YES

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

Proof:
 String Reversal Processor:
  a(x1) -> x1
  b(b(x1)) -> a(x1)
  c(c(b(x1))) -> b(c(b(c(c(x1)))))
  DP Processor:
   DPs:
    b#(b(x1)) -> a#(x1)
    c#(c(b(x1))) -> c#(x1)
    c#(c(b(x1))) -> c#(c(x1))
    c#(c(b(x1))) -> b#(c(c(x1)))
    c#(c(b(x1))) -> c#(b(c(c(x1))))
    c#(c(b(x1))) -> b#(c(b(c(c(x1)))))
   TRS:
    a(x1) -> x1
    b(b(x1)) -> a(x1)
    c(c(b(x1))) -> b(c(b(c(c(x1)))))
   TDG Processor:
    DPs:
     b#(b(x1)) -> a#(x1)
     c#(c(b(x1))) -> c#(x1)
     c#(c(b(x1))) -> c#(c(x1))
     c#(c(b(x1))) -> b#(c(c(x1)))
     c#(c(b(x1))) -> c#(b(c(c(x1))))
     c#(c(b(x1))) -> b#(c(b(c(c(x1)))))
    TRS:
     a(x1) -> x1
     b(b(x1)) -> a(x1)
     c(c(b(x1))) -> b(c(b(c(c(x1)))))
    graph:
     c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> b#(c(b(c(c(x1)))))
     c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(b(c(c(x1))))
     c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> b#(c(c(x1)))
     c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(c(x1))
     c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(x1)
     c#(c(b(x1))) -> c#(b(c(c(x1)))) ->
     c#(c(b(x1))) -> b#(c(b(c(c(x1)))))
     c#(c(b(x1))) -> c#(b(c(c(x1)))) ->
     c#(c(b(x1))) -> c#(b(c(c(x1))))
     c#(c(b(x1))) -> c#(b(c(c(x1)))) -> c#(c(b(x1))) -> b#(c(c(x1)))
     c#(c(b(x1))) -> c#(b(c(c(x1)))) -> c#(c(b(x1))) -> c#(c(x1))
     c#(c(b(x1))) -> c#(b(c(c(x1)))) -> c#(c(b(x1))) -> c#(x1)
     c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> b#(c(b(c(c(x1)))))
     c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(b(c(c(x1))))
     c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> b#(c(c(x1)))
     c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(c(x1))
     c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
     c#(c(b(x1))) -> b#(c(c(x1))) -> b#(b(x1)) -> a#(x1)
     c#(c(b(x1))) -> b#(c(b(c(c(x1))))) -> b#(b(x1)) -> a#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 17/36
     DPs:
      c#(c(b(x1))) -> c#(c(x1))
      c#(c(b(x1))) -> c#(x1)
      c#(c(b(x1))) -> c#(b(c(c(x1))))
     TRS:
      a(x1) -> x1
      b(b(x1)) -> a(x1)
      c(c(b(x1))) -> b(c(b(c(c(x1)))))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> x1
       b(b(x1)) -> a(x1)
       c(c(b(x1))) -> b(c(b(c(c(x1)))))
      interpretation:
                 [1  0 ]     [2]
       [b](x0) = [0  -&]x0 + [0],
       
       [c#](x0) = [0 2]x0 + [0],
       
                 [0  -&]  
       [a](x0) = [0  0 ]x0,
       
                 [-& 0 ]     [0]
       [c](x0) = [0  -&]x0 + [1]
      orientation:
       c#(c(b(x1))) = [3 2]x1 + [4] >= [2 0]x1 + [3] = c#(c(x1))
       
       c#(c(b(x1))) = [3 2]x1 + [4] >= [0 2]x1 + [0] = c#(x1)
       
       c#(c(b(x1))) = [3 2]x1 + [4] >= [2 0]x1 + [3] = c#(b(c(c(x1))))
       
               [0  -&]             
       a(x1) = [0  0 ]x1 >= x1 = x1
       
                  [2 1]     [3]    [0  -&]          
       b(b(x1)) = [1 0]x1 + [2] >= [0  0 ]x1 = a(x1)
       
                     [1  0 ]     [2]    [1  0 ]     [2]                    
       c(c(b(x1))) = [0  -&]x1 + [1] >= [0  -&]x1 + [1] = b(c(b(c(c(x1)))))
      problem:
       DPs:
        c#(c(b(x1))) -> c#(x1)
       TRS:
        a(x1) -> x1
        b(b(x1)) -> a(x1)
        c(c(b(x1))) -> b(c(b(c(c(x1)))))
      Restore Modifier:
       DPs:
        c#(c(b(x1))) -> c#(x1)
       TRS:
        a(x1) -> x1
        b(b(x1)) -> a(x1)
        c(c(b(x1))) -> b(c(b(c(c(x1)))))
       EDG Processor:
        DPs:
         c#(c(b(x1))) -> c#(x1)
        TRS:
         a(x1) -> x1
         b(b(x1)) -> a(x1)
         c(c(b(x1))) -> b(c(b(c(c(x1)))))
        graph:
         c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
        Usable Rule Processor:
         DPs:
          c#(c(b(x1))) -> c#(x1)
         TRS:
          
         Arctic Interpretation Processor:
          dimension: 1
          usable rules:
           
          interpretation:
           [b](x0) = 1x0 + 13,
           
           [c#](x0) = x0,
           
           [c](x0) = x0 + 0
          orientation:
           c#(c(b(x1))) = 1x1 + 13 >= x1 = c#(x1)
          problem:
           DPs:
            
           TRS:
            
          Qed