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