NO

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

Proof:
 DP Processor:
  DPs:
   a#(a(a(x1))) -> b#(x1)
   a#(a(a(x1))) -> c#(b(x1))
   a#(a(a(x1))) -> c#(c(b(x1)))
   b#(b(b(x1))) -> c#(x1)
   b#(b(b(x1))) -> c#(c(x1))
   b#(b(b(x1))) -> c#(c(c(x1)))
   c#(c(c(x1))) -> b#(x1)
   c#(c(c(x1))) -> b#(b(x1))
   c#(c(c(x1))) -> a#(b(b(x1)))
  TRS:
   a(a(a(x1))) -> c(c(b(x1)))
   b(b(b(x1))) -> c(c(c(x1)))
   c(c(c(x1))) -> a(b(b(x1)))
  TDG Processor:
   DPs:
    a#(a(a(x1))) -> b#(x1)
    a#(a(a(x1))) -> c#(b(x1))
    a#(a(a(x1))) -> c#(c(b(x1)))
    b#(b(b(x1))) -> c#(x1)
    b#(b(b(x1))) -> c#(c(x1))
    b#(b(b(x1))) -> c#(c(c(x1)))
    c#(c(c(x1))) -> b#(x1)
    c#(c(c(x1))) -> b#(b(x1))
    c#(c(c(x1))) -> a#(b(b(x1)))
   TRS:
    a(a(a(x1))) -> c(c(b(x1)))
    b(b(b(x1))) -> c(c(c(x1)))
    c(c(c(x1))) -> a(b(b(x1)))
   graph:
    c#(c(c(x1))) -> b#(b(x1)) -> b#(b(b(x1))) -> c#(c(c(x1)))
    c#(c(c(x1))) -> b#(b(x1)) -> b#(b(b(x1))) -> c#(c(x1))
    c#(c(c(x1))) -> b#(b(x1)) -> b#(b(b(x1))) -> c#(x1)
    c#(c(c(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(c(c(x1)))
    c#(c(c(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(c(x1))
    c#(c(c(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(x1)
    c#(c(c(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> c#(c(b(x1)))
    c#(c(c(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> c#(b(x1))
    c#(c(c(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> b#(x1)
    b#(b(b(x1))) -> c#(c(c(x1))) -> c#(c(c(x1))) -> a#(b(b(x1)))
    b#(b(b(x1))) -> c#(c(c(x1))) -> c#(c(c(x1))) -> b#(b(x1))
    b#(b(b(x1))) -> c#(c(c(x1))) -> c#(c(c(x1))) -> b#(x1)
    b#(b(b(x1))) -> c#(c(x1)) -> c#(c(c(x1))) -> a#(b(b(x1)))
    b#(b(b(x1))) -> c#(c(x1)) -> c#(c(c(x1))) -> b#(b(x1))
    b#(b(b(x1))) -> c#(c(x1)) -> c#(c(c(x1))) -> b#(x1)
    b#(b(b(x1))) -> c#(x1) -> c#(c(c(x1))) -> a#(b(b(x1)))
    b#(b(b(x1))) -> c#(x1) -> c#(c(c(x1))) -> b#(b(x1))
    b#(b(b(x1))) -> c#(x1) -> c#(c(c(x1))) -> b#(x1)
    a#(a(a(x1))) -> c#(c(b(x1))) -> c#(c(c(x1))) -> a#(b(b(x1)))
    a#(a(a(x1))) -> c#(c(b(x1))) -> c#(c(c(x1))) -> b#(b(x1))
    a#(a(a(x1))) -> c#(c(b(x1))) -> c#(c(c(x1))) -> b#(x1)
    a#(a(a(x1))) -> c#(b(x1)) -> c#(c(c(x1))) -> a#(b(b(x1)))
    a#(a(a(x1))) -> c#(b(x1)) -> c#(c(c(x1))) -> b#(b(x1))
    a#(a(a(x1))) -> c#(b(x1)) -> c#(c(c(x1))) -> b#(x1)
    a#(a(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(c(c(x1)))
    a#(a(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(c(x1))
    a#(a(a(x1))) -> b#(x1) -> b#(b(b(x1))) -> c#(x1)
   Arctic Interpretation Processor:
    dimension: 2
    usable rules:
     a(a(a(x1))) -> c(c(b(x1)))
     b(b(b(x1))) -> c(c(c(x1)))
     c(c(c(x1))) -> a(b(b(x1)))
    interpretation:
     [c#](x0) = [0 2]x0 + [0],
     
