YES

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

Proof:
 DP Processor:
  DPs:
   b#(c(x1)) -> a#(x1)
   b#(c(x1)) -> a#(a(x1))
   c#(a(x1)) -> c#(x1)
   c#(a(x1)) -> c#(c(x1))
   c#(a(x1)) -> b#(c(c(x1)))
   c#(a(x1)) -> b#(b(c(c(x1))))
  TRS:
   a(b(x1)) -> x1
   b(c(x1)) -> a(a(x1))
   c(a(x1)) -> b(b(c(c(x1))))
  TDG Processor:
   DPs:
    b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> a#(a(x1))
    c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> c#(c(x1))
    c#(a(x1)) -> b#(c(c(x1)))
    c#(a(x1)) -> b#(b(c(c(x1))))
   TRS:
    a(b(x1)) -> x1
    b(c(x1)) -> a(a(x1))
    c(a(x1)) -> b(b(c(c(x1))))
   graph:
    c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> b#(b(c(c(x1))))
    c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> b#(c(c(x1)))
    c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(c(x1))
    c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(b(c(c(x1))))
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> b#(c(c(x1)))
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(c(x1))
    c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> b#(c(c(x1))) -> b#(c(x1)) -> a#(a(x1))
    c#(a(x1)) -> b#(c(c(x1))) -> b#(c(x1)) -> a#(x1)
    c#(a(x1)) -> b#(b(c(c(x1)))) -> b#(c(x1)) -> a#(a(x1))
    c#(a(x1)) -> b#(b(c(c(x1)))) -> b#(c(x1)) -> a#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 12/36
    DPs:
     c#(a(x1)) -> c#(c(x1))
     c#(a(x1)) -> c#(x1)
    TRS:
     a(b(x1)) -> x1
     b(c(x1)) -> a(a(x1))
     c(a(x1)) -> b(b(c(c(x1))))
    Arctic Interpretation Processor:
     dimension: 2
     interpretation:
      [c#](x0) = [0 2]x0 + [0],
      
                [1 2]     [0 ]
      [c](x0) = [0 1]x0 + [-&],
      
                [-& 0 ]     [0]
      [a](x0) = [0  1 ]x0 + [0],
      
                [-& 0 ]     [1]
      [b](x0) = [0  -&]x0 + [1]
     orientation:
      c#(a(x1)) = [2 3]x1 + [2] >= [2 3]x1 + [0] = c#(c(x1))
      
      c#(a(x1)) = [2 3]x1 + [2] >= [0 2]x1 + [0] = c#(x1)
      
                 [0  -&]     [1]           
      a(b(x1)) = [1  0 ]x1 + [2] >= x1 = x1
      
                 [0 1]     [1]    [0 1]     [0]           
      b(c(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = a(a(x1))
      
                 [2 3]     [2]    [2 3]     [1]                 
      c(a(x1)) = [1 2]x1 + [1] >= [1 2]x1 + [1] = b(b(c(c(x1))))
     problem:
      DPs:
       c#(a(x1)) -> c#(c(x1))
      TRS:
       a(b(x1)) -> x1
       b(c(x1)) -> a(a(x1))
       c(a(x1)) -> b(b(c(c(x1))))
     EDG Processor:
      DPs:
       c#(a(x1)) -> c#(c(x1))
      TRS:
       a(b(x1)) -> x1
       b(c(x1)) -> a(a(x1))
       c(a(x1)) -> b(b(c(c(x1))))
      graph:
       c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> c#(c(x1))
      Arctic Interpretation Processor:
       dimension: 3
       interpretation:
        [c#](x0) = [-& -& 0 ]x0 + [0],
        
                  [0  0  0 ]     [-&]
        [c](x0) = [0  0  1 ]x0 + [1 ]
                  [-& -& 0 ]     [0 ],
        
                  [-& -& 0 ]     [0 ]
        [a](x0) = [0  -& -&]x0 + [-&]
                  [0  0  1 ]     [1 ],
        
                  [0  0  -&]     [0]
        [b](x0) = [-& -& 0 ]x0 + [0]
                  [0  1  -&]     [0]
       orientation:
        c#(a(x1)) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = c#(c(x1))
        
                   [0  1  -&]     [0]           
        a(b(x1)) = [0  0  -&]x1 + [0] >= x1 = x1
                   [1  2  0 ]     [1]           
        
                   [0  0  1 ]     [1]    [0  0  1 ]     [1]           
        b(c(x1)) = [-& -& 0 ]x1 + [0] >= [-& -& 0 ]x1 + [0] = a(a(x1))
                   [1  1  2 ]     [2]    [1  1  2 ]     [2]           
        
                   [0 0 1]     [1]    [0 0 1]     [1]                 
        c(a(x1)) = [1 1 2]x1 + [2] >= [1 1 2]x1 + [2] = b(b(c(c(x1))))
                   [0 0 1]     [1]    [0 0 1]     [1]                 
       problem:
        DPs:
         
        TRS:
         a(b(x1)) -> x1
         b(c(x1)) -> a(a(x1))
         c(a(x1)) -> b(b(c(c(x1))))
       Qed