YES

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> c#(x1)
   a#(a(x1)) -> b#(c(x1))
   c#(b(x1)) -> c#(x1)
   c#(b(x1)) -> b#(c(x1))
   c#(b(x1)) -> a#(b(c(x1)))
  TRS:
   a(x1) -> x1
   a(a(x1)) -> b(c(x1))
   b(x1) -> x1
   c(x1) -> x1
   c(b(x1)) -> a(b(c(x1)))
  TDG Processor:
   DPs:
    a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> b#(c(x1))
    c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> b#(c(x1))
    c#(b(x1)) -> a#(b(c(x1)))
   TRS:
    a(x1) -> x1
    a(a(x1)) -> b(c(x1))
    b(x1) -> x1
    c(x1) -> x1
    c(b(x1)) -> a(b(c(x1)))
   graph:
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(x1))
    c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
    c#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(c(x1))
    c#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> c#(x1)
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(x1))
    a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 8/25
    DPs:
     c#(b(x1)) -> c#(x1)
     c#(b(x1)) -> a#(b(c(x1)))
     a#(a(x1)) -> c#(x1)
    TRS:
     a(x1) -> x1
     a(a(x1)) -> b(c(x1))
     b(x1) -> x1
     c(x1) -> x1
     c(b(x1)) -> a(b(c(x1)))
    Arctic Interpretation Processor:
     dimension: 4
     usable rules:
      a(x1) -> x1
      a(a(x1)) -> b(c(x1))
      b(x1) -> x1
      c(x1) -> x1
      c(b(x1)) -> a(b(c(x1)))
     interpretation:
      [c#](x0) = [-& 0  0  0 ]x0 + [0],
      
      [a#](x0) = [0 0 0 0]x0 + [0],
      
                [0  0  0  1 ]     [-&]
                [-& 0  1  1 ]     [0 ]
      [b](x0) = [-& -& 0  0 ]x0 + [0 ]
                [0  1  0  0 ]     [1 ],
      
                [0  0  1  0 ]     [-&]
                [-& 0  0  0 ]     [0 ]
      [c](x0) = [-& 0  0  0 ]x0 + [-&]
                [-& 0  0  0 ]     [-&],
      
                [0 0 1 0]     [0]
                [0 0 1 0]     [0]
      [a](x0) = [0 0 0 0]x0 + [0]
                [0 0 1 0]     [0]
     orientation:
      c#(b(x1)) = [0 1 1 1]x1 + [1] >= [-& 0  0  0 ]x1 + [0] = c#(x1)
      
      c#(b(x1)) = [0 1 1 1]x1 + [1] >= [0 1 1 1]x1 + [1] = a#(b(c(x1)))
      
      a#(a(x1)) = [0 0 1 0]x1 + [0] >= [-& 0  0  0 ]x1 + [0] = c#(x1)
      
              [0 0 1 0]     [0]           
              [0 0 1 0]     [0]           
      a(x1) = [0 0 0 0]x1 + [0] >= x1 = x1
              [0 0 1 0]     [0]           
      
                 [1 1 1 1]     [1]    [0  1  1  1 ]     [0]           
                 [1 1 1 1]     [1]    [-& 1  1  1 ]     [0]           
      a(a(x1)) = [0 0 1 0]x1 + [0] >= [-& 0  0  0 ]x1 + [0] = b(c(x1))
                 [1 1 1 1]     [1]    [0  1  1  1 ]     [1]           
      
              [0  0  0  1 ]     [-&]           
              [-& 0  1  1 ]     [0 ]           
      b(x1) = [-& -& 0  0 ]x1 + [0 ] >= x1 = x1
              [0  1  0  0 ]     [1 ]           
      
              [0  0  1  0 ]     [-&]           
              [-& 0  0  0 ]     [0 ]           
      c(x1) = [-& 0  0  0 ]x1 + [-&] >= x1 = x1
              [-& 0  0  0 ]     [-&]           
      
