) -> x1
      b(b(a(x1))) -> c(b(b(b(x1))))
      b(c(x1)) -> a(a(x1))
     Arctic Interpretation Processor:
      dimension: 3
      interpretation:
       [b#](x0) = [0  0  -&]x0 + [0],
       
                 [-& -& 0 ]     [0]
       [c](x0) = [-& -& 0 ]x0 + [1]
                 [0  0  1 ]     [1],
       
                 [-& -& 0 ]     [0]
       [b](x0) = [1  -& 0 ]x0 + [0]
                 [0  0  -&]     [1],
       
                 [0  0  1 ]     [1 ]
       [a](x0) = [-& 0  0 ]x0 + [-&]
                 [-& -& 0 ]     [0 ]
      orientation:
       b#(b(a(x1))) = [1 1 2]x1 + [2] >= [0 0 1]x1 + [1] = b#(b(b(x1)))
       
       b#(b(a(x1))) = [1 1 2]x1 + [2] >= [0  0  -&]x1 + [0] = b#(x1)
       
       b#(b(a(x1))) = [1 1 2]x1 + [2] >= [1  -& 0 ]x1 + [0] = b#(b(x1))
       
               [0  0  1 ]     [1 ]           
       a(x1) = [-& 0  0 ]x1 + [-&] >= x1 = x1
               [-& -& 0 ]     [0 ]           
       
                     [0 0 1]     [1]    [0 0 1]     [1]                 
       b(b(a(x1))) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = c(b(b(b(x1))))
                     [1 1 2]     [2]    [1 1 2]     [2]                 
       
                  [0  0  1 ]     [1]    [0  0  1 ]     [1]           
       b(c(x1)) = [0  0  1 ]x1 + [1] >= [-& 0  0 ]x1 + [0] = a(a(x1))
                  [-& -& 0 ]     [1]    [-& -& 0 ]     [0]           
      problem:
       DPs:
        b#(b(a(x1))) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(b(b(b(x1))))
        b(c(x1)) -> a(a(x1))
      EDG Processor:
       DPs:
        b#(b(a(x1))) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(b(b(b(x1))))
        b(c(x1)) -> a(a(x1))
       graph:
        b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1))
       CDG Processor:
        DPs:
         b#(b(a(x1))) -> b#(b(x1))
        TRS:
         a(x1) -> x1
         b(b(a(x1))) -> c(b(b(b(x1))))
         b(c(x1)) -> a(a(x1))
        graph:
         
        Qed