YES

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

Proof:
 String Reversal Processor:
  a(x1) -> c(b(x1))
  b(b(x1)) -> x1
  c(c(b(x1))) -> b(a(c(c(x1))))
  DP Processor:
   DPs:
    a#(x1) -> b#(x1)
    a#(x1) -> c#(b(x1))
    c#(c(b(x1))) -> c#(x1)
    c#(c(b(x1))) -> c#(c(x1))
    c#(c(b(x1))) -> a#(c(c(x1)))
    c#(c(b(x1))) -> b#(a(c(c(x1))))
   TRS:
    a(x1) -> c(b(x1))
    b(b(x1)) -> x1
    c(c(b(x1))) -> b(a(c(c(x1))))
   TDG Processor:
    DPs:
     a#(x1) -> b#(x1)
     a#(x1) -> c#(b(x1))
     c#(c(b(x1))) -> c#(x1)
     c#(c(b(x1))) -> c#(c(x1))
     c#(c(b(x1))) -> a#(c(c(x1)))
     c#(c(b(x1))) -> b#(a(c(c(x1))))
    TRS:
     a(x1) -> c(b(x1))
     b(b(x1)) -> x1
     c(c(b(x1))) -> b(a(c(c(x1))))
    graph:
     c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> b#(a(c(c(x1))))
     c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> a#(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#(x1) -> c#(c(b(x1))) -> b#(a(c(c(x1))))
     c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(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))) -> a#(c(c(x1))) -> a#(x1) -> c#(b(x1))
     c#(c(b(x1))) -> a#(c(c(x1))) -> a#(x1) -> b#(x1)
     a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> b#(a(c(c(x1))))
     a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> a#(c(c(x1)))
     a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> c#(c(x1))
     a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> c#(x1)
    SCC Processor:
     #sccs: 1
     #rules: 4
     #arcs: 14/36
     DPs:
      c#(c(b(x1))) -> c#(c(x1))
      c#(c(b(x1))) -> c#(x1)
      c#(c(b(x1))) -> a#(c(c(x1)))
      a#(x1) -> c#(b(x1))
     TRS:
      a(x1) -> c(b(x1))
      b(b(x1)) -> x1
      c(c(b(x1))) -> b(a(c(c(x1))))
     Arctic Interpretation Processor:
      dimension: 2
      usable rules:
       a(x1) -> c(b(x1))
       b(b(x1)) -> x1
       c(c(b(x1))) -> b(a(c(c(x1))))
      interpretation:
       [c#](x0) = [0  -&]x0 + [0],
       
       [a#](x0) = [-& 2 ]x0 + [3],
       
                 [-& 0 ]     [1]
       [b](x0) = [0  2 ]x0 + [3],
       
                 [-& 0 ]     [0]
       [c](x0) = [0  -&]x0 + [0],
       
                 [0  2 ]     [3]
       [a](x0) = [-& 0 ]x0 + [1]
      orientation:
       c#(c(b(x1))) = [0 2]x1 + [3] >= [-& 0 ]x1 + [0] = c#(c(x1))
       
       c#(c(b(x1))) = [0 2]x1 + [3] >= [0  -&]x1 + [0] = c#(x1)
       
       c#(c(b(x1))) = [0 2]x1 + [3] >= [-& 2 ]x1 + [3] = a#(c(c(x1)))
       
       a#(x1) = [-& 2 ]x1 + [3] >= [-& 0 ]x1 + [1] = c#(b(x1))
       
               [0  2 ]     [3]    [0  2 ]     [3]           
       a(x1) = [-& 0 ]x1 + [1] >= [-& 0 ]x1 + [1] = c(b(x1))
       
                  [0 2]     [3]           
       b(b(x1)) = [2 4]x1 + [5] >= x1 = x1
       
                     [-& 0 ]     [1]    [-& 0 ]     [1]                 
       c(c(b(x1))) = [0  2 ]x1 + [3] >= [0  2 ]x1 + [3] = b(a(c(c(x1))))
      problem:
       DPs:
        c#(c(b(x1))) -> c#(x1)
        c#(c(b(x1))) -> a#(c(c(x1)))
       TRS:
        a(x1) -> c(b(x1))
        b(b(x1)) -> x1
        c(c(b(x1))) -> b(a(c(c(x1))))
      Restore Modifier:
       DPs:
        c#(c(b(x1))) -> c#(x1)
        c#(c(b(x1))) -> a#(c(c(x1)))
       TRS:
        a(x1) -> c(b(x1))
        b(b(x1)) -> x1
        c(c(b(x1))) -> b(a(c(c(x1))))
       EDG Processor:
        DPs:
         c#(c(b(x1))) -> c#(x1)
         c#(c(b(x1))) -> a#(c(c(x1)))
        TRS:
         a(x1) -> c(b(x1))
         b(b(x1)) -> x1
         c(c(b(x1))) -> b(a(c(c(x1))))
        graph:
         c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
         c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(c(x1)))
        SCC Processor:
         #sccs: 1
         #rules: 1
         #arcs: 2/4
         DPs:
          c#(c(b(x1))) -> c#(x1)
         TRS:
          a(x1) -> c(b(x1))
          b(b(x1)) -> x1
          c(c(b(x1))) -> b(a(c(c(x1))))
         Usable Rule Processor:
          DPs:
           c#(c(b(x1))) -> c#(x1)
          TRS:
           
          Arctic Interpretation Processor:
           dimension: 4
           usable rules:
            
           interpretation:
            [c#](x0) = [0  -& -& -&]x0,
            
                      [0  -& 0  -&]     [-&]
                      [1  0  1  0 ]     [1 ]
            [b](x0) = [-& 0  0  0 ]x0 + [0 ]
                      [1  0  1  0 ]     [-&],
            
                      [1  -& 1  -&]     [0 ]
                      [1  -& 1  -&]     [0 ]
            [c](x0) = [1  -& -& -&]x0 + [0 ]
                      [0  -& -& 0 ]     [-&]
           orientation:
            c#(c(b(x1))) = [1 1 1 1]x1 + [1] >= [0  -& -& -&]x1 = c#(x1)
           problem:
            DPs:
             
            TRS:
             
           Qed