YES

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

Proof:
 DP Processor:
  DPs:
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> b#(a(x1))
   a#(b(x1)) -> b#(b(a(x1)))
   b#(c(x1)) -> b#(x1)
   b#(c(x1)) -> b#(b(x1))
   b#(c(x1)) -> c#(b(b(x1)))
   c#(a(x1)) -> c#(x1)
   c#(a(x1)) -> c#(c(x1))
   c#(a(x1)) -> a#(c(c(x1)))
  TRS:
   a(b(x1)) -> b(b(a(x1)))
   b(c(x1)) -> c(b(b(x1)))
   c(a(x1)) -> a(c(c(x1)))
  TDG Processor:
   DPs:
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> b#(a(x1))
    a#(b(x1)) -> b#(b(a(x1)))
    b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> c#(b(b(x1)))
    c#(a(x1)) -> c#(x1)
    c#(a(x1)) -> c#(c(x1))
    c#(a(x1)) -> a#(c(c(x1)))
   TRS:
    a(b(x1)) -> b(b(a(x1)))
    b(c(x1)) -> c(b(b(x1)))
    c(a(x1)) -> a(c(c(x1)))
   graph:
    c#(a(x1)) -> c#(c(x1)) -> c#(a(x1)) -> a#(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)) -> a#(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)) -> a#(c(c(x1))) -> a#(b(x1)) -> b#(b(a(x1)))
    c#(a(x1)) -> a#(c(c(x1))) -> a#(b(x1)) -> b#(a(x1))
    c#(a(x1)) -> a#(c(c(x1))) -> a#(b(x1)) -> a#(x1)
    b#(c(x1)) -> c#(b(b(x1))) -> c#(a(x1)) -> a#(c(c(x1)))
    b#(c(x1)) -> c#(b(b(x1))) -> c#(a(x1)) -> c#(c(x1))
    b#(c(x1)) -> c#(b(b(x1))) -> c#(a(x1)) -> c#(x1)
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> c#(b(b(x1)))
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> c#(b(b(x1)))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
    b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
    a#(b(x1)) -> b#(a(x1)) -> b#(c(x1)) -> c#(b(b(x1)))
    a#(b(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(b(x1))
    a#(b(x1)) -> b#(a(x1)) -> b#(c(x1)) -> b#(x1)
    a#(b(x1)) -> b#(b(a(x1))) -> b#(c(x1)) -> c#(b(b(x1)))
    a#(b(x1)) -> b#(b(a(x1))) -> b#(c(x1)) -> b#(b(x1))
    a#(b(x1)) -> b#(b(a(x1))) -> b#(c(x1)) -> b#(x1)
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(b(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
   Arctic Interpretation Processor:
    dimension: 1
    interpretation:
     [c#](x0) = 2x0 + 0,
     
     [b#](x0) = 8,
     
     [a#](x0) = 9,
     
     [c](x0) = x0,
     
     [a](x0) = 8x0 + 15,
     
     [b](x0) = 0
    orientation:
     a#(b(x1)) = 9 >= 9 = a#(x1)
     
     a#(b(x1)) = 9 >= 8 = b#(a(x1))
     
     a#(b(x1)) = 9 >= 8 = b#(b(a(x1)))
     
     b#(c(x1)) = 8 >= 8 = b#(x1)
     
     b#(c(x1)) = 8 >= 8 = b#(b(x1))
     
     b#(c(x1)) = 8 >= 2 = c#(b(b(x1)))
     
     c#(a(x1)) = 10x1 + 17 >= 2x1 + 0 = c#(x1)
     
     c#(a(x1)) = 10x1 + 17 >= 2x1 + 0 = c#(c(x1))
     
     c#(a(x1)) = 10x1 + 17 >= 9 = a#(c(c(x1)))
     
     a(b(x1)) = 15 >= 0 = b(b(a(x1)))
     
     b(c(x1)) = 0 >= 0 = c(b(b(x1)))
     
     c(a(x1)) = 8x1 + 15 >= 8x1 + 15 = a(c(c(x1)))
    problem:
     DPs:
      a#(b(x1)) -> a#(x1)
      b#(c(x1)) -> b#(x1)
      b#(c(x1)) -> b#(b(x1))
     TRS:
      a(b(x1)) -> b(b(a(x1)))
      b(c(x1)) -> c(b(b(x1)))
      c(a(x1)) -> a(c(c(x1)))
    EDG Processor:
     DPs:
      a#(b(x1)) -> a#(x1)
      b#(c(x1)) -> b#(x1)
      b#(c(x1)) -> b#(b(x1))
     TRS:
      a(b(x1)) -> b(b(a(x1)))
      b(c(x1)) -> c(b(b(x1)))
      c(a(x1)) -> a(c(c(x1)))
     graph:
      b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
      b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
      b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
      b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
      a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     CDG Processor:
      DPs:
       a#(b(x1)) -> a#(x1)
       b#(c(x1)) -> b#(x1)
       b#(c(x1)) -> b#(b(x1))
      TRS:
       a(b(x1)) -> b(b(a(x1)))
       b(c(x1)) -> c(b(b(x1)))
       c(a(x1)) -> a(c(c(x1)))
      graph:
       b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(b(x1))
       b#(c(x1)) -> b#(b(x1)) -> b#(c(x1)) -> b#(x1)
       b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(b(x1))
       b#(c(x1)) -> b#(x1) -> b#(c(x1)) -> b#(x1)
      SCC Processor:
       #sccs: 1
       #rules: 2
       #arcs: 4/9
       DPs:
        b#(c(x1)) -> b#(b(x1))
        b#(c(x1)) -> b#(x1)
       TRS:
        a(b(x1)) -> b(b(a(x1)))
        b(c(x1)) -> c(b(b(x1)))
        c(a(x1)) -> a(c(c(x1)))
       Arctic Interpretation Processor:
        dimension: 1
        interpretation:
         [b#](x0) = x0,
         
         [c](x0) = 9x0,
         
         [a](x0) = 0,
         
         [b](x0) = x0
        orientation:
         b#(c(x1)) = 9x1 >= x1 = b#(b(x1))
         
         b#(c(x1)) = 9x1 >= x1 = b#(x1)
         
         a(b(x1)) = 0 >= 0 = b(b(a(x1)))
         
         b(c(x1)) = 9x1 >= 9x1 = c(b(b(x1)))
         
         c(a(x1)) = 9 >= 0 = a(c(c(x1)))
        problem:
         DPs:
          
         TRS:
          a(b(x1)) -> b(b(a(x1)))
          b(c(x1)) -> c(b(b(x1)))
          c(a(x1)) -> a(c(c(x1)))
        Qed