YES
O(n^3)
TRS:
 {  f(f(x)) -> f(x),
    f(s(x)) -> f(x),
  g(s(0())) -> g(f(s(0())))}
 DUP: We consider a non-duplicating system.
  Trs:
   {  f(f(x)) -> f(x),
      f(s(x)) -> f(x),
    g(s(0())) -> g(f(s(0())))}
  Matrix Interpretation:
   Interpretation class: triangular
         [0]
   [0] = [0]
         [0]
   
       [X2]    [1 0 1][X2]   [0]
   [g]([X1]) = [0 0 1][X1] + [0]
       [X0]    [0 0 0][X0]   [0]
   
       [X2]    [1 0 0][X2]   [1]
   [s]([X1]) = [0 1 0][X1] + [0]
       [X0]    [0 0 0][X0]   [1]
   
       [X2]    [1 1 0][X2]   [0]
   [f]([X1]) = [0 0 0][X1] + [1]
       [X0]    [0 0 0][X0]   [0]
   
   
   Qed