YES

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

Proof:
 DP Processor:
  DPs:
   a#(x1) -> c#(x1)
   a#(x1) -> b#(c(x1))
   b#(a(b(x1))) -> c#(x1)
   c#(c(x1)) -> b#(x1)
   c#(c(x1)) -> a#(b(x1))
   c#(c(x1)) -> a#(a(b(x1)))
  TRS:
   a(x1) -> b(c(x1))
   b(a(b(x1))) -> c(x1)
   c(c(x1)) -> a(a(b(x1)))
  TDG Processor:
   DPs:
    a#(x1) -> c#(x1)
    a#(x1) -> b#(c(x1))
    b#(a(b(x1))) -> c#(x1)
    c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> a#(b(x1))
    c#(c(x1)) -> a#(a(b(x1)))
   TRS:
    a(x1) -> b(c(x1))
    b(a(b(x1))) -> c(x1)
    c(c(x1)) -> a(a(b(x1)))
   graph:
    b#(a(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(a(b(x1)))
    b#(a(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(b(x1))
    b#(a(b(x1))) -> c#(x1) -> c#(c(x1)) -> b#(x1)
    c#(c(x1)) -> b#(x1) -> b#(a(b(x1))) -> c#(x1)
    c#(c(x1)) -> a#(b(x1)) -> a#(x1) -> b#(c(x1))
    c#(c(x1)) -> a#(b(x1)) -> a#(x1) -> c#(x1)
    c#(c(x1)) -> a#(a(b(x1))) -> a#(x1) -> b#(c(x1))
    c#(c(x1)) -> a#(a(b(x1))) -> a#(x1) -> c#(x1)
    a#(x1) -> b#(c(x1)) -> b#(a(b(x1))) -> c#(x1)
    a#(x1) -> c#(x1) -> c#(c(x1)) -> a#(a(b(x1)))
    a#(x1) -> c#(x1) -> c#(c(x1)) -> a#(b(x1))
    a#(x1) -> c#(x1) -> c#(c(x1)) -> b#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [b#](x0) = -2x0 + 0,
     
     [c#](x0) = 4x0 + -16,
     
     [a#](x0) = 4x0 + 4,
     
     [b](x0) = x0,
     
     [c](x0) = 6x0 + 0,
     
     [a](x0) = 6x0 + 0
    orientation:
     a#(x1) = 4x1 + 4 >= 4x1 + -16 = c#(x1)
     
     a#(x1) = 4x1 + 4 >= 4x1 + 0 = b#(c(x1))
     
     b#(a(b(x1))) = 4x1 + 0 >= 4x1 + -16 = c#(x1)
     
     c#(c(x1)) = 10x1 + 4 >= -2x1 + 0 = b#(x1)
     
     c#(c(x1)) = 10x1 + 4 >= 4x1 + 4 = a#(b(x1))
     
     c#(c(x1)) = 10x1 + 4 >= 10x1 + 4 = a#(a(b(x1)))
     
     a(x1) = 6x1 + 0 >= 6x1 + 0 = b(c(x1))
     
     b(a(b(x1))) = 6x1 + 0 >= 6x1 + 0 = c(x1)
     
     c(c(x1)) = 12x1 + 6 >= 12x1 + 6 = a(a(b(x1)))
    problem:
     DPs:
      a#(x1) -> c#(x1)
      a#(x1) -> b#(c(x1))
      b#(a(b(x1))) -> c#(x1)
      c#(c(x1)) -> a#(b(x1))
      c#(c(x1)) -> a#(a(b(x1)))
     TRS:
      a(x1) -> b(c(x1))
      b(a(b(x1))) -> c(x1)
      c(c(x1)) -> a(a(b(x1)))
    EDG Processor:
     DPs:
      a#(x1) -> c#(x1)
      a#(x1) -> b#(c(x1))
      b#(a(b(x1))) -> c#(x1)
      c#(c(x1)) -> a#(b(x1))
      c#(c(x1)) -> a#(a(b(x1)))
     TRS:
      a(x1) -> b(c(x1))
      b(a(b(x1))) -> c(x1)
      c(c(x1)) -> a(a(b(x1)))
     graph:
      b#(a(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(b(x1))
      b#(a(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(a(b(x1)))
      c#(c(x1)) -> a#(b(x1)) -> a#(x1) -> c#(x1)
      c#(c(x1)) -> a#(b(x1)) -> a#(x1) -> b#(c(x1))
      c#(c(x1)) -> a#(a(b(x1))) -> a#(x1) -> c#(x1)
      c#(c(x1)) -> a#(a(b(x1))) -> a#(x1) -> b#(c(x1))
      a#(x1) -> b#(c(x1)) -> b#(a(b(x1))) -> c#(x1)
      a#(x1) -> c#(x1) -> c#(c(x1)) -> a#(b(x1))
      a#(x1) -> c#(x1) -> c#(c(x1)) -> a#(a(b(x1)))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [b#](x0) = 2x0,
       
