YES(?,O(n^3))
TRS:
 {
  f(b(), f(c(), x)) -> f(c(), f(b(), x)),
  f(a(), f(b(), x)) -> f(b(), f(a(), x)),
  f(c(), f(a(), x)) -> f(a(), f(c(), x))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
    f(b(), f(c(), x)) -> f(c(), f(b(), x)),
    f(a(), f(b(), x)) -> f(b(), f(a(), x)),
    f(c(), f(a(), x)) -> f(a(), f(c(), x))
   }
  RLAB:
   Strict:
    {
     f([b,f])(b(), f([c,f])(c(), x)) -> f([c,f])(c(), f([b,f])(b(), x)),
     f([b,f])(b(), f([c,b])(c(), x)) -> f([c,f])(c(), f([b,b])(b(), x)),
     f([b,f])(b(), f([c,a])(c(), x)) -> f([c,f])(c(), f([b,a])(b(), x)),
     f([b,f])(b(), f([c,c])(c(), x)) -> f([c,f])(c(), f([b,c])(b(), x)),
     f([c,f])(c(), f([a,f])(a(), x)) -> f([a,f])(a(), f([c,f])(c(), x)),
     f([c,f])(c(), f([a,b])(a(), x)) -> f([a,f])(a(), f([c,b])(c(), x)),
     f([c,f])(c(), f([a,a])(a(), x)) -> f([a,f])(a(), f([c,a])(c(), x)),
     f([c,f])(c(), f([a,c])(a(), x)) -> f([a,f])(a(), f([c,c])(c(), x)),
     f([a,f])(a(), f([b,f])(b(), x)) -> f([b,f])(b(), f([a,f])(a(), x)),
     f([a,f])(a(), f([b,b])(b(), x)) -> f([b,f])(b(), f([a,b])(a(), x)),
     f([a,f])(a(), f([b,a])(b(), x)) -> f([b,f])(b(), f([a,a])(a(), x)),
     f([a,f])(a(), f([b,c])(b(), x)) -> f([b,f])(b(), f([a,c])(a(), x))
    }
   Weak:
    {}
   Matrix Interpretation:
    Interpretation class: triangular
          [2]
    [c] = [0]
          [3]
    
          [0]
    [a] = [3]
          [1]
    
          [1]
    [b] = [2]
          [1]
    
            [X5]  [X2]    [1 0 3][X5]   [1 0 3][X2]   [3]
    [f(11)]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [0]
            [X3]  [X0]    [0 0 0][X3]   [0 0 0][X0]   [3]
    
            [X5]  [X2]    [1 1 0][X5]   [1 2 0][X2]   [2]
    [f(10)]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [2]
            [X3]  [X0]    [0 0 1][X3]   [0 0 0][X0]   [0]
    
           [X5]  [X2]    [1 0 0][X5]   [1 0 1][X2]   [2]
    [f(9)]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [0]
           [X3]  [X0]    [0 0 1][X3]   [0 0 0][X0]   [3]
    
           [X5]  [X2]    [1 2 0][X5]   [1 2 0][X2]   [0]
    [f(8)]([X4], [X1]) = [0 0 0][X4] + [0 1 0][X1] + [0]
           [X3]  [X0]    [0 0 0][X3]   [0 0 1][X0]   [2]
    
           [X5]  [X2]    [1 0 0][X5]   [1 0 3][X2]   [1]
    [f(7)]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [0]
           [X3]  [X0]    [0 0 1][X3]   [0 0 0][X0]   [1]
    
           [X5]  [X2]    [1 2 0][X5]   [1 0 3][X2]   [3]
    [f(6)]([X4], [X1]) = [0 0 3][X4] + [0 0 0][X1] + [1]
           [X3]  [X0]    [0 0 0][X3]   [0 0 0][X0]   [2]
    
           [X5]  [X2]    [1 0 0][X5]   [1 0 0][X2]   [0]
    [f(5)]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [0]
           [X3]  [X0]    [0 0 0][X3]   [0 0 0][X0]   [2]
    
           [X5]  [X2]    [1 2 0][X5]   [1 0 0][X2]   [0]
    [f(4)]([X4], [X1]) = [0 1 1][X4] + [0 1 0][X1] + [3]
           [X3]  [X0]    [0 0 0][X3]   [0 0 0][X0]   [0]
    
           [X5]  [X2]    [1 0 0][X5]   [1 0 1][X2]   [0]
    [f(3)]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [0]
           [X3]  [X0]    [0 0 1][X3]   [0 0 0][X0]   [2]
    
           [X5]  [X2]    [1 0 0][X5]   [1 0 0][X2]   [3]
    [f(2)]([X4], [X1]) = [0 1 3][X4] + [0 0 3][X1] + [3]
           [X3]  [X0]    [0 0 0][X3]   [0 0 0][X0]   [3]
    
           [X5]  [X2]    [1 0 0][X5]   [1 0 2][X2]   [0]
    [f(1)]([X4], [X1]) = [0 0 0][X4] + [0 0 0][X1] + [1]
           [X3]  [X0]    [0 0 1][X3]   [0 0 1][X0]   [0]
    
           [X5]  [X2]    [1 1 0][X5]   [1 0 3][X2]   [2]
    [f(0)]([X4], [X1]) = [0 1 1][X4] + [0 1 0][X1] + [1]
           [X3]  [X0]    [0 0 1][X3]   [0 0 1][X0]   [0]
    
    
    Qed