YES
O(n^2)
TRS:
 {g(g(x)) -> f(x),
  f(f(x)) -> g(f(x))}
 DUP: We consider a non-duplicating system.
  Trs:
   {g(g(x)) -> f(x),
    f(f(x)) -> g(f(x))}
  Matrix Interpretation:
   Interpretation class: triangular
       [X1]    [1 3][X1]   [1]
   [f]([X0]) = [0 0][X0] + [1]
   
       [X1]    [1 3][X1]   [0]
   [g]([X0]) = [0 0][X0] + [1]
   
   
   Qed