YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> b#(a(x1))
   a#(b(x1)) -> c#(b(a(x1)))
   a#(b(x1)) -> a#(c(b(a(x1))))
   a#(b(x1)) -> b#(a(c(b(a(x1)))))
  TRS:
   a(x1) -> x1
   a(b(x1)) -> b(a(c(b(a(x1)))))
   b(x1) -> x1
   c(c(c(x1))) -> x1
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(a(x1))
    a#(b(x1)) -> c#(b(a(x1)))
    a#(b(x1)) -> a#(c(b(a(x1))))
    a#(b(x1)) -> b#(a(c(b(a(x1)))))
   TRS:
    a(x1) -> x1
    a(b(x1)) -> b(a(c(b(a(x1)))))
    b(x1) -> x1
    c(c(c(x1))) -> x1
   graph:
    a#(b(x1)) -> a#(c(b(a(x1)))) -> a#(b(x1)) -> b#(a(c(b(a(x1)))))
    a#(b(x1)) -> a#(c(b(a(x1)))) -> a#(b(x1)) -> a#(c(b(a(x1))))
    a#(b(x1)) -> a#(c(b(a(x1)))) -> a#(b(x1)) -> c#(b(a(x1)))
    a#(b(x1)) -> a#(c(b(a(x1)))) -> a#(b(x1)) -> b#(a(x1))
    a#(b(x1)) -> a#(c(b(a(x1)))) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(c(b(a(x1)))))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(c(b(a(x1))))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(b(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 10/25
    DPs:
     a#(b(x1)) -> a#(c(b(a(x1))))
     a#(b(x1)) -> a#(x1)
    TRS:
     a(x1) -> x1
     a(b(x1)) -> b(a(c(b(a(x1)))))
     b(x1) -> x1
     c(c(c(x1))) -> x1
    Arctic Interpretation Processor:
     dimension: 3
     usable rules:
      a(x1) -> x1
      a(b(x1)) -> b(a(c(b(a(x1)))))
      b(x1) -> x1
      c(c(c(x1))) -> x1
     interpretation:
      [a#](x0) = [1 0 1]x0 + [0],
      
                [-& 0  -&]     [0 ]
      [c](x0) = [0  1  0 ]x0 + [0 ]
                [0  -& -&]     [-&],
      
                [0  -& -&]     [-&]
      [b](x0) = [-& 0  -&]x0 + [0 ]
                [1  0  1 ]     [1 ],
      
                [0  -& 0 ]     [-&]
      [a](x0) = [-& 0  1 ]x0 + [0 ]
                [0  -& 1 ]     [1 ]
     orientation:
      a#(b(x1)) = [2 1 2]x1 + [2] >= [1 1 2]x1 + [2] = a#(c(b(a(x1))))
      
      a#(b(x1)) = [2 1 2]x1 + [2] >= [1 0 1]x1 + [0] = a#(x1)
      
              [0  -& 0 ]     [-&]           
      a(x1) = [-& 0  1 ]x1 + [0 ] >= x1 = x1
              [0  -& 1 ]     [1 ]           
      
                 [1 0 1]     [1]    [0 0 1]     [0]                    
      a(b(x1)) = [2 1 2]x1 + [2] >= [1 1 2]x1 + [2] = b(a(c(b(a(x1)))))
                 [2 1 2]     [2]    [2 1 2]     [2]                    
      
              [0  -& -&]     [-&]           
      b(x1) = [-& 0  -&]x1 + [0 ] >= x1 = x1
              [1  0  1 ]     [1 ]           
      
                    [1 2 1]     [1]           
      c(c(c(x1))) = [2 3 2]x1 + [2] >= x1 = x1
                    [0 1 0]     [0]           
     problem:
      DPs:
       a#(b(x1)) -> a#(c(b(a(x1))))
      TRS:
       a(x1) -> x1
       a(b(x1)) -> b(a(c(b(a(x1)))))
       b(x1) -> x1
       c(c(c(x1))) -> x1
     Restore Modifier:
      DPs:
       a#(b(x1)) -> a#(c(b(a(x1))))
      TRS:
       a(x1) -> x1
       a(b(x1)) -> b(a(c(b(a(x1)))))
       b(x1) -> x1
       c(c(c(x1))) -> x1
      EDG Processor:
       DPs:
        a#(b(x1)) -> a#(c(b(a(x1))))
       TRS:
        a(x1) -> x1
        a(b(x1)) -> b(a(c(b(a(x1)))))
        b(x1) -> x1
        c(c(c(x1))) -> x1
       graph:
        a#(b(x1)) -> a#(c(b(a(x1)))) -> a#(b(x1)) -> a#(c(b(a(x1))))
       Arctic Interpretation Processor:
        dimension: 2
        usable rules:
         a(x1) -> x1
         a(b(x1)) -> b(a(c(b(a(x1)))))
         b(x1) -> x1
         c(c(c(x1))) -> x1
        interpretation:
         [a#](x0) = [-4 0 ]x0 + [0],
         
                   [1  2 ]     [3 ]
         [c](x0) = [-3 -&]x0 + [-&],
         
                   [0  0 ]     [-4]
         [b](x0) = [-2 1 ]x0 + [1 ],
         
                   [0  3 ]     [-4]
         [a](x0) = [-4 1 ]x0 + [-&]
        orientation:
         a#(b(x1)) = [-2 1 ]x1 + [1] >= [-3 0 ]x1 + [0] = a#(c(b(a(x1))))
         
                 [0  3 ]     [-4]           
         a(x1) = [-4 1 ]x1 + [-&] >= x1 = x1
         
                    [1  4 ]     [4]    [1  4 ]     [3]                    
         a(b(x1)) = [-1 2 ]x1 + [2] >= [-1 2 ]x1 + [1] = b(a(c(b(a(x1)))))
         
                 [0  0 ]     [-4]           
         b(x1) = [-2 1 ]x1 + [1 ] >= x1 = x1
         
                       [3  4 ]     [5]           
         c(c(c(x1))) = [-1 0 ]x1 + [1] >= x1 = x1
        problem:
         DPs:
          
         TRS:
          a(x1) -> x1
          a(b(x1)) -> b(a(c(b(a(x1)))))
          b(x1) -> x1
          c(c(c(x1))) -> x1
        Qed