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