YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> b#(x1)
   a#(a(x1)) -> c#(b(x1))
   a#(a(x1)) -> b#(c(b(x1)))
   a#(a(x1)) -> a#(b(c(b(x1))))
   c#(b(x1)) -> c#(x1)
   c#(b(x1)) -> a#(c(x1))
  TRS:
   a(a(x1)) -> a(b(c(b(x1))))
   b(c(x1)) -> x1
   c(b(x1)) -> a(c(x1))
  TDG Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> c#(b(x1))
    a#(a(x1)) -> b#(c(b(x1)))
    a#(a(x1)) -> a#(b(c(b(x1))))
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1))
   TRS:
    a(a(x1)) -> a(b(c(b(x1))))
    b(c(x1)) -> x1
    c(b(x1)) -> a(c(x1))
   graph:
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(c(b(x1))))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(c(b(x1)))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(x1))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> c#(b(x1)) -> c#(b(x1)) -> a#(c(x1))
    a#(a(x1)) -> c#(b(x1)) -> c#(b(x1)) -> c#(x1)
    a#(a(x1)) -> a#(b(c(b(x1)))) -> a#(a(x1)) -> a#(b(c(b(x1))))
    a#(a(x1)) -> a#(b(c(b(x1)))) -> a#(a(x1)) -> b#(c(b(x1)))
    a#(a(x1)) -> a#(b(c(b(x1)))) -> a#(a(x1)) -> c#(b(x1))
    a#(a(x1)) -> a#(b(c(b(x1)))) -> a#(a(x1)) -> b#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 4
    #arcs: 12/36
    DPs:
     c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> a#(c(x1))
     a#(a(x1)) -> c#(b(x1))
     a#(a(x1)) -> a#(b(c(b(x1))))
    TRS:
     a(a(x1)) -> a(b(c(b(x1))))
     b(c(x1)) -> x1
     c(b(x1)) -> a(c(x1))
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [c#](x0) = [-& 0 ]x0 + [0],
      
      [a#](x0) = [1 0]x0 + [0],
      
                [-& 0 ]     [0]
      [c](x0) = [0  -&]x0 + [1],
      
                [-& 0 ]     [1]
      [b](x0) = [0  1 ]x0 + [3],
      
                [1  0 ]     [3]
      [a](x0) = [-& -&]x0 + [0]
     orientation:
      c#(b(x1)) = [0 1]x1 + [3] >= [-& 0 ]x1 + [0] = c#(x1)
      
      c#(b(x1)) = [0 1]x1 + [3] >= [0 1]x1 + [1] = a#(c(x1))
      
      a#(a(x1)) = [2 1]x1 + [4] >= [0 1]x1 + [3] = c#(b(x1))
      
      a#(a(x1)) = [2 1]x1 + [4] >= [0 1]x1 + [3] = a#(b(c(b(x1))))
      
                 [2  1 ]     [4]    [0  1 ]     [3]                 
      a(a(x1)) = [-& -&]x1 + [0] >= [-& -&]x1 + [0] = a(b(c(b(x1))))
      
                 [0  -&]     [1]           
      b(c(x1)) = [1  0 ]x1 + [3] >= x1 = x1
      
                 [0  1 ]     [3]    [0  1 ]     [3]           
      c(b(x1)) = [-& 0 ]x1 + [1] >= [-& -&]x1 + [0] = a(c(x1))
     problem:
      DPs:
       c#(b(x1)) -> a#(c(x1))
       a#(a(x1)) -> c#(b(x1))
       a#(a(x1)) -> a#(b(c(b(x1))))
      TRS:
       a(a(x1)) -> a(b(c(b(x1))))
       b(c(x1)) -> x1
       c(b(x1)) -> a(c(x1))
     EDG Processor:
      DPs:
       c#(b(x1)) -> a#(c(x1))
       a#(a(x1)) -> c#(b(x1))
       a#(a(x1)) -> a#(b(c(b(x1))))
      TRS:
       a(a(x1)) -> a(b(c(b(x1))))
       b(c(x1)) -> x1
       c(b(x1)) -> a(c(x1))
      graph:
       c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(b(x1))
       c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(c(b(x1))))
       a#(a(x1)) -> c#(b(x1)) -> c#(b(x1)) -> a#(c(x1))
       a#(a(x1)) -> a#(b(c(b(x1)))) -> a#(a(x1)) -> c#(b(x1))
       a#(a(x1)) -> a#(b(c(b(x1)))) -> a#(a(x1)) -> a#(b(c(b(x1))))
      Arctic Interpretation Processor:
       dimension: 3
       interpretation:
        [c#](x0) = [0 0 0]x0 + [0],
        
        [a#](x0) = [-& 0  0 ]x0 + [0],
        
                  [0  0  0 ]     [0]
        [c](x0) = [-& -& -&]x0 + [0]
                  [-& 0  -&]     [0],
        
