YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> b#(c(x1))
   a#(a(x1)) -> b#(b(c(x1)))
   a#(a(x1)) -> a#(b(b(c(x1))))
   c#(b(x1)) -> c#(x1)
   c#(b(x1)) -> a#(c(x1))
  TRS:
   a(a(x1)) -> a(b(b(c(x1))))
   b(a(x1)) -> x1
   c(b(x1)) -> a(c(x1))
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> b#(b(c(x1)))
    a#(a(x1)) -> a#(b(b(c(x1))))
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1))
   TRS:
    a(a(x1)) -> a(b(b(c(x1))))
    b(a(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(b(c(x1))))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(b(c(x1)))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(c(x1))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> a#(b(b(c(x1))))
    a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> b#(b(c(x1)))
    a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> c#(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#(x1)
     a#(a(x1)) -> a#(b(b(c(x1))))
    TRS:
     a(a(x1)) -> a(b(b(c(x1))))
     b(a(x1)) -> x1
     c(b(x1)) -> a(c(x1))
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [c#](x0) = [0  -&]x0 + [0],
      
      [a#](x0) = [0  -&]x0 + [0],
      
                [0 0]     [-&]
      [b](x0) = [0 1]x0 + [1 ],
      
                [-& 0 ]     [0]
      [c](x0) = [0  -&]x0 + [0],
      
                [1  0 ]     [1]
      [a](x0) = [0  -&]x0 + [0]
     orientation:
      c#(b(x1)) = [0 0]x1 + [0] >= [0  -&]x1 + [0] = c#(x1)
      
      c#(b(x1)) = [0 0]x1 + [0] >= [-& 0 ]x1 + [0] = a#(c(x1))
      
      a#(a(x1)) = [1 0]x1 + [1] >= [0  -&]x1 + [0] = c#(x1)
      
      a#(a(x1)) = [1 0]x1 + [1] >= [1 0]x1 + [1] = a#(b(b(c(x1))))
      
                 [2 1]     [2]    [2 1]     [2]                 
      a(a(x1)) = [1 0]x1 + [1] >= [1 0]x1 + [1] = a(b(b(c(x1))))
      
                 [1 0]     [1]           
      b(a(x1)) = [1 0]x1 + [1] >= x1 = x1
      
                 [0 1]     [1]    [0  1 ]     [1]           
      c(b(x1)) = [0 0]x1 + [0] >= [-& 0 ]x1 + [0] = a(c(x1))
     problem:
      DPs:
       c#(b(x1)) -> c#(x1)
       c#(b(x1)) -> a#(c(x1))
       a#(a(x1)) -> a#(b(b(c(x1))))
      TRS:
       a(a(x1)) -> a(b(b(c(x1))))
       b(a(x1)) -> x1
       c(b(x1)) -> a(c(x1))
     EDG Processor:
      DPs:
       c#(b(x1)) -> c#(x1)
       c#(b(x1)) -> a#(c(x1))
       a#(a(x1)) -> a#(b(b(c(x1))))
      TRS:
       a(a(x1)) -> a(b(b(c(x1))))
       b(a(x1)) -> x1
       c(b(x1)) -> a(c(x1))
      graph:
       c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
       c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
       c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(b(c(x1))))
       a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> a#(b(b(c(x1))))
      CDG Processor:
       DPs:
        c#(b(x1)) -> c#(x1)
        c#(b(x1)) -> a#(c(x1))
        a#(a(x1)) -> a#(b(b(c(x1))))
       TRS:
        a(a(x1)) -> a(b(b(c(x1))))
        b(a(x1)) -> x1
        c(b(x1)) -> a(c(x1))
       graph:
        c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(b(c(x1))))
        a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> a#(b(b(c(x1))))
       SCC Processor:
        #sccs: 1
        #rules: 1
        #arcs: 2/9
        DPs:
         a#(a(x1)) -> a#(b(b(c(x1))))
        TRS:
         a(a(x1)) -> a(b(b(c(x1))))
         b(a(x1)) -> x1
         c(b(x1)) -> a(c(x1))
        Arctic Interpretation Processor:
         dimension: 3
         interpretation:
          [a#](x0) = [-& -& 0 ]x0 + [0],
          
                    [-& 0  -&]     [0]
          [b](x0) = [0  1  0 ]x0 + [1]
                    [0  -& -&]     [0],
          
                    [-& 0  -&]     [0]
          [c](x0) = [0  -& -&]x0 + [0]
                    [0  0  0 ]     [1],
          
                    [1  0  0 ]     [1]
          [a](x0) = [0  -& -&]x0 + [0]
                    [1  0  0 ]     [1]
         orientation:
          a#(a(x1)) = [1 0 0]x1 + [1] >= [0  -& -&]x1 + [0] = a#(b(b(c(x1))))
          
                     [2 1 1]     [2]    [2 1 1]     [2]                 
          a(a(x1)) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = a(b(b(c(x1))))
                     [2 1 1]     [2]    [2 1 1]     [2]                 
          
                     [0  -& -&]     [0]           
          b(a(x1)) = [1  0  0 ]x1 + [1] >= x1 = x1
                     [1  0  0 ]     [1]           
          
                     [0  1  0 ]     [1]    [0  1  0 ]     [1]           
          c(b(x1)) = [-& 0  -&]x1 + [0] >= [-& 0  -&]x1 + [0] = a(c(x1))
                     [0  1  0 ]     [1]    [0  1  0 ]     [1]           
         problem:
          DPs:
           
          TRS:
           a(a(x1)) -> a(b(b(c(x1))))
           b(a(x1)) -> x1
           c(b(x1)) -> a(c(x1))
         Qed