       [c#](x0) = 10x0,
       
       [a#](x0) = 10x0,
       
       [b](x0) = x0,
       
       [c](x0) = 8x0,
       
       [a](x0) = 8x0
      orientation:
       a#(x1) = 10x1 >= 10x1 = c#(x1)
       
       a#(x1) = 10x1 >= 10x1 = b#(c(x1))
       
       b#(a(b(x1))) = 10x1 >= 10x1 = c#(x1)
       
       c#(c(x1)) = 18x1 >= 10x1 = a#(b(x1))
       
       c#(c(x1)) = 18x1 >= 18x1 = a#(a(b(x1)))
       
       a(x1) = 8x1 >= 8x1 = b(c(x1))
       
       b(a(b(x1))) = 8x1 >= 8x1 = c(x1)
       
       c(c(x1)) = 16x1 >= 16x1 = a(a(b(x1)))
      problem:
       DPs:
        a#(x1) -> c#(x1)
        a#(x1) -> b#(c(x1))
        b#(a(b(x1))) -> c#(x1)
        c#(c(x1)) -> a#(a(b(x1)))
       TRS:
        a(x1) -> b(c(x1))
        b(a(b(x1))) -> c(x1)
        c(c(x1)) -> a(a(b(x1)))
      EDG Processor:
       DPs:
        a#(x1) -> c#(x1)
        a#(x1) -> b#(c(x1))
        b#(a(b(x1))) -> c#(x1)
        c#(c(x1)) -> a#(a(b(x1)))
       TRS:
        a(x1) -> b(c(x1))
        b(a(b(x1))) -> c(x1)
        c(c(x1)) -> a(a(b(x1)))
       graph:
        b#(a(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(a(b(x1)))
        c#(c(x1)) -> a#(a(b(x1))) -> a#(x1) -> b#(c(x1))
        c#(c(x1)) -> a#(a(b(x1))) -> a#(x1) -> c#(x1)
        a#(x1) -> b#(c(x1)) -> b#(a(b(x1))) -> c#(x1)
        a#(x1) -> c#(x1) -> c#(c(x1)) -> a#(a(b(x1)))
       Arctic Interpretation Processor:
        dimension: 2
        interpretation:
         [b#](x0) = [-& -1]x0 + [0],
         
         [c#](x0) = [0  -&]x0 + [0],
         
         [a#](x0) = [1  -1]x0 + [3],
         
                   [-& -1]     [1]
         [b](x0) = [0  1 ]x0 + [3],
         
                   [0  1 ]     [3]
         [c](x0) = [2  -&]x0 + [2],
         
                   [1  -&]     [2]
         [a](x0) = [3  1 ]x0 + [3]
        orientation:
         a#(x1) = [1  -1]x1 + [3] >= [0  -&]x1 + [0] = c#(x1)
         
         a#(x1) = [1  -1]x1 + [3] >= [1  -&]x1 + [1] = b#(c(x1))
         
         b#(a(b(x1))) = [0 1]x1 + [3] >= [0  -&]x1 + [0] = c#(x1)
         
         c#(c(x1)) = [0 1]x1 + [3] >= [0 1]x1 + [3] = a#(a(b(x1)))
         
                 [1  -&]     [2]    [1  -&]     [1]           
         a(x1) = [3  1 ]x1 + [3] >= [3  1 ]x1 + [3] = b(c(x1))
         
