YES
O(n^4)
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
       [X3]    [1 0 1 0][X3]   [0]
       [X2]    [0 0 1 1][X2]   [0]
   [f]([X1]) = [0 0 1 1][X1] + [1]
       [X0]    [0 0 0 1][X0]   [1]
   
       [X3]    [1 1 0 0][X3]   [0]
       [X2]    [0 0 1 0][X2]   [1]
   [g]([X1]) = [0 0 1 1][X1] + [1]
       [X0]    [0 0 0 1][X0]   [1]
   
   
   Qed