YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(b(a(x1))) -> c(b(b(b(x1))))
  c(b(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#(b(a(x1))) -> c#(b(b(b(x1))))
    c#(b(x1)) -> a#(x1)
    c#(b(x1)) -> a#(a(x1))
   TRS:
    a(x1) -> x1
    b(b(a(x1))) -> c(b(b(b(x1))))
    c(b(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#(b(a(x1))) -> c#(b(b(b(x1))))
     c#(b(x1)) -> a#(x1)
     c#(b(x1)) -> a#(a(x1))
    TRS:
     a(x1) -> x1
     b(b(a(x1))) -> c(b(b(b(x1))))
     c(b(x1)) -> a(a(x1))
    graph:
     b#(b(a(x1))) -> c#(b(b(b(x1)))) -> c#(b(x1)) -> a#(a(x1))
     b#(b(a(x1))) -> c#(b(b(b(x1)))) -> c#(b(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(b(b(x1))) -> b#(b(a(x1))) -> c#(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(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#(b(a(x1))) -> c#(b(b(b(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#(b(a(x1))) -> c#(b(b(b(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: 14/36
     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))))
      c(b(x1)) -> a(a(x1))
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [b#](x0) = [0  -&]x0,
       
                 [-& 0 ]     [0]
       [c](x0) = [0  1 ]x0 + [0],
       
                 [-& 0 ]     [0]
       [b](x0) = [0  -&]x0 + [1],
       
                 [0  -&]     [0]
       [a](x0) = [1  0 ]x0 + [2]
      orientation:
       b#(b(a(x1))) = [1 0]x1 + [2] >= [0  -&]x1 + [1] = b#(b(b(x1)))
       
       b#(b(a(x1))) = [1 0]x1 + [2] >= [0  -&]x1 = b#(x1)
       
       b#(b(a(x1))) = [1 0]x1 + [2] >= [-& 0 ]x1 + [0] = b#(b(x1))
       
               [0  -&]     [0]           
       a(x1) = [1  0 ]x1 + [2] >= x1 = x1
       
                     [0  -&]     [1]    [0  -&]     [1]                 
       b(b(a(x1))) = [1  0 ]x1 + [2] >= [1  0 ]x1 + [2] = c(b(b(b(x1))))
       
                  [0  -&]     [1]    [0  -&]     [0]           
       c(b(x1)) = [1  0 ]x1 + [2] >= [1  0 ]x1 + [2] = a(a(x1))
      problem:
       DPs:
        b#(b(a(x1))) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(b(b(b(x1))))
        c(b(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))))
        c(b(x1)) -> a(a(x1))
       graph:
        b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(b(x1))
       Matrix Interpretation Processor: dim=1
        
        interpretation:
         [b#](x0) = 1/2x0 + 13/2,
         
         [c](x0) = 1/2x0 + 1/2,
         
         [b](x0) = 2x0 + 3,
         
         [a](x0) = x0 + 1
        orientation:
         b#(b(a(x1))) = x1 + 9 >= x1 + 8 = b#(b(x1))
         
         a(x1) = x1 + 1 >= x1 = x1
         
         b(b(a(x1))) = 4x1 + 13 >= 4x1 + 11 = c(b(b(b(x1))))
         
         c(b(x1)) = x1 + 2 >= x1 + 2 = a(a(x1))
        problem:
         DPs:
          
         TRS:
          a(x1) -> x1
          b(b(a(x1))) -> c(b(b(b(x1))))
          c(b(x1)) -> a(a(x1))
        Qed