                       [0 1]     [3]    [0  1 ]     [3]        
         b(a(b(x1))) = [2 3]x1 + [5] >= [2  -&]x1 + [2] = c(x1)
         
                    [3 1]     [3]    [-& 1 ]     [3]              
         c(c(x1)) = [2 3]x1 + [5] >= [2  3 ]x1 + [5] = a(a(b(x1)))
        problem:
         DPs:
          a#(x1) -> b#(c(x1))
          b#(a(b(x1))) -> c#(x1)
          c#(c(x1)) -> a#(a(b(x1)))
         TRS:
          a(x1) -> b(c(x1))
          b(a(b(x1))) -> c(x1)
          c(c(x1)) -> a(a(b(x1)))
        EDG Processor:
         DPs:
          a#(x1) -> b#(c(x1))
          b#(a(b(x1))) -> c#(x1)
          c#(c(x1)) -> a#(a(b(x1)))
         TRS:
          a(x1) -> b(c(x1))
          b(a(b(x1))) -> c(x1)
          c(c(x1)) -> a(a(b(x1)))
         graph:
          b#(a(b(x1))) -> c#(x1) -> c#(c(x1)) -> a#(a(b(x1)))
          c#(c(x1)) -> a#(a(b(x1))) -> a#(x1) -> b#(c(x1))
          a#(x1) -> b#(c(x1)) -> b#(a(b(x1))) -> c#(x1)
         Arctic Interpretation Processor:
          dimension: 3
          interpretation:
           [b#](x0) = [-& 0  1 ]x0 + [0],
           
           [c#](x0) = [1 0 0]x0 + [0],
           
           [a#](x0) = [1 0 0]x0 + [1],
           
                     [-& -& 0 ]     [0 ]
           [b](x0) = [0  0  1 ]x0 + [1 ]
                     [-& -& 0 ]     [-&],
           
                     [0  0  1 ]     [1]
           [c](x0) = [1  0  0 ]x0 + [1]
                     [0  -& -&]     [0],
           
                     [0  -& 0 ]     [0]
           [a](x0) = [1  0  1 ]x0 + [1]
                     [0  0  0 ]     [0]
          orientation:
           a#(x1) = [1 0 0]x1 + [1] >= [1 0 0]x1 + [1] = b#(c(x1))
           
           b#(a(b(x1))) = [1 1 2]x1 + [2] >= [1 0 0]x1 + [0] = c#(x1)
           
           c#(c(x1)) = [1 1 2]x1 + [2] >= [0 0 1]x1 + [1] = a#(a(b(x1)))
           
                   [0  -& 0 ]     [0]    [0  -& -&]     [0]           
           a(x1) = [1  0  1 ]x1 + [1] >= [1  0  1 ]x1 + [1] = b(c(x1))
                   [0  0  0 ]     [0]    [0  -& -&]     [0]           
           
                         [0 0 1]     [1]    [0  0  1 ]     [1]        
           b(a(b(x1))) = [1 1 2]x1 + [2] >= [1  0  0 ]x1 + [1] = c(x1)
                         [0 0 1]     [1]    [0  -& -&]     [0]        
           
                      [1 0 1]     [1]    [0 0 1]     [1]              
           c(c(x1)) = [1 1 2]x1 + [2] >= [1 1 2]x1 + [2] = a(a(b(x1)))
                      [0 0 1]     [1]    [0 0 1]     [1]              
          problem:
           DPs:
            a#(x1) -> b#(c(x1))
            b#(a(b(x1))) -> c#(x1)
           TRS:
            a(x1) -> b(c(x1))
            b(a(b(x1))) -> c(x1)
            c(c(x1)) -> a(a(b(x1)))
          EDG Processor:
           DPs:
            a#(x1) -> b#(c(x1))
            b#(a(b(x1))) -> c#(x1)
           TRS:
            a(x1) -> b(c(x1))
            b(a(b(x1))) -> c(x1)
            c(c(x1)) -> a(a(b(x1)))
           graph:
            a#(x1) -> b#(c(x1)) -> b#(a(b(x1))) -> c#(x1)
           SCC Processor:
            #sccs: 0
            #rules: 0
            #arcs: 1/4