YES

Problem:
 a(x1) -> x1
 a(a(x1)) -> b(a(b(c(x1))))
 b(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)) -> a#(b(c(x1)))
   a#(a(x1)) -> b#(a(b(c(x1))))
   c#(b(x1)) -> c#(x1)
   c#(b(x1)) -> a#(c(x1))
  TRS:
   a(x1) -> x1
   a(a(x1)) -> b(a(b(c(x1))))
   b(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)) -> a#(b(c(x1)))
    a#(a(x1)) -> b#(a(b(c(x1))))
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(c(x1))
   TRS:
    a(x1) -> x1
    a(a(x1)) -> b(a(b(c(x1))))
    b(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)) -> b#(a(b(c(x1))))
    c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(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(c(x1))) -> a#(a(x1)) -> b#(a(b(c(x1))))
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1)))
    a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(c(x1))
    a#(a(x1)) -> a#(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(c(x1)))
    TRS:
     a(x1) -> x1
     a(a(x1)) -> b(a(b(c(x1))))
     b(x1) -> x1
     c(b(x1)) -> a(c(x1))
    Arctic Interpretation Processor:
     dimension: 2
     usable rules:
      a(x1) -> x1
      a(a(x1)) -> b(a(b(c(x1))))
      b(x1) -> x1
      c(b(x1)) -> a(c(x1))
     interpretation:
      [c#](x0) = [0 0]x0 + [1],
      
      [a#](x0) = [0 0]x0 + [0],
      
                [0  1 ]     [0]
      [b](x0) = [-& 1 ]x0 + [0],
      
                [-& 1 ]     [0 ]
      [c](x0) = [-& 0 ]x0 + [-&],
      
                [1 2]     [1]
      [a](x0) = [0 0]x0 + [0]
     orientation:
      c#(b(x1)) = [0 1]x1 + [1] >= [0 0]x1 + [1] = c#(x1)
      
      c#(b(x1)) = [0 1]x1 + [1] >= [-& 1 ]x1 + [0] = a#(c(x1))
      
      a#(a(x1)) = [1 2]x1 + [1] >= [0 0]x1 + [1] = c#(x1)
      
      a#(a(x1)) = [1 2]x1 + [1] >= [-& 1 ]x1 + [0] = a#(b(c(x1)))
      
              [1 2]     [1]           
      a(x1) = [0 0]x1 + [0] >= x1 = x1
      
                 [2 3]     [2]    [-& 3 ]     [2]                 
      a(a(x1)) = [1 2]x1 + [1] >= [-& 2 ]x1 + [1] = b(a(b(c(x1))))
      
              [0  1 ]     [0]           
      b(x1) = [-& 1 ]x1 + [0] >= x1 = x1
      
                 [-& 2 ]     [1]    [-& 2 ]     [1]           
      c(b(x1)) = [-& 1 ]x1 + [0] >= [-& 1 ]x1 + [0] = a(c(x1))
     problem:
      DPs:
       c#(b(x1)) -> c#(x1)
       c#(b(x1)) -> a#(c(x1))
       a#(a(x1)) -> c#(x1)
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(a(b(c(x1))))
       b(x1) -> x1
       c(b(x1)) -> a(c(x1))
     Restore Modifier:
      DPs:
       c#(b(x1)) -> c#(x1)
       c#(b(x1)) -> a#(c(x1))
       a#(a(x1)) -> c#(x1)
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(a(b(c(x1))))
       b(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)) -> c#(x1)
       TRS:
        a(x1) -> x1
        a(a(x1)) -> b(a(b(c(x1))))
        b(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)) -> c#(x1)
        a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
        a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1))
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(x1) -> x1
         a(a(x1)) -> b(a(b(c(x1))))
         b(x1) -> x1
         c(b(x1)) -> a(c(x1))
        interpretation:
         [c#](x0) = [0 1]x0 + [3],
         
         [a#](x0) = [0 0]x0 + [0],
         
                   [1 0]     [3]
         [b](x0) = [0 0]x0 + [2],
         
                   [0  -&]     [-&]
         [c](x0) = [0  -&]x0 + [1 ],
         
                   [0 1]     [0]
         [a](x0) = [1 1]x0 + [3]
        orientation:
         c#(b(x1)) = [1 1]x1 + [3] >= [0 1]x1 + [3] = c#(x1)
         
         c#(b(x1)) = [1 1]x1 + [3] >= [0  -&]x1 + [1] = a#(c(x1))
         
         a#(a(x1)) = [1 1]x1 + [3] >= [0 1]x1 + [3] = c#(x1)
         
                 [0 1]     [0]           
         a(x1) = [1 1]x1 + [3] >= x1 = x1
         
                    [2 2]     [4]    [2  -&]     [4]                 
         a(a(x1)) = [2 2]x1 + [4] >= [2  -&]x1 + [4] = b(a(b(c(x1))))
         
                 [1 0]     [3]           
         b(x1) = [0 0]x1 + [2] >= x1 = x1
         
                    [1 0]     [3]    [1  -&]     [2]           
         c(b(x1)) = [1 0]x1 + [3] >= [1  -&]x1 + [3] = a(c(x1))
        problem:
         DPs:
          c#(b(x1)) -> c#(x1)
          a#(a(x1)) -> c#(x1)
         TRS:
          a(x1) -> x1
          a(a(x1)) -> b(a(b(c(x1))))
          b(x1) -> x1
          c(b(x1)) -> a(c(x1))
        Restore Modifier:
         DPs:
          c#(b(x1)) -> c#(x1)
          a#(a(x1)) -> c#(x1)
         TRS:
          a(x1) -> x1
          a(a(x1)) -> b(a(b(c(x1))))
          b(x1) -> x1
          c(b(x1)) -> a(c(x1))
         EDG Processor:
          DPs:
           c#(b(x1)) -> c#(x1)
           a#(a(x1)) -> c#(x1)
          TRS:
           a(x1) -> x1
           a(a(x1)) -> b(a(b(c(x1))))
           b(x1) -> x1
           c(b(x1)) -> a(c(x1))
          graph:
           c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
           a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
          CDG Processor:
           DPs:
            c#(b(x1)) -> c#(x1)
            a#(a(x1)) -> c#(x1)
           TRS:
            a(x1) -> x1
            a(a(x1)) -> b(a(b(c(x1))))
            b(x1) -> x1
            c(b(x1)) -> a(c(x1))
           graph:
            
           Qed