                  [0 1 0]     [-&]
        [b](x0) = [0 1 0]x0 + [1 ]
                  [0 0 0]     [-&],
        
                  [0  1  1 ]     [-&]
        [a](x0) = [-& -& -&]x0 + [0 ]
                  [0  1  1 ]     [1 ]
       orientation:
        c#(b(x1)) = [0 1 0]x1 + [1] >= [-& 0  -&]x1 + [0] = a#(c(x1))
        
        a#(a(x1)) = [0 1 1]x1 + [1] >= [0 1 0]x1 + [1] = c#(b(x1))
        
        a#(a(x1)) = [0 1 1]x1 + [1] >= [0 1 0]x1 + [1] = a#(b(c(b(x1))))
        
                   [1  2  2 ]     [2]    [1  2  1 ]     [2]                 
        a(a(x1)) = [-& -& -&]x1 + [0] >= [-& -& -&]x1 + [0] = a(b(c(b(x1))))
                   [1  2  2 ]     [2]    [1  2  1 ]     [2]                 
        
                   [0 0 0]     [1]           
        b(c(x1)) = [0 0 0]x1 + [1] >= x1 = x1
                   [0 0 0]     [0]           
        
                   [0  1  0 ]     [1]    [0  1  0 ]     [1]           
        c(b(x1)) = [-& -& -&]x1 + [0] >= [-& -& -&]x1 + [0] = a(c(x1))
                   [0  1  0 ]     [1]    [0  1  0 ]     [1]           
       problem:
        DPs:
         a#(a(x1)) -> c#(b(x1))
         a#(a(x1)) -> a#(b(c(b(x1))))
        TRS:
         a(a(x1)) -> a(b(c(b(x1))))
         b(c(x1)) -> x1
         c(b(x1)) -> a(c(x1))
       EDG Processor:
        DPs:
         a#(a(x1)) -> c#(b(x1))
         a#(a(x1)) -> a#(b(c(b(x1))))
        TRS:
         a(a(x1)) -> a(b(c(b(x1))))
         b(c(x1)) -> x1
         c(b(x1)) -> a(c(x1))
        graph:
         a#(a(x1)) -> a#(b(c(b(x1)))) -> a#(a(x1)) -> a#(b(c(b(x1))))
         a#(a(x1)) -> a#(b(c(b(x1)))) -> a#(a(x1)) -> c#(b(x1))
        SCC Processor:
         #sccs: 1
         #rules: 1
         #arcs: 2/4
         DPs:
          a#(a(x1)) -> a#(b(c(b(x1))))
         TRS:
          a(a(x1)) -> a(b(c(b(x1))))
          b(c(x1)) -> x1
          c(b(x1)) -> a(c(x1))
         Arctic Interpretation Processor:
          dimension: 4
          interpretation:
           [a#](x0) = [-& 0  0  0 ]x0 + [0],
           
                     [1  1  0  0 ]     [-&]
                     [-& 0  0  0 ]     [0 ]
           [c](x0) = [1  1  1  0 ]x0 + [0 ]
                     [-& 0  0  0 ]     [0 ],
           
                     [0  0  0  0 ]     [0 ]
                     [-& 0  -& 0 ]     [-&]
           [b](x0) = [-& 0  -& 0 ]x0 + [-&]
                     [-& 0  -& 0 ]     [0 ],
           
                     [-& 0  0  0 ]     [0]
                     [-& -& -& -&]     [0]
           [a](x0) = [-& 1  0  1 ]x0 + [1]
                     [-& -& -& -&]     [0]
          orientation:
           a#(a(x1)) = [-& 1  0  1 ]x1 + [1] >= [-& 0  -& 0 ]x1 + [0] = a#(b(c(b(x1))))
           
                      [-& 1  0  1 ]     [1]    [-& 0  -& 0 ]     [0]                 
                      [-& -& -& -&]     [0]    [-& -& -& -&]     [0]                 
           a(a(x1)) = [-& 1  0  1 ]x1 + [1] >= [-& 1  -& 1 ]x1 + [1] = a(b(c(b(x1))))
                      [-& -& -& -&]     [0]    [-& -& -& -&]     [0]                 
           
                      [1  1  1  0 ]     [0]           
                      [-& 0  0  0 ]     [0]           
           b(c(x1)) = [-& 0  0  0 ]x1 + [0] >= x1 = x1
                      [-& 0  0  0 ]     [0]           
           
                      [1  1  1  1 ]     [1]    [1  1  1  0 ]     [0]           
                      [-& 0  -& 0 ]     [0]    [-& -& -& -&]     [0]           
           c(b(x1)) = [1  1  1  1 ]x1 + [1] >= [1  1  1  1 ]x1 + [1] = a(c(x1))
                      [-& 0  -& 0 ]     [0]    [-& -& -& -&]     [0]           
          problem:
           DPs:
            
           TRS:
            a(a(x1)) -> a(b(c(b(x1))))
            b(c(x1)) -> x1
            c(b(x1)) -> a(c(x1))
          Qed