                 [0 1 1 1]     [1]    [0 1 1 1]     [1]              
                 [0 1 1 1]     [1]    [0 1 1 1]     [1]              
      c(b(x1)) = [0 1 1 1]x1 + [1] >= [0 1 1 1]x1 + [1] = a(b(c(x1)))
                 [0 1 1 1]     [1]    [0 1 1 1]     [1]              
     problem:
      DPs:
       c#(b(x1)) -> a#(b(c(x1)))
       a#(a(x1)) -> c#(x1)
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(c(x1))
       b(x1) -> x1
       c(x1) -> x1
       c(b(x1)) -> a(b(c(x1)))
     Restore Modifier:
      DPs:
       c#(b(x1)) -> a#(b(c(x1)))
       a#(a(x1)) -> c#(x1)
      TRS:
       a(x1) -> x1
       a(a(x1)) -> b(c(x1))
       b(x1) -> x1
       c(x1) -> x1
       c(b(x1)) -> a(b(c(x1)))
      EDG Processor:
       DPs:
        c#(b(x1)) -> a#(b(c(x1)))
        a#(a(x1)) -> c#(x1)
       TRS:
        a(x1) -> x1
        a(a(x1)) -> b(c(x1))
        b(x1) -> x1
        c(x1) -> x1
        c(b(x1)) -> a(b(c(x1)))
       graph:
        c#(b(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> c#(x1)
        a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(x1)))
       Arctic Interpretation Processor:
        dimension: 3
        usable rules:
         a(x1) -> x1
         a(a(x1)) -> b(c(x1))
         b(x1) -> x1
         c(x1) -> x1
         c(b(x1)) -> a(b(c(x1)))
        interpretation:
         [c#](x0) = [0 0 0]x0,
         
         [a#](x0) = [0  -& -&]x0 + [0],
         
                   [0 0 0]     [0]
         [b](x0) = [0 1 0]x0 + [0]
                   [1 0 1]     [1],
         
                   [0  0  0 ]     [0 ]
         [c](x0) = [-& 0  0 ]x0 + [-&]
                   [0  0  0 ]     [-&],
         
                   [0 0 0]     [0 ]
         [a](x0) = [1 0 0]x0 + [-&]
                   [1 0 0]     [0 ]
        orientation:
         c#(b(x1)) = [1 1 1]x1 + [1] >= [0 0 0]x1 + [0] = a#(b(c(x1)))
         
         a#(a(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c#(x1)
         
                 [0 0 0]     [0 ]           
         a(x1) = [1 0 0]x1 + [-&] >= x1 = x1
                 [1 0 0]     [0 ]           
         
                    [1 0 0]     [0]    [0 0 0]     [0]           
         a(a(x1)) = [1 1 1]x1 + [1] >= [0 1 1]x1 + [0] = b(c(x1))
                    [1 1 1]     [1]    [1 1 1]     [1]           
         
                 [0 0 0]     [0]           
         b(x1) = [0 1 0]x1 + [0] >= x1 = x1
                 [1 0 1]     [1]           
         
                 [0  0  0 ]     [0 ]           
         c(x1) = [-& 0  0 ]x1 + [-&] >= x1 = x1
                 [0  0  0 ]     [-&]           
         
                    [1 1 1]     [1]    [1 1 1]     [1]              
         c(b(x1)) = [1 1 1]x1 + [1] >= [1 1 1]x1 + [1] = a(b(c(x1)))
                    [1 1 1]     [1]    [1 1 1]     [1]              
        problem:
         DPs:
          a#(a(x1)) -> c#(x1)
         TRS:
          a(x1) -> x1
          a(a(x1)) -> b(c(x1))
          b(x1) -> x1
          c(x1) -> x1
          c(b(x1)) -> a(b(c(x1)))
        Restore Modifier:
         DPs:
          a#(a(x1)) -> c#(x1)
         TRS:
          a(x1) -> x1
          a(a(x1)) -> b(c(x1))
          b(x1) -> x1
          c(x1) -> x1
          c(b(x1)) -> a(b(c(x1)))
         EDG Processor:
          DPs:
           a#(a(x1)) -> c#(x1)
          TRS:
           a(x1) -> x1
           a(a(x1)) -> b(c(x1))
           b(x1) -> x1
           c(x1) -> x1
           c(b(x1)) -> a(b(c(x1)))
          graph:
           
          Qed