YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(b(a(x1))) -> c(b(a(b(b(x1)))))
  c(b(x1)) -> a(x1)
  DP Processor:
   DPs:
    b#(b(a(x1))) -> b#(x1)
    b#(b(a(x1))) -> b#(b(x1))
    b#(b(a(x1))) -> a#(b(b(x1)))
    b#(b(a(x1))) -> b#(a(b(b(x1))))
    b#(b(a(x1))) -> c#(b(a(b(b(x1)))))
    c#(b(x1)) -> a#(x1)
   TRS:
    a(x1) -> x1
    b(b(a(x1))) -> c(b(a(b(b(x1)))))
    c(b(x1)) -> a(x1)
   TDG Processor:
    DPs:
     b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> a#(b(b(x1)))
     b#(b(a(x1))) -> b#(a(b(b(x1))))
     b#(b(a(x1))) -> c#(b(a(b(b(x1)))))
     c#(b(x1)) -> a#(x1)
    TRS:
     a(x1) -> x1
     b(b(a(x1))) -> c(b(a(b(b(x1)))))
     c(b(x1)) -> a(x1)
    graph:
     b#(b(a(x1))) -> c#(b(a(b(b(x1))))) -> c#(b(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> c#(b(a(b(b(x1)))))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> b#(a(b(b(x1))))
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> a#(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#(a(b(b(x1)))) ->
     b#(b(a(x1))) -> c#(b(a(b(b(x1)))))
     b#(b(a(x1))) -> b#(a(b(b(x1)))) ->
     b#(b(a(x1))) -> b#(a(b(b(x1))))
     b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> a#(b(b(x1)))
     b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(x1))
     b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(x1)
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> c#(b(a(b(b(x1)))))
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> b#(a(b(b(x1))))
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> a#(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: 16/36
     DPs:
      b#(b(a(x1))) -> b#(b(x1))
      b#(b(a(x1))) -> b#(x1)
      b#(b(a(x1))) -> b#(a(b(b(x1))))
     TRS:
      a(x1) -> x1
      b(b(a(x1))) -> c(b(a(b(b(x1)))))
      c(b(x1)) -> a(x1)
     Arctic Interpretation Processor:
      dimension: 2
      interpretation:
       [b#](x0) = [0  -&]x0 + [-4],
       
                 [-& -3]     [1 ]
       [c](x0) = [0  0 ]x0 + [-4],
       
                 [-& 0 ]     [0]
       [b](x0) = [3  -&]x0 + [0],
       
                 [0  -&]     [0 ]
       [a](x0) = [3  0 ]x0 + [-4]
      orientation:
       b#(b(a(x1))) = [3 0]x1 + [0] >= [-& 0 ]x1 + [0] = b#(b(x1))
       
       b#(b(a(x1))) = [3 0]x1 + [0] >= [0  -&]x1 + [-4] = b#(x1)
       
       b#(b(a(x1))) = [3 0]x1 + [0] >= [3  -&]x1 + [0] = b#(a(b(b(x1))))
       
               [0  -&]     [0 ]           
       a(x1) = [3  0 ]x1 + [-4] >= x1 = x1
       
                     [3  -&]     [3]    [3  -&]     [1]                    
       b(b(a(x1))) = [6  3 ]x1 + [3] >= [6  3 ]x1 + [3] = c(b(a(b(b(x1)))))
       
                  [0  -&]     [1]    [0  -&]     [0 ]        
       c(b(x1)) = [3  0 ]x1 + [0] >= [3  0 ]x1 + [-4] = a(x1)
      problem:
       DPs:
        b#(b(a(x1))) -> b#(b(x1))
        b#(b(a(x1))) -> b#(a(b(b(x1))))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(b(a(b(b(x1)))))
        c(b(x1)) -> a(x1)
      EDG Processor:
       DPs:
        b#(b(a(x1))) -> b#(b(x1))
        b#(b(a(x1))) -> b#(a(b(b(x1))))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(b(a(b(b(x1)))))
        c(b(x1)) -> a(x1)
       graph:
        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#(a(b(b(x1))))
        b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(b(x1))
        b#(b(a(x1))) -> b#(a(b(b(x1)))) -> b#(b(a(x1))) -> b#(a(b(b(x1))))
       Arctic Interpretation Processor:
        dimension: 2
        interpretation:
         [b#](x0) = [-& 0 ]x0 + [0],
         
                   [1  0 ]     [2]
         [c](x0) = [0  -&]x0 + [0],
         
                   [-& 0 ]     [0]
         [b](x0) = [0  -&]x0 + [0],
         
                   [0  1 ]     [2]
         [a](x0) = [-& 0 ]x0 + [0]
        orientation:
         b#(b(a(x1))) = [0 1]x1 + [2] >= [0  -&]x1 + [0] = b#(b(x1))
         
         b#(b(a(x1))) = [0 1]x1 + [2] >= [-& 0 ]x1 + [0] = b#(a(b(b(x1))))
         
                 [0  1 ]     [2]           
         a(x1) = [-& 0 ]x1 + [0] >= x1 = x1
         
                       [0  1 ]     [2]    [0  1 ]     [2]                    
         b(b(a(x1))) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = c(b(a(b(b(x1)))))
         
                    [0  1 ]     [2]    [0  1 ]     [2]        
         c(b(x1)) = [-& 0 ]x1 + [0] >= [-& 0 ]x1 + [0] = a(x1)
        problem:
         DPs:
          b#(b(a(x1))) -> b#(b(x1))
         TRS:
          a(x1) -> x1
          b(b(a(x1))) -> c(b(a(b(b(x1)))))
          c(b(x1)) -> a(x1)
        EDG Processor:
         DPs:
          b#(b(a(x1))) -> b#(b(x1))
         TRS:
          a(x1) -> x1
          b(b(a(x1))) -> c(b(a(b(b(x1)))))
          c(b(x1)) -> 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) = 4x0 + 4,
           
           [c](x0) = 1/2x0 + 4,
           
           [b](x0) = 2x0,
           
           [a](x0) = x0 + 4
          orientation:
           b#(b(a(x1))) = 8x1 + 36 >= 8x1 + 4 = b#(b(x1))
           
           a(x1) = x1 + 4 >= x1 = x1
           
           b(b(a(x1))) = 4x1 + 16 >= 4x1 + 8 = c(b(a(b(b(x1)))))
           
           c(b(x1)) = x1 + 4 >= x1 + 4 = a(x1)
          problem:
           DPs:
            
           TRS:
            a(x1) -> x1
            b(b(a(x1))) -> c(b(a(b(b(x1)))))
            c(b(x1)) -> a(x1)
          Qed