     [b#](x0) = [1 2]x0 + [0],
     
     [a#](x0) = [0 2]x0 + [0],
     
               [1  -&]     [-&]
     [c](x0) = [-& 2 ]x0 + [0 ],
     
               [1  -&]     [-&]
     [b](x0) = [-& 2 ]x0 + [0 ],
     
               [1  -&]     [-&]
     [a](x0) = [-& 2 ]x0 + [0 ]
    orientation:
     a#(a(a(x1))) = [2 6]x1 + [4] >= [1 2]x1 + [0] = b#(x1)
     
     a#(a(a(x1))) = [2 6]x1 + [4] >= [1 4]x1 + [2] = c#(b(x1))
     
     a#(a(a(x1))) = [2 6]x1 + [4] >= [2 6]x1 + [4] = c#(c(b(x1)))
     
     b#(b(b(x1))) = [3 6]x1 + [4] >= [0 2]x1 + [0] = c#(x1)
     
     b#(b(b(x1))) = [3 6]x1 + [4] >= [1 4]x1 + [2] = c#(c(x1))
     
     b#(b(b(x1))) = [3 6]x1 + [4] >= [2 6]x1 + [4] = c#(c(c(x1)))
     
     c#(c(c(x1))) = [2 6]x1 + [4] >= [1 2]x1 + [0] = b#(x1)
     
     c#(c(c(x1))) = [2 6]x1 + [4] >= [2 4]x1 + [2] = b#(b(x1))
     
     c#(c(c(x1))) = [2 6]x1 + [4] >= [2 6]x1 + [4] = a#(b(b(x1)))
     
                   [3  -&]     [-&]    [3  -&]     [-&]              
     a(a(a(x1))) = [-& 6 ]x1 + [4 ] >= [-& 6 ]x1 + [4 ] = c(c(b(x1)))
     
                   [3  -&]     [-&]    [3  -&]     [-&]              
     b(b(b(x1))) = [-& 6 ]x1 + [4 ] >= [-& 6 ]x1 + [4 ] = c(c(c(x1)))
     
                   [3  -&]     [-&]    [3  -&]     [-&]              
     c(c(c(x1))) = [-& 6 ]x1 + [4 ] >= [-& 6 ]x1 + [4 ] = a(b(b(x1)))
    problem:
     DPs:
      a#(a(a(x1))) -> c#(c(b(x1)))
      b#(b(b(x1))) -> c#(c(c(x1)))
      c#(c(c(x1))) -> b#(b(x1))
      c#(c(c(x1))) -> a#(b(b(x1)))
     TRS:
      a(a(a(x1))) -> c(c(b(x1)))
      b(b(b(x1))) -> c(c(c(x1)))
      c(c(c(x1))) -> a(b(b(x1)))
    Restore Modifier:
     DPs:
      a#(a(a(x1))) -> c#(c(b(x1)))
      b#(b(b(x1))) -> c#(c(c(x1)))
      c#(c(c(x1))) -> b#(b(x1))
      c#(c(c(x1))) -> a#(b(b(x1)))
     TRS:
      a(a(a(x1))) -> c(c(b(x1)))
      b(b(b(x1))) -> c(c(c(x1)))
      c(c(c(x1))) -> a(b(b(x1)))
     EDG Processor:
      DPs:
       a#(a(a(x1))) -> c#(c(b(x1)))
       b#(b(b(x1))) -> c#(c(c(x1)))
       c#(c(c(x1))) -> b#(b(x1))
       c#(c(c(x1))) -> a#(b(b(x1)))
      TRS:
       a(a(a(x1))) -> c(c(b(x1)))
       b(b(b(x1))) -> c(c(c(x1)))
       c(c(c(x1))) -> a(b(b(x1)))
      graph:
       c#(c(c(x1))) -> b#(b(x1)) -> b#(b(b(x1))) -> c#(c(c(x1)))
       c#(c(c(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> c#(c(b(x1)))
       b#(b(b(x1))) -> c#(c(c(x1))) -> c#(c(c(x1))) -> b#(b(x1))
       b#(b(b(x1))) -> c#(c(c(x1))) -> c#(c(c(x1))) -> a#(b(b(x1)))
       a#(a(a(x1))) -> c#(c(b(x1))) -> c#(c(c(x1))) -> b#(b(x1))
       a#(a(a(x1))) -> c#(c(b(x1))) -> c#(c(c(x1))) -> a#(b(b(x1)))
      Arctic Interpretation Processor:
       dimension: 1
       usable rules:
        a(a(a(x1))) -> c(c(b(x1)))
        b(b(b(x1))) -> c(c(c(x1)))
        c(c(c(x1))) -> a(b(b(x1)))
       interpretation:
        [c#](x0) = 1x0,
        
