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)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
     [c#](x0) = [0 0 2]x0 + [1],
     
     [b#](x0) = [1 0 0]x0 + [1],
     
     [a#](x0) = [0 2 0]x0,
     
               [2 0 0]     [1]
     [c](x0) = [0 0 0]x0 + [0]
               [0 0 1]     [0],
     
               [0 0 0]     [0]
     [a](x0) = [0 2 0]x0 + [0]
               [0 0 2]     [1],
     
               [1 0 0]     [0]
     [b](x0) = [0 1 0]x0 + [3]
               [0 0 0]     [0]
    orientation:
     a#(b(x1)) = [0 2 0]x1 + [6] >= [0 2 0]x1 = a#(x1)
     
     a#(b(x1)) = [0 2 0]x1 + [6] >= [1] = b#(a(x1))
     
     a#(b(x1)) = [0 2 0]x1 + [6] >= [1] = b#(b(a(x1)))
     
     b#(c(x1)) = [2 0 0]x1 + [2] >= [1 0 0]x1 + [1] = b#(x1)
     
     b#(c(x1)) = [2 0 0]x1 + [2] >= [1 0 0]x1 + [1] = b#(b(x1))
     
     b#(c(x1)) = [2 0 0]x1 + [2] >= [1] = c#(b(b(x1)))
     
     c#(a(x1)) = [0 0 4]x1 + [3] >= [0 0 2]x1 + [1] = c#(x1)
     
     c#(a(x1)) = [0 0 4]x1 + [3] >= [0 0 2]x1 + [1] = c#(c(x1))
     
     c#(a(x1)) = [0 0 4]x1 + [3] >= [0] = a#(c(c(x1)))
     
                [0 0 0]     [0]    [0 0 0]     [0]              
     a(b(x1)) = [0 2 0]x1 + [6] >= [0 2 0]x1 + [6] = b(b(a(x1)))
                [0 0 0]     [1]    [0 0 0]     [0]              
     
                [2 0 0]     [1]    [2 0 0]     [1]              
     b(c(x1)) = [0 0 0]x1 + [3] >= [0 0 0]x1 + [0] = c(b(b(x1)))
                [0 0 0]     [0]    [0 0 0]     [0]              
     
                [0 0 0]     [1]    [0 0 0]     [0]              
     c(a(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(c(c(x1)))
                [0 0 2]     [1]    [0 0 2]     [1]              
    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