YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(b(a(x1))) -> c(a(b(b(b(x1)))))
  b(c(x1)) -> 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))) -> a#(b(b(b(x1))))
    b#(c(x1)) -> a#(x1)
   TRS:
    a(x1) -> x1
    b(b(a(x1))) -> c(a(b(b(b(x1)))))
    b(c(x1)) -> 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))) -> a#(b(b(b(x1))))
     b#(c(x1)) -> a#(x1)
    TRS:
     a(x1) -> x1
     b(b(a(x1))) -> c(a(b(b(b(x1)))))
     b(c(x1)) -> a(x1)
    graph:
     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))) -> a#(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#(c(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> a#(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#(c(x1)) -> a#(x1)
     b#(b(a(x1))) -> b#(x1) -> b#(b(a(x1))) -> a#(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: 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(a(b(b(b(x1)))))
      b(c(x1)) -> a(x1)
     Arctic Interpretation Processor:
      dimension: 3
      usable rules:
       a(x1) -> x1
       b(b(a(x1))) -> c(a(b(b(b(x1)))))
       b(c(x1)) -> a(x1)
      interpretation:
       [b#](x0) = [-& -& 0 ]x0 + [0],
       
                 [1  0  0 ]     [1 ]
       [c](x0) = [0  -& 0 ]x0 + [1 ]
                 [0  -& -&]     [-&],
       
                 [-& -& 0 ]     [0]
       [b](x0) = [0  -& -&]x0 + [0]
                 [-& 0  -&]     [0],
       
                 [0  -& -&]     [0]
       [a](x0) = [1  0  0 ]x0 + [1]
                 [0  -& 0 ]     [1]
      orientation:
       b#(b(a(x1))) = [1 0 0]x1 + [1] >= [0  -& -&]x1 + [0] = b#(b(b(x1)))
       
       b#(b(a(x1))) = [1 0 0]x1 + [1] >= [-& -& 0 ]x1 + [0] = b#(x1)
       
       b#(b(a(x1))) = [1 0 0]x1 + [1] >= [-& 0  -&]x1 + [0] = b#(b(x1))
       
               [0  -& -&]     [0]           
       a(x1) = [1  0  0 ]x1 + [1] >= x1 = x1
               [0  -& 0 ]     [1]           
       
                     [1  0  0 ]     [1]    [1  0  0 ]     [1]                    
       b(b(a(x1))) = [0  -& 0 ]x1 + [1] >= [0  -& 0 ]x1 + [1] = c(a(b(b(b(x1)))))
                     [0  -& -&]     [0]    [0  -& -&]     [0]                    
       
                  [0  -& -&]     [0]    [0  -& -&]     [0]        
       b(c(x1)) = [1  0  0 ]x1 + [1] >= [1  0  0 ]x1 + [1] = a(x1)
                  [0  -& 0 ]     [1]    [0  -& 0 ]     [1]        
      problem:
       DPs:
        b#(b(a(x1))) -> b#(x1)
        b#(b(a(x1))) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(a(b(b(b(x1)))))
        b(c(x1)) -> a(x1)
      Restore Modifier:
       DPs:
        b#(b(a(x1))) -> b#(x1)
        b#(b(a(x1))) -> b#(b(x1))
       TRS:
        a(x1) -> x1
        b(b(a(x1))) -> c(a(b(b(b(x1)))))
        b(c(x1)) -> a(x1)
       EDG Processor:
        DPs:
         b#(b(a(x1))) -> b#(x1)
         b#(b(a(x1))) -> b#(b(x1))
        TRS:
         a(x1) -> x1
         b(b(a(x1))) -> c(a(b(b(b(x1)))))
         b(c(x1)) -> a(x1)
        graph:
         b#(b(a(x1))) -> b#(b(x1)) -> b#(b(a(x1))) -> 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))) -> b#(x1) -> b#(b(a(x1))) -> b#(b(x1))
        CDG Processor:
         DPs:
          b#(b(a(x1))) -> b#(x1)
          b#(b(a(x1))) -> b#(b(x1))
         TRS:
          a(x1) -> x1
          b(b(a(x1))) -> c(a(b(b(b(x1)))))
          b(c(x1)) -> a(x1)
         graph:
          
         Qed