        [b#](x0) = 1x0,
        
        [a#](x0) = 1x0,
        
        [c](x0) = 8x0,
        
        [b](x0) = 8x0,
        
        [a](x0) = 8x0
       orientation:
        a#(a(a(x1))) = 17x1 >= 17x1 = c#(c(b(x1)))
        
        b#(b(b(x1))) = 17x1 >= 17x1 = c#(c(c(x1)))
        
        c#(c(c(x1))) = 17x1 >= 9x1 = b#(b(x1))
        
        c#(c(c(x1))) = 17x1 >= 17x1 = a#(b(b(x1)))
        
        a(a(a(x1))) = 24x1 >= 24x1 = c(c(b(x1)))
        
        b(b(b(x1))) = 24x1 >= 24x1 = c(c(c(x1)))
        
        c(c(c(x1))) = 24x1 >= 24x1 = a(b(b(x1)))
       problem:
        DPs:
         a#(a(a(x1))) -> c#(c(b(x1)))
         b#(b(b(x1))) -> c#(c(c(x1)))
         c#(c(c(x1))) -> a#(b(b(x1)))
        TRS:
         a(a(a(x1))) -> c(c(b(x1)))
         b(b(b(x1))) -> c(c(c(x1)))
         c(c(c(x1))) -> a(b(b(x1)))
       Restore Modifier:
        DPs:
         a#(a(a(x1))) -> c#(c(b(x1)))
         b#(b(b(x1))) -> c#(c(c(x1)))
         c#(c(c(x1))) -> a#(b(b(x1)))
        TRS:
         a(a(a(x1))) -> c(c(b(x1)))
         b(b(b(x1))) -> c(c(c(x1)))
         c(c(c(x1))) -> a(b(b(x1)))
        EDG Processor:
         DPs:
          a#(a(a(x1))) -> c#(c(b(x1)))
          b#(b(b(x1))) -> c#(c(c(x1)))
          c#(c(c(x1))) -> a#(b(b(x1)))
         TRS:
          a(a(a(x1))) -> c(c(b(x1)))
          b(b(b(x1))) -> c(c(c(x1)))
          c(c(c(x1))) -> a(b(b(x1)))
         graph:
          c#(c(c(x1))) -> a#(b(b(x1))) -> a#(a(a(x1))) -> c#(c(b(x1)))
          b#(b(b(x1))) -> c#(c(c(x1))) -> c#(c(c(x1))) -> a#(b(b(x1)))
          a#(a(a(x1))) -> c#(c(b(x1))) -> c#(c(c(x1))) -> a#(b(b(x1)))
         SCC Processor:
          #sccs: 1
          #rules: 2
          #arcs: 3/9
          DPs:
           c#(c(c(x1))) -> a#(b(b(x1)))
           a#(a(a(x1))) -> c#(c(b(x1)))
          TRS:
           a(a(a(x1))) -> c(c(b(x1)))
           b(b(b(x1))) -> c(c(c(x1)))
           c(c(c(x1))) -> a(b(b(x1)))
          Loop Processor:
           loop length: 19
           terms:
            c(a(a(a(b(b(b(b(b(b(a(x1)))))))))))
            c(c(c(b(b(b(b(b(b(b(a(x1)))))))))))
            c(c(c(c(c(c(b(b(b(b(a(x1)))))))))))
            c(c(c(a(b(b(b(b(b(b(a(x1)))))))))))
            c(c(c(a(c(c(c(b(b(b(a(x1)))))))))))
            c(c(c(a(a(b(b(b(b(b(a(x1)))))))))))
            c(c(c(a(a(c(c(c(b(b(a(x1)))))))))))
            c(c(c(a(a(a(b(b(b(b(a(x1)))))))))))
            c(c(c(c(c(b(b(b(b(b(a(x1)))))))))))
            c(c(a(b(b(b(b(b(b(b(a(x1)))))))))))
            c(c(a(c(c(c(b(b(b(b(a(x1)))))))))))
            c(c(a(a(b(b(b(b(b(b(a(x1)))))))))))
            c(c(a(a(c(c(c(b(b(b(a(x1)))))))))))
            c(c(a(a(a(b(b(b(b(b(a(x1)))))))))))
            c(c(c(c(b(b(b(b(b(b(a(x1)))))))))))
            c(a(b(b(b(b(b(b(b(b(a(x1)))))))))))
            c(a(c(c(c(b(b(b(b(b(a(x1)))))))))))
            c(a(a(b(b(b(b(b(b(b(a(x1)))))))))))
            c(a(a(c(c(c(b(b(b(b(a(x1)))))))))))
           context: []
           substitution:
            x1 -> x1
           Qed