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