YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   c#(b(b(x1))) -> a#(x1)
   c#(b(b(x1))) -> a#(b(a(x1)))
   c#(b(b(x1))) -> a#(a(b(a(x1))))
  TRS:
   a(x1) -> x1
   a(a(x1)) -> b(c(x1))
   c(b(b(x1))) -> a(a(b(a(x1))))
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    c#(b(b(x1))) -> a#(x1)
    c#(b(b(x1))) -> a#(b(a(x1)))
    c#(b(b(x1))) -> a#(a(b(a(x1))))
   TRS:
    a(x1) -> x1
    a(a(x1)) -> b(c(x1))
    c(b(b(x1))) -> a(a(b(a(x1))))
   graph:
    c#(b(b(x1))) -> a#(b(a(x1))) -> a#(a(x1)) -> c#(x1)
    c#(b(b(x1))) -> a#(a(b(a(x1)))) -> a#(a(x1)) -> c#(x1)
    c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(b(x1))) -> a#(a(b(a(x1))))
    a#(a(x1)) -> c#(x1) -> c#(b(b(x1))) -> a#(b(a(x1)))
    a#(a(x1)) -> c#(x1) -> c#(b(b(x1))) -> a#(x1)
   EDG Processor:
    DPs:
     a#(a(x1)) -> c#(x1)
     c#(b(b(x1))) -> a#(x1)
     c#(b(b(x1))) -> a#(b(a(x1)))
     c#(b(b(x1))) -> a#(a(b(a(x1))))
    TRS:
     a(x1) -> x1
     a(a(x1)) -> b(c(x1))
     c(b(b(x1))) -> a(a(b(a(x1))))
    graph:
     c#(b(b(x1))) -> a#(a(b(a(x1)))) -> a#(a(x1)) -> c#(x1)
     c#(b(b(x1))) -> a#(x1) -> a#(a(x1)) -> c#(x1)
     a#(a(x1)) -> c#(x1) -> c#(b(b(x1))) -> a#(x1)
     a#(a(x1)) -> c#(x1) -> c#(b(b(x1))) -> a#(b(a(x1)))
     a#(a(x1)) -> c#(x1) -> c#(b(b(x1))) -> a#(a(b(a(x1))))
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 5/16
     DPs:
      c#(b(b(x1))) -> a#(a(b(a(x1))))
      a#(a(x1)) -> c#(x1)
      c#(b(b(x1))) -> a#(x1)
     TRS:
      a(x1) -> x1
      a(a(x1)) -> b(c(x1))
      c(b(b(x1))) -> a(a(b(a(x1))))
     Arctic Interpretation Processor:
      dimension: 4
      interpretation:
       [c#](x0) = [0 1 0 0]x0 + [0],
       
       [a#](x0) = [0 0 0 0]x0 + [0],
       
                 [-& 0  0  0 ]     [0]
                 [-& 0  0  0 ]     [0]
       [b](x0) = [-& 0  0  0 ]x0 + [0]
                 [0  0  0  0 ]     [0],
       
                 [0 1 0 0]     [1 ]
                 [0 1 0 0]     [-&]
       [c](x0) = [0 1 0 0]x0 + [0 ]
                 [0 1 0 0]     [1 ],
       
                 [0  1  0  0 ]     [1 ]
                 [0  0  -& -&]     [-&]
       [a](x0) = [0  0  0  0 ]x0 + [-&]
                 [0  0  0  0 ]     [-&]
      orientation:
       c#(b(b(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1] = a#(a(b(a(x1))))
       
       a#(a(x1)) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 + [0] = c#(x1)
       
       c#(b(b(x1))) = [1 1 1 1]x1 + [1] >= [0 0 0 0]x1 + [0] = a#(x1)
       
               [0  1  0  0 ]     [1 ]           
               [0  0  -& -&]     [-&]           
       a(x1) = [0  0  0  0 ]x1 + [-&] >= x1 = x1
               [0  0  0  0 ]     [-&]           
       
                  [1 1 0 0]     [1]    [0 1 0 0]     [1]           
                  [0 1 0 0]     [1]    [0 1 0 0]     [1]           
       a(a(x1)) = [0 1 0 0]x1 + [1] >= [0 1 0 0]x1 + [1] = b(c(x1))
                  [0 1 0 0]     [1]    [0 1 0 0]     [1]           
       
                     [1 1 1 1]     [1]    [1 1 1 1]     [1]                 
                     [1 1 1 1]     [1]    [1 1 1 1]     [1]                 
       c(b(b(x1))) = [1 1 1 1]x1 + [1] >= [1 1 1 1]x1 + [1] = a(a(b(a(x1))))
                     [1 1 1 1]     [1]    [1 1 1 1]     [1]                 
      problem:
       DPs:
        c#(b(b(x1))) -> a#(a(b(a(x1))))
        a#(a(x1)) -> c#(x1)
       TRS:
        a(x1) -> x1
        a(a(x1)) -> b(c(x1))
        c(b(b(x1))) -> a(a(b(a(x1))))
      EDG Processor:
       DPs:
        c#(b(b(x1))) -> a#(a(b(a(x1))))
        a#(a(x1)) -> c#(x1)
       TRS:
        a(x1) -> x1
        a(a(x1)) -> b(c(x1))
        c(b(b(x1))) -> a(a(b(a(x1))))
       graph:
        c#(b(b(x1))) -> a#(a(b(a(x1)))) -> a#(a(x1)) -> c#(x1)
        a#(a(x1)) -> c#(x1) -> c#(b(b(x1))) -> a#(a(b(a(x1))))
       Arctic Interpretation Processor:
        dimension: 3
        interpretation:
         [c#](x0) = [0  -& -&]x0 + [0],
         
         [a#](x0) = [0 0 0]x0 + [0],
         
                   [1  1  0 ]     [1 ]
         [b](x0) = [-& 0  1 ]x0 + [-&]
                   [0  -& 0 ]     [0 ],
         
                   [0  -& -&]     [-&]
         [c](x0) = [0  -& -&]x0 + [0 ]
                   [0  -& -&]     [0 ],
         
                   [0  -& 0 ]     [-&]
         [a](x0) = [0  0  0 ]x0 + [0 ]
                   [1  0  0 ]     [1 ]
        orientation:
         c#(b(b(x1))) = [2 2 2]x1 + [2] >= [2 2 2]x1 + [2] = a#(a(b(a(x1))))
         
         a#(a(x1)) = [1 0 0]x1 + [1] >= [0  -& -&]x1 + [0] = c#(x1)
         
                 [0  -& 0 ]     [-&]           
         a(x1) = [0  0  0 ]x1 + [0 ] >= x1 = x1
                 [1  0  0 ]     [1 ]           
         
                    [1 0 0]     [1]    [1  -& -&]     [1]           
         a(a(x1)) = [1 0 0]x1 + [1] >= [1  -& -&]x1 + [1] = b(c(x1))
                    [1 0 1]     [1]    [0  -& -&]     [0]           
         
                       [2 2 2]     [2]    [2 2 2]     [2]                 
         c(b(b(x1))) = [2 2 2]x1 + [2] >= [2 2 2]x1 + [2] = a(a(b(a(x1))))
                       [2 2 2]     [2]    [2 2 2]     [2]                 
        problem:
         DPs:
          c#(b(b(x1))) -> a#(a(b(a(x1))))
         TRS:
          a(x1) -> x1
          a(a(x1)) -> b(c(x1))
          c(b(b(x1))) -> a(a(b(a(x1))))
        EDG Processor:
         DPs:
          c#(b(b(x1))) -> a#(a(b(a(x1))))
         TRS:
          a(x1) -> x1
          a(a(x1)) -> b(c(x1))
          c(b(b(x1))) -> a(a(b(a(x1))))
         graph:
